An Algorithmic Lucidity

(originally published at Less Wrong)

In this 2019 paper published in Studies in History and Philosophy of Science Part C, Manolo Martínez argues that our understanding of how communication works has been grievously impaired by philosophers not knowing enough math.

A classic reduction of meaning dates back to David Lewis's analysis of signaling games, more recently elaborated on by Brian Skyrms. Two agents play a simple game: a sender observes one of several possible states of the world (chosen randomly by Nature), and sends one of several possible signals. A receiver observes the signal, and chooses one of several possible actions. The agents get a reward (as specified in a payoff matrix) based on what state was observed by the sender and what action was chosen by the receiver. This toy model explains how communication can be a thing: the incentives to choose the right action in the right state, shape the evolution of a convention that assigns meaning to otherwise opaque signals.

The math in Skyrms's presentation is simple—the information content of a signal is just how it changes the probabilities of states. Too simple, according to Martínez! When Skyrms and other authors (following Fred Dreske) use information theory, they tend to only reach for the basic probability tools you find in the first chapter of the textbook. (Skyrms's Signals book occasionally takes logarithms of probabilities, but the word "entropy" doesn't actually appear.) The study of information transmission only happens after the forces of evolutionary game theory have led sender and receiver to choose their strategies.

Martínez thinks information theory has more to say about what kind of cognitive work evolution is accomplishing. The "State → Sender → Signals → Receiver → Action" pipeline of the Lewis–Skyrms signaling game is exactly isomorphic to the "Source → Encoder → Channel → Decoder → Decoded Message" pipeline of the noisy-channel coding theorem and other results you'd find beyond the very first chapter in the textbook. Martínez proposes we take the analogy literally: sender and receiver collude to form an information channel between states and actions.

The "channel" story draws our attention to different aspects of the situation than the framing focused on individual signals. In particular, Skyrms wants to characterize deception as being about when a sender benefits by sending a misleading signal—one that decreases the receiver's probability assigned to the true state, or increases the probability assigned to a false state. (Actually, as Don Fallis and Peter J. Lewis point out, Skyrms's characterization of misleadingness is too broad: one would think we wouldn't want to say that merely ruling out a false state is misleading, but it does increase the probability assigned to any other false states. But let this pass for now.) But for Martínez, a signal is just a codeword in the code being cooperatively constructed by the sender/encoder and receiver/decoder in response to the problems they jointly face. We don't usually think of it being possible for individual words in a language to be deceptive in themselves ... right? (Hold that thought.)

Martínez's key later-textbook-chapter tool is rate–distortion theory. A distortion measure quantifies how costly or "bad" it is to decode a given input as a given output. If the symbol was transmitted accurately, the distortion is zero; if there was some noise on the channel, then more noise is worse, although different applications can call for different distortion measures. (In audio applications, for example, we probably want a distortion measure that tracks how similar the decoded audio sounds to humans, which could be different from the measure you'd naturally think of if you were looking at the raw bits.)

Given a choice of distortion measure, there exists a rate–distortion function \(R(D)\) that, for a given level of distortion, tells us the rate of how "wide" the channel needs to be in order to communicate with no more than that amount of distortion. This "width", more formally, is channel capacity: for a particular channel (a conditional distribution of outputs given inputs), the capacity is the maximum, over possible input distributions, of the mutual information between the input and output distributions—the most information that could possibly be sent over the channel, if we get to pick the input distribution and the code. The rate is looking at "width" from the other direction: it's the minimum of the mutual information between the input and output distributions, over possible channels (conditional distributions) that meet the distortion goal.

What does this have to do with signaling games? Well, the payoff matrix of the game specifies how "good" it is (for each of the sender and receiver) if the receiver chooses a given act in a given state. But knowing how "good" it is to perform a given act in a given state amounts to the same thing (modulo a negative affine transformation) as knowing how "bad" it is for the communication channel to "decode" a given state as a given act! We can thus see the payoff matrix of the game giving us two different distortion measures, one each for the sender and receiver.

Following an old idea from Richard Blahut about designing a code for multiple end-user use cases, we can have a rate–distortion function \(R(D_S, D_R)\) with a two-dimensional domain (visualizable as a surface or heatmap) that takes as arguments a distortion target for each of the two measures, and gives the minimum rate that can meet both. Because this function depends only on the distribution of states from Nature, and on the payoff matrix, the sender and receiver don't need to have already chosen their strategies for us to talk about it; rather, we can see the strategies as chosen in response to this rate–distortion landscape.

Take one of the simplest possible signaling games: three states, three signals, three actions, with sender and receiver each getting a payoff of 1 if the receiver chooses the i-th act in the i-th state for 1 ≤ i ≤ 3—or rather, let's convert how-"good"-it-is payoffs, into equivalent how-"bad"-it-is distortions: sender and receiver measures both give a distortion of 1 when the j-th act is taken in the i-th state for i ≠ j, and 0 when i = j.

This rate–distortion function characterizes the outcomes of possible behaviors in the game. The fact that \(R(\frac{2}{3}, \frac{2}{3}) = 0\) means that a distortion of \(\frac{2}{3}\) can be achieved without communicating at all. (Just guess.) The fact that \(D(0, 0) = \lg 3\) means that, to communicate perfectly, the sender/encoder and receiver/decoder need to form a channel/code whose rate matches the entropy of the three states of nature.

But there's a continuum of possible intermediate behaviors: consider the "trembling hand" strategy under which the sender sends the i-th signal and the receiver chooses the j-th act with probability \(1 - p\) when i = j, but probability \(\frac{p}{2}\) when i ≠ j. Then the mutual information between states and acts would be \((1 - p) \lg \frac{1}{1 - p} + p \lg \frac{2}{p}\), smoothly interpolating between the perfect-signaling case and the no-communication-just-guessing case.

This introductory case of perfect common interest is pretty boring. Where the rate–distortion framing really shines is in analyzing games of imperfect common interest, where sender and receiver can benefit from communicating at all, but also have a motive to fight about exactly what. To illustrate his account of deception, Skyrms considers a three-state, three-act game with the following payoff matrix, where the rows represent states and the columns represent actions, and the payoffs are given as (sender's payoff, receiver's payoff)—

(Note that this state–act payoff matrix is not a normal-form game matrix in which the rows and columns represent would represent player strategy choices; the sender's choice of what signal to send is not depicted.)

In this game, the sender would prefer to equivocate between the first and second states, in order to force the receiver into picking the third action, for which the sender achieves his maximum payoff. The receiver would prefer to know which of the first and second states actually obtains, in order to get a payout of 10. But the sender doesn't have the incentive to reveal that, because if he did, he would get a payout of only 2. Instead, if the sender sends the same signal for the first and second states so that the receiver can't tell the difference between them, the receiver does best for herself by picking the third action for a guaranteed payoff of 8, rather than taking the risk of guessing wrong between the first and second actions for an expected payout of ½ · 10 + ½ · 0 = 5.

That's one Nash equilibrium, the one that's best for the sender. But the situation that's best for the receiver, where the sender emits a different signal for each state (or conflates the second and third states—the receiver's decisionmaking doesn't care about that distinction) is also Nash: if the sender was already distinguishing the first and second states, then, keeping the receiver's strategy fixed, the sender can't unilaterally do better by starting to equivocate by sending (without loss of generality) the first signal in the second state, because that would mean eating zero payouts in the second state for as long as the receiver continued to "believe" the first signal "meant" the first state.

There's a Pareto frontier of possible compromise encoding/decoding strategies that interpolate between these best-for-sender and best-for-receiver equilibria. For example, the sender (again with trembling hands) could send signals that distinguish the first and second states with probability p, or a signal that conflates them with probability 1 − p, for an expected payout (depending on p) of \(\frac{2}{3} \cdot (2p + 10(1 - p)) + \frac{10}{3}\). These intermediate strategies are not stable equilibria, however. They also have a lower rate—the "trembles" in the sender's behavior are noise on the channel, meaning less information is being transmitted.

In a world of speech with propositional meaning, deception can only be something speakers (senders) do to listeners (receivers). But propositional meaning is a fragile and advanced technology. The underlying world of signal processing is much more symmetrical, because it has no way to distinguish between statements and commands: in the joint endeavor of constructing an information channel between states and actions, the sender can manipulate the receiver using his power to show or withhold appropriate signals—but similarly, the receiver can manipulate the sender using her power to perform or withhold appropriate actions.

Imagine that, facing a supply shortage of personal protective equipment in the face of a pandemic, a country's public health agency were to recommend against individuals acquiring filtered face masks—reasoning that, if the agency did recommend masks, panic-buying would make the shortage worse for doctors who needed the masks more. If you interpret the agency's signals as an attempt to "tell the truth" about how to avoid disease, they would appear "dishonest"—but even saying that requires an ontology of communication in which "lying" is a thing. If you haven't already been built to believe that lying is bad, there's nothing to object to: the agency is just doing straightforwardly correct consequentialist optimization of the information channel between states of the world, and actions.

Martínez laments that functional accounts of deception have focused on individual signals, while ignoring that signals only make sense as part of a broader code, which necessarily involves some shared interests between sender and receiver. (If the game were zero-sum, no information transfer could happen at all.) In that light, it could seem unnecessarily antagonistic to pick a particular codeword from a shared communication code and disparagingly call it "deceptive"—tantamount to the impudent claim that there's some objective sense in which a word can be "wrong."

I am, ultimately, willing to bite this bullet. Martínez is right to point out that different agents have different interests in communicating, leading them to be strategic about what information to add to or withhold from shared maps, and in particular, where to draw the boundaries in state-space corresponding to a particular signal. Whether or not it can straightforwardly be called "lying", we can still strive to notice the difference between maps optimized to reflect decision-relevant aspects of territory, and maps optimized to control other agents' decisions.

(originally published at Less Wrong)

If a lion could speak, we could not understand her.

—Ludwig Wittgenstein

In order for information to be transmitted from one place to another, it needs to be conveyed by some physical medium: material links of cause and effect that vary in response to variation at the source, correlating the states of different parts of the universe—a "map" that reflects a "territory." When you see a rock, that's only possible because the pattern of light reflected from the rock into your eyes is different from what it would have been if the rock were a different color, or if it weren't there.

This is the rudimentary cognitive technology of perception. Notably, perception only requires technology on the receiving end. Your brain and your eyes were optimized by natural selection to be able to do things like interpreting light as conveying information from elsewhere in the universe. The rock wasn't: rocks were just the same before any animals evolved to see them. The light wasn't, either: light reflected off rocks just the same before, too.

In contrast, the advanced cognitive technology of communication is more capital-intensive: not only the receiver but also the source (now called the "sender") and the medium (now called "signals") must be optimized for the task. When you read a blog post about a rock, not only did the post author need to use the technology of perception to see the rock, you and the author also needed to have a language in common, from which the author would have used different words if the rock were a different color, or if it weren't there.

Like many advanced technologies, communication is fragile and needs to be delicately maintained. A common language requires solving the coordination problem of agreeing on a convention that assigns meanings to signals—and maintaining that convention through continued usage. The existence of stable solutions to the coordination problem ends up depending on the communicating agents' goals, even if the meaning of the convention (should the agents succeed in establishing one) is strictly denotative. If the sender and receiver's interests are aligned, a convention can be discovered by simple reinforcement learning from trial and error. This doesn't work if the sender and receiver's interests diverge—if the sender would profit by making the receiver update in the wrong direction. Deception is parasitic on conventional meaning: it is impossible for there to be a language in which most sentences were lies—because then there could be no way to learn what the "intended" meaning was. The incentive to deceive thus threatens to snowball to undermine the preconditions for signals to refer to anything at all.

There is, however, another way to solve the coordination problem of meaning. If the sender pays different costs for sending different signals, communication between adversaries becomes possible, using an assignment of meanings to signals that makes it more expensive to say things when they aren't true. If somehow granted a telegraph wire, a gazelle and a cheetah would have nothing to say to each other: any gazelle would prefer to have the language to say, "Don't tire yourself out chasing me; I'm too fast"—but precisely because any gazelle would say it, no cheetah would have an incentive to learn Morse code. But if the gazelle leaps in the air with its legs stiffened—higher than weak or injured gazelles could leap—then the message can be received.

Costly signals are both wasteful, and sharply limited in their expressive power: it's hard to imagine doing any complex grammar and logic under such constraints. Is this really the only possible way to talk to people who aren't your friends? The situation turns out not to be nearly that bleak: Michael Lachmann, Szabolcs Számadó, and Carl T. Bergstrom point out that maintaining a convention only requires that departing from it be costly. In the extreme case, if people straight-up died if they ever told a lie, then the things people actually said would be true. More realistically, social sanction against liars is enough to decouple the design of signaling conventions from the enforcement mechanism that holds them in place, enabling the development of complex language. Still, this works better for the aspects of conflicting interests that are verifiable; communication on more contentious issues may fall back to costly signaling.

The fragility of communication lends plausibility to theories that attribute signaling functions to human and other animal behavior. To the novice, this seems counterintuitive and unmotivatedly cynical. "Art is signaling! Charity is signaling! Conversation is signaling!" Really? Why should anyone believe that?

The thing to remember is this: the "signal" in "virtue signal" is the same sense of the same word as the "signal" in "communication signal." Flares are distress signals: if people only fire them in an emergency, then the presence of the flare communicates the danger. In the same way, if more virtuous people are better at virtue signaling, then the presence of the signal indicates virtue. If natural selection designs creatures that both have diverging interests, and have needs to communicate with each other, then those creatures will probably have lots of adaptations for providing expensive-to-fake evidence of the information they need to communicate. That's the only way to do it!

(originally published at Less Wrong)

Followup to: Where to Draw the Boundaries?

There is an important difference between having a utility function defined over a statistical model's performance against specific real-world data (even if another mind with different values would be interested in different data), and having a utility function defined over features of the model itself.

Arbitrariness in the map doesn't correspond to arbitrariness in the territory. Whatever criterion your brain is using to decide which word you want, is your non-arbitrary reason ...

So the one comes back to you and says:

That seems wrong—why wouldn't I care about the utility of having a particular model? I agree that categories derive much of their usefulness from "carving reality at the joints"—that's one very important kind of consequence of choosing to draw category boundaries in a particular way. But other consequences might matter too, if we have some moral reason to value drawing our categories a particular way. I don't see why I shouldn't be willing to trade off one unit of categorizational nonawkwardness for \(X\) units of morality, even if trading off a million units of categorizational nonawkwardness for the same \(X\) units of morality would be bad.

I once read about an analogy between category boundaries and national borders. Imagine a diplomat trying to come up with a proposal for a two-state solution to the Israeli–Palestinian conflict. There's no such thing as the "correct" border between Israel and Palestine, but there are consequences of choosing one border or another. For example, awarding territory to one side risks angering the other. For another, if the West Bank and Gaza Strip are to be part of Palestine, but Tel-Aviv and the southern city of Eilat are to be part of Israel, then topology forces you to decide which of Israel and Palestine gets to be continuous, and which will be split into two parts, because a "land bridge" between Gaza and the West Bank would separate Tel Aviv and Eilat, and vice versa. Since borders can't be "true" or "false", the diplomat's task is and can only be to weigh these kinds of trade-offs.

Analogously, I think of language, following Eliezer Yudkowsky's "A Human's Guide to Words", as being a human-made project intended to help people understand each other. It draws on the structure of reality, but has many free variables, so that the structure of reality doesn't constrain it completely. This forces us to make decisions, and since these are not about factual states of the world—what the definition of a word really is, in God's dictionary—we have nothing to make those decisions on except consequences.

... okay, I think I see the problem. I see how one might have gotten that out of "A Human's Guide to Words"—if you skipped all the parts with math. I am now prepared to explain exactly what's wrong here in more detail than my previous attempt: not just that this position is not in harmony with the hidden Bayesian structure of language and cognition, but how the hidden Bayesian structure of language and cognition explains why an intelligent system might find this particular mistake tempting in the first place, and what breaks as a result.

Category "boundaries" are a useful visual metaphor for helping explain the cognitive function of categorization. If you have the visualization but you don't have the math, you might think you have the freedom to "redraw" the category "boundaries". Simple, compact boundaries might tend to be more useful, but more complicated boundaries aren't false and therefore aren't forbidden if you have some non-epistemic reason to prefer them ... right?

Only in the sense that no hypothesis is "false"! Categories, words, correspond to hypotheses—probabilistic models that make predictions. If I see a dolphin in the water, and I say, "Hey, there's a dolphin!", and you understand me, that enables you to predict quite a lot about there being this-and-such kind of aquatic mammal with fins, a tail, &c. in the water.

This AI capability of "speech" is not only very powerful; it's also easy to understand the cause-and-effect evidential entanglement which explains how it works—at least at a very high level.

Photons bounce off the dolphin and hit my eyes. I recognize the photons as forming an image that matches a concept that I associate with the word/symbol "dolphin" (implementation details omitted). I emit a "dolphin" signal composed of sound waves which hit your eardrum. By a convention that culturally evolved due to our predecessors having a shared interest in communicating with each other, you map the "dolphin" signal to an internal concept that closely resembles the one I associate with that same signal. This works because we happen to live in a world where the distribution of creatures has cluster-structure whereby dolphins have lots of things in common with each other, such that it's possible to use observations about an entity to infer that it "is a dolphin", and then use the dolphin concept to make good predictions about aspects of the entity that have not yet been observed; we owe our confidence that we've learned "the same" dolphin model to the fact that dolphins actually exist.

But the dolphin concept/model/hypothesis is subject to the universal mathematical laws of reasoning under uncertainty. In particular, probability-mass flows between hypotheses: as long as you never assign a probability of zero (which is a log-odds of negative infinity), nothing you believe can ever be definitively (infinitely) "falsified"—it "just" makes quantitatively worse predictions as compared to other hypotheses.

Because category "boundaries" are merely a visualization for a probabilistic model that makes predictions about the real world, you can't "redraw the boundaries" associated with a communication signal without messing with the model that generates them, which means messing with your predictions about the real world.

Might there be some non-epistemic reason for an agent to prefer a model that makes worse predictions? Sure! Correct maps are useful for steering reality into configurations ranked higher in your preference ordering—but causing a different agent to have incorrect maps might make them mis-navigate reality in a way that benefits you! We call this deception.

In a related phenomenon, a poorly-designed agent might get confused and end up manipulating its own beliefs: optimizing its map to inaccurately portray a high-value territory (rather than optimizing the territory to be high-value by using a map that reflects the territory), a kind of self-deception. We call this wireheading.

The laws of probability and information theory allow us to calculate how information can be efficiently encoded and transmitted from one place to another. Given some distribution of random variables, and some specification of what information about those variables you want to transmit, some encodings—some ways of "drawing" category "boundaries"—quantitatively perform better than others. Agents that want to communicate with each other will tend to invent or discover conventions that efficiently encode the information they're trying to communicate. Agents that communicate in ways that systematically depart from efficient encodings are better modeled as trying to deceive each other or wirehead themselves.

Let's walk through a simple example. Imagine that you have a peculiar job in a peculiar factory: specifically, you're a machine-learning engineer tasked with automating away the jobs of humans who sort objects from a mysterious conveyor belt.

Another engineer has already written a system that processes camera and sensor data about the objects into more convenient "features": color (measured on an eight-point blueness scale), shape (measured on an eight-point "eggness" scale), and vanadium content (a boolean Yes or No). Your task is to further process this information into a format suitable for giving commands to other systems—for example, the robot arm that will physically move the objects into appropriate bins.

The feature data consists of the blueness–eggness–vanadium-content joint distribution given by this 128-entry table:

This seems like ... not the most useful representation? The data is all there, so in principle, you could code whatever you needed to do based off the full table, but it seems like it would be an unmaintainable mess: you'd sooner resign than write a 128-case switch statement. Furthermore, when the system is deployed, you hope to typically be able to give the binning robot messages based on only the color and shape observations, because the Sorting Scanner that the vanadium readings come from is expensive to run. You could just do a Bayesian update on the entire joint distribution, of course, but it seems like it should be possible to be more efficient by exploiting regularities in the data, not entirely unlike how your colleague's system has already made your job much simpler by giving you blueness and eggness feature scores rather than raw camera data. Eyeballing the table, you notice it seems to have a lot of redundancy: most of the probability-mass is concentrated in two regions where the blueness and eggness scores are either both high or both low—and vanadium is only found when both blueness and eggness are high.

O tragedy O the stars! If only there were some more convenient and flexible way to represent this knowledge—some kind of deep structural insight to rescue you from this cruel predicament!

... alright, dear reader—I shouldn't patronize. You already know how this story ends. The distribution factorizes!

(The distribution in this made-up toy example factorizes exactly, but in a messy real-world application, you might have a spectrum of approximate models to choose from.)

We can simplify our representation of our observations by using a naïve Bayes model, a "star-shaped" Bayesian network where a central "category" node is posited to underlie all of our observations: we believe that each object either "is a blegg" (and therefore contains vanadium and has high blueness and eggness scores) with probability 0.48, "is a rube" (and therefore has no vanadium and low blueness and eggness scores) with probability 0.48, or belongs to a catch-all "other"/error class with probability 0.04. (Maybe the camera is buggy sometimes, or maybe there are some other random objects mixed in with the rubes and bleggs?)

The full joint distribution had 127 degrees of freedom (a table of \(8 \cdot 8 \cdot 2 = 128\) separate probabilities, constrained to add up to 1), whereas the naïve-Bayes representation only needs 57 parameters (\(3 \cdot 1\) prior probabilities for the categories, plus \(3 \cdot 8 = 24\), \(3 \cdot 8 = 24\), and \(3 \cdot 2 = 6\)-entry conditional probability tables for each of the features). The advantage would be much larger for more complicated problems: the joint distribution table grows exponentially with more features, quickly becoming infeasible to store and represent, let alone learn.

It must be stressed that our "categories" here are a specific mathematical model that makes specific (probabilistic) predictions. Suppose we see a black-and-white photo of an egg-shaped object: specifically, one with an eggness score of 7. Given that observation of \(\mathrm{eggness} = 7\), we can update our probabilities of category-membership.

We think the egg-shaped object is almost certainly a blegg (specifically, with probability 0.96), even if the black-and-white photo doesn't directly tell us how blue it is, because

We can then use our updated beliefs about category membership (0.96 blegg/0 rube/0.04 unknown, as contrasted to the 0.48/0.48/0.04 prior) to get our updated posterior distribution on the 0–7 blueness score (0.005/0.005/0.005/0.005/0.005/0.245/0.485/0.245—left as an exercise for the reader).

In addition to categories facilitating efficient probabilistic inference within the system that you're currently programming, labels for categories turn out to be useful for communicating with other systems. The robot arm in the Sorting room puts bleggs in a blegg bin, which gets taken to a room elsewhere in the factory where there's sophisticated vanadium-ore-processing machinery that has to handle both bleggs and gretrahedrons.

But suppose the binning arm doesn't need to know about the blueness and eggness scores: it can close its claws around rubes and bleggs alike, and you only need to program it to pick up an object from a certain spot on the conveyor belt and place it into the correct bin. However, the vanadium-ore-processing machine does need to do further information processing before it can operate on an object—perhaps it needs to vary its drill speed in proportion to the density of a particular blegg's flexible outer material (which it can estimate based on how brightly the blegg glows in the dark), but it uses a different drilling pattern for gretrahedrons.

If you need to send commands to both the binning arm and the ore-processing machine, it's a more efficient communication protocol to just be able to send the 28-byte JSON payload {"object_category": "BLEGG"} and let the other machines do their work using their own models of bleggs, rather than having to send over the raw camera data plus the binary code of the Bayesian network and feature extractors that you initially used to identify bleggs. Intelligence is prediction is compression: our ability to find an encoding that compresses the length of the message needed to convey information about the objects is fundamental to our having learned something about the distribution of objects.

The {"object_category": "BLEGG"} message is a useful shorthand for "linking up" the models between different machines. Different machines might not use the same model: the classifier system uses blueness and eggness scores to identify bleggs, but the ore-processing machine, having been told that an object is a blegg, can take its approximate blueness and eggness for granted and only needs to reason about its luminescence and vanadium content.

But this trick of using a signal to correlate the models between different machines only works because and insofar as both models are pointing to the same cluster-structure in reality. If the model in the classifier system doesn't meaningfully match the model in the ore-processing system—if the classifier code sends the {"object_category": "BLEGG"} message given a object with blueness score between 5 and 7, but the ore-processor, upon receiving the {"object_category": "BLEGG"} message, positions its drills in the expectation of processing an object with an eggness score between 0 and 2—then the factory doesn't work.

As a human learning math, it's helpful to examine multiple representations of the same mathematical object. We've already seen our blueness–eggness–vanadium model represented as a table, and factorized into a graphical model. We've done also some algebraic calculations with it. But we can also visualize it: the set of camera observations that the model classifies as a blegg with probability \(\ge 0.96\) can be thought of a area with a boundary in two-dimensional blueness–eggness space:

("With probability \(\ge 0.96\)" because our catch-all "other"/error category can also generate examples with high blueness and eggness scores; we can't say things like "Everything inside the boundary in the diagram is a blegg" when we're talking about a formal model where some of the categories generate overlapping observations in whatever subspace the diagram is depicting.)

If you were trying to teach someone about the hidden Bayesian structure of language and cognition, but thought your audience was too stupid or lazy to understand the actual math, you might be tempted to skip the part about factorizing a joint distribution into a star-shaped Bayesian network and just talk about "drawing" "boundaries" in configuration space for human convenience, perhaps with a hokey metaphor about national borders. Then the audience might walk away with the idea that there's no reason not to replace the old blegg concept and its boring compact boundary, with a new blegg* concept that has an exciting squiggly border.

Alaska isn't even contiguous with the rest of the United States. If that's okay, why can't the borders of bleggness be a little squiggly?

Because the "national borders" metaphor is just a metaphor. It immediately breaks down as soon as you try to do any calculations.

When we say that the United States purchased Alaska from the Russian Empire, that means that this-and-such physical area on the Earth's surface went from being the territory of the Russian government, to being territory of the United States government, where land being the "territory of" a "government" is a complicated idea that has something to do Schelling points over who gives orders to policemen and soldiers in that area.

When you reprogram your machine-learning system to send an {"object_category": "BLEGG"} message when it sees an object with an eggness score of 2 and a blueness score of 1, then your vanadium-ore-processing machine wears down its drill bits trying to process a rube.

Other than the fact that some aspects of both of these situations can be usefully visualized as changes to a two-dimensional diagram depicting an area with a boundary, what do these situations have to do with each other? They don't. Countries aren't Bayesian networks. They just aren't. When we depict a country on a map, we're not talking about a cognitive system that can use observations of latitude to estimate probabilities of country-membership and then use that distribution on country-membership to get an updated probability distribution on longitude. (I mean, given a world map, you could program such a thing, but it seems kind of useless—it's not clear why anyone would want that particular program.) Why would you expect to understand an AI-theory concept by telling a story about national borders?

So, that's what's wrong with the national-borders metaphor. But we haven't yet really explained the problem with "unnatural" categories—those that you would visualize as a squiggly, "gerrymandered" boundary. The squiggly blegg* boundary doesn't have the nice property of corresponding to the category labels in our nice factorized naïve Bayes model, but it still contains information. You can still do a Bayesian update on being told that an object lies within a squiggly boundary in configuration space. If that update eliminates half of your probability-mass, that's one information-theoretic bit, no matter how the category is shaped in Thingspace.

If you only care about how much probability you assign to the exact answer, then a bit is a bit. But if an approximate answer is approximately as good—if your answerspace has a metric on it, so that "approximate" can mean something—then some bits can be more valuable than others.

Suppose some random variable \(X\) is uniformly distributed on the set \(\{1, 2, 3, 4, 5, 6, 7, 8\}\). You have the option of being told either whether an observation \(x\) sampled from \(X\) is even or odd, or whether \(x\) is greater or less than 4.5. Either way, you eliminate half of your hypotheses: the entropy of your probability distribution goes from \(\log_2 8 = 3\) to \(\log_2 4 = 2\). Either way, you've learned 1 bit.

Still, if you have to make a decision that depends on "how big" \(x\) is, it seems like the "1–4 or 5–8" category system is going to be more useful than the "even/odd" category system, even though they both provide the same amount of information about the exact answer. If you learn that \(x \in \{1, 2, 3, 4\}\), then you know that \(x\) is "small", but if you learn that \(x\) is odd, you haven't learned much about how big it is: it could be 1, but it could just as well be 7.

To formalize this, let's measure how "good" a category is using the expected squared error. "Error" is how much a prediction is wrong by: if you guessed \(x\) was 2, but it was actually 5, your error would be \(5 - 2 = 3\), and your squared error would be the square of that, \(3^2 = 9\). The expected squared error of a probability distribution is, on average, the square of how much your guess about a sample from that distribution will be wrong. (The squared error has nicer mathematical properties than the absolute error.)

For our example of \(x\) sampled from \(X\) uniformly distributed on \(\{1, 2, 3, 4, 5, 6, 7, 8\}\), your best-guess estimate \(\hat{x}\) of \(x\) is going to be the expected value

And the initial expected squared error is

Suppose you then learn whether \(x\) is even or odd.

With probability 0.5, you learn that \(x\) is even. In that case, your new estimate \(\hat{x}\) taking that into account would be

and your new expected squared error (in the "even" possible world) would be

With probability 0.5, you learn that \(x\) is odd. Similar calculations (left as an exercise) also give a new expected squared error of 5 in the "odd" possible world. Averaging over both cases (trivially, \(0.5 \cdot 5 + 0.5 \cdot 5 = 5\)), learning whether \(x\) is even or odd only brought our expected squared error down from 5.25 to 5, barely changing at all.

In contrast, if you learn whether \(x\) is 1–4 or 5–8, your expected squared error plummets to 1.25. (Exercise.) By being compact, the "1–4 or 5–8" category system is much more useful for getting close to the right answer than the "even/odd" category system.

The same goes for natural categories versus squiggly category "boundaries" in configuration space; we just need to supply some metric to define what "close" means.

For our blueness–eggness–vanadium distribution, suppose we use the Euclidean distance on blueness-score ✕ eggness-score ✕ 1-if-vanadium-present-else-0. (So, for example, the "distance" between the typical blegg and the typical rube is \(\sqrt{(6 - 1)^2 + (6 - 1)^2 + (1 - 0)^2} = \sqrt{25 + 25 + 1} = \sqrt{51} \approx 7.14\) under this metric.)

Then our expected squared error before being told anything about an object is about 13.63. On being told whether an object is a blegg, rube, or other (according to the categories in our nice factorized naïve Bayes model), our expected squared error plummets to 1.38.

But suppose that, instead of our nice factorized naïve Bayes model, we use a category system based on drawing squiggly "boundaries" in configuration space: everything inside the blegg* boundary in the diagram is a blegg*, everything within the rube* boundary in a rube*, and anything outside belongs to a catch-all "other*" category.

On learning whether an object is a blegg*, rube*, or other*, our expected squared error only goes down to about 4.12.¹

In this sense, the gerrymandered blegg* concept is quantitatively less informative than the original, compact blegg concept. The metric we assigned to blueness–eggness–vanadium space was our choice, and could depend on our values: for example, if we simply don't care about predicting how blue an object is, we could disregard the blueness score and only define a concept on the eggness–vanadium subspace (in which case our initial expected squared error is about 6.94, plummets to 0.69 given knowledge of blegg/rube/other category-membership, but only goes down to about 1.81 given knowledge of the gerrymandered blegg*/rube*/other* category). Or if we don't care about predicting blueness very much, we could calculate our error score with respect to a metric that gave blueness very little weight. (Exercise.)

But given a metric on the variables that you care about predicting and using to inform predictions, which categories are cognitively useful depends on the the distribution of data in the world. You can't define a word any way you want.

The dependence on a choice of metric on configuration space—and really, a choice of the space—gives a sense in which optimal categories are value-laden, but it's a specific kind of lawful dependence between your values and the distribution of data in the world, not an atomic preference for using a particular encoding for its own sake.

The cognitive function of categorization is to group similar things together so that we can make similar decisions about them. A function measuring the extent to which things are "similar" has to take the things as input, but the extent to which things are decision-relevantly similar also depends on what you're trying to accomplish with your decisions, and that can be algorithmically complex. It might not be just a matter of only looking at some decision-relevant subspace of a natural, "obvious" configuration space that's available to all possible minds (like not caring what color your toothbrush handle is—um, if we pretend that all possible minds had human-like color vision); the dimensions of the space you do your similarity-clustering in might themselves be complicated features (in the sense of machine learning) of which agents with different values would have no reason to logically pinpoint that particular criterion by which things may be judged. How you should define words depends on what you want, but that's not the same as defining words any way you want.

For example, poison isn't a natural category to a generic mind studying chemistry: we group cyanide and hemlock together as poison because we value human health, and so we want to have a category for scary chemicals that disrupt human metabolism, causing death or serious illness. But this determination depends on the intricate details of human biochemistry. (The theobromine in chocolate is okay for humans at typical doses, but potentially fatal to dogs, which are actually pretty close to us in animalspace.) The compact category "boundary" that minimizes predictive error on human-healthspace, corresponds to a squiggly "boundary" in the chemicalspace you would be looking at if you've never seen a human and just want to make predictions about the chemicals themselves.

Or tiny molecular smileyfaces and real human smiles might be grouped together as similar as far as an image-classifier's curve detector is concerned, even if they're not similar as far as the abstracted idealized dynamic of human morality is concerned.

The technical sense in which optimal categories can be value-laden doesn't alter the basic morals of our basic Bayesian philosophy of language. Your values can give you a particular configuration space and a metric on the space, but given that, sane agents want to "carve it at the joints" in order to get a communication system that minimizes predictive error. If you're trying to find an efficient encoding of your observations, there's no reason to want squiggly, gerrymandered categories in the decision-relevant space.

The one replies:

You're still not addressing my crux! I don't doubt what you say about minimizing prediction error with respect to some squared metric thingy. But what if that's not what I care about? My utility function assigns high value to using the squiggly blegg* category boundary—such that the utility of using my preferred category outweighs the disutility of making less accurate predictions. You can define a word any way you want—if you're willing to pay the costs.

So, what, you just intrinsically assign high utility to using the same communication signal to encode eggness-2/blueness-1 observations as eggness-6/blueness-6 observations, given the joint distribution specified in my story problem about sorting objects in a factory? Really?

"... yes!"

Okay, but where would that kind of exotic utility function come from? How would it arise naturally in an intelligent system?

There's a trivial sense in which you can interpret any action taken by an agent as being taken because the agent values taking that action. This theory is compatible with all possible behaviors and therefore explains nothing.

The value of decision-theoretic utility functions isn't that "Because utility!" serves as an all-purpose excuse for any possible behavior. It's that simple coherence desiderata imply that an agent's behavior should be describable as maximizing expected utility for some utility function—with corresponding constraints on the shape of that behavior.

Situations like the Allais paradox illustrate what these constraints look like. Consider an AI faced with playing the following game. There's a switch that can be turned On or Off, that starts out on in the Off position. At midnight, a coin is flipped. If the coin comes up Tails, the game ends. If the coin comes up Heads, then at a quarter past midnight, if the switch is Off, then the AI gets paid $100, and if the switch is On, a six-sided die is rolled, and the AI gets paid $110 if the die doesn't come up 6.

Suppose that, before midnight, the AI is willing to pay a dollar to flip the switch On (as if it thought that winning $110 with a probability of 5/12 is better than winning $100 with a probability of 1/2). Suppose the coin comes up Heads, and the AI is then willing to pay another dollar to flip the switch Off again (as if it thought that $100 with certainty is better than $110 with probability 5/6). Then the AI is two dollars poorer in exchange for the switch being in the same position it started in.

These gambling preferences violate the independence axiom of the von Neumann–Morgenstern utility theorem. You can't have a utility function \(U\) for which

and

because the sides of the second inequality are just those of the first multiplied by two, and multiplying by two should preserve the direction of inequality.

Having shown this, can we say that an AI with such behavior is "irrational"? But what does that even mean? If, for some reason, you specifically programmed the AI to prefer options it considers "certain", or to want switches to be "On" before midnight but "Off" after midnight, then it would be functioning as designed.

What we can say about such an AI, is that it doesn't have a utility function in terms of money, and is therefore not coherently optimizing for acquiring money. Recall that we say that a system is an optimizer if it systematically steers the future into configurations that rank higher with respect to some preference ordering. This helps us make predictions about what effects the system has, without having to model the details of how it brings those effects about. A well-designed agent that was optimizing for acquiring money would be expected to obey the independence axiom.

If the AI playing this game isn't coherently optimizing for acquiring money, what is it optimizing for? To tell, we'd need to observe its behavior in different environments and see how it responds to perturbations. If it is trying to acquire money but is just biased to prefer certainty (in violation of the von Neumann–Morgenstern axioms), then we'd expect it to make choices that result in money but continue to exhibit Allais-like glitches around gambles involving probabilities close to 1. If it just likes switches to be off after midnight, then we'd expect it to turn switches off at that time even if there's no gambling game going on.

This methodology for attributing goals to an agent—consider it to be "optimizing for" outcomes that it systematically achieves across a variety of environments—applies to the behavior of sending communication signals, just as it does to the behavior of flipping switches.

Back to the factory. Our classifier system sends a {"object_category": "BLEGG"} message when it gets feature data corresponding to the compact blegg concept. This behavior is optimized for sending messages that allow other systems to minimize the expected squared error of their predictions of objects with respect to our standard metric on blueness–eggness–vanadium space. We don't intrinsically "assign utility" to using that particular category system; the category is the solution to an optimization problem about how to efficiently get blueness–eggness–vanadium information from one place to another.

A system that sends a {"object_category": "BLEGG"} message when it gets camera data corresponding to the gerrymandered blegg* concept would be optimized for ... what? If you don't intrinsically assign utility to using that particular category system, then why would you program the system that way? What could possibly be the problem for which the gerrymandered category is an optimized solution?

Well. Suppose that, besides your dayjob as a machine-learning engineer, you also happen to own a side interest in the firm that supplies bleggs and rubes to this very factory. And suppose that vanadium fetches higher market prices than palladium, such that the factory is to pay the supplier $2 per blegg but only $1 per rube—and that the accounts-payable records are to be compiled based on how much the classifier you're currently programming sends {"object_category": "BLEGG"} and {"object_category": "RUBE"} messages, not how much metal actually gets harvested.

You can't help but notice that you stand to make more money if the system you're programming sends BLEGG messages more often. You can't just make it send BLEGG messages all the time—someone would notice and you'd get fired. But the ore-processing room can cope with a few suboptimally-sorted objects. Surely it's no big deal if you just ... adjusted the category boundary of BLEGG-ness a bit?

We saw earlier that the blegg concept does better than the blegg* concept with respect to mean squared error (given a metric on the feature space).

That's not the only possible scoring function with which one could formalize how "good" a category system is. Suppose that instead we score our category system by which one best minimizes the expected squared error minus supplier revenue in cents. With respect to this criterion, accurate predictions are still good, but supplier revenue is also good.

Learning whether an object is a blegg, rube, or other (according to the "natural" categories in our naïve Bayes model) yields a squared-error-minus-revenue score of about −142.62. (Don't ask me what the units are on this.) But learning whether an object is a blegg*, rube*, or other* yields a squared-error-minus-revenue of −151.57, which is lower (which is better, because we formulated this as a minimization problem). So with respect to that scoring function, the blegg* category "boundary" is preferable.

The one says:

But now it sounds like you're agreeing with me! The compact blegg category serves the factory owner's goals better, which you formalized in terms of minimizing average squared error. The squiggly blegg* boundary makes the factory perform less well, but it serves the moonlighting engineer's goals better, which you formalized in terms of minimizing squared error minus supplier revenue. There's no rule of rationality against the engineer programming the system using the blegg* category boundary if it suits their goals better.

Only in the sense that there's no rule of rationality against lying! Suppose I'm selling you some number of gold and silver bars, but you can't examine the metal yourself until later; you can only hope that the receipt I give you is accurate. Consider the following two scenarios.

In the first scenario, I lie: the receipt says I delivered 60 gold bars and 20 silver bars, but I actually delivered 40 gold bars and 40 silver bars. You live in a low-trust world where lying is very common and contract enforcement isn't really a thing: a third of the time an object is claimed to be gold, it turns out to be silver. So when you discover the fraud, you feel disappointed but not surprised: you would have preferred to get what you paid for, but you can't say you anticipated it.

In the second scenario, I tell the truth—with respect to a category system that suits my goals. The receipt says I delivered 60 gold bars and 20 silver bars—and I did. It's just that what I prefer to call "gold bars", you prefer to call "gold bars, or silver bars with odd serial numbers", and what I call "silver bars", you call "silver bars with even serial numbers". You know this, so when you examine the actual contents of the delivery, you feel disappointed but not surprised: you would have preferred to transact under your definitions of 'gold' and 'silver', but you can't say you anticipated it.

We might question whether these are two different scenarios, or two descriptions of the same scenario: the same physical receipt, the same physical metal, the same buyer anticipations about the metal conditional on observing the receipt. If we just pay attention to the evidential entanglements instead of being confused by words, then there's no functional difference between saying "I reserve the right to lie p% of the time about whether something belongs to category C", and adopting a new, less-accurate category system that misclassifies p% of instances with respect to the old system.

Minimizing the squared-error score is about map–territory correspondence: ways of communicating that help the factory machines make better predictions about the objects, get a higher score.

Minimizing the squared-error-minus-supplier-revenue score is a compromise between map–territory correspondence and saying whatever makes the supplier the most money.

The degree of compromise is quantitative: there's a continuum of possible scoring functions between "minimize expected squared error, only" (for which the naïve-Bayes categorizer is a good solution), and "maximize supplier revenue, only" (for which "always say BLEGG" is the optimal solution). If always saying whatever profits you and not revealing any information about the territory is deception pure and simple, then the intermediate points on a continuum with that can be thought of as partially deceptive.

Depending on your goals, deception can be rational! If you don't care about other agents having accurate models and just want to intervene on them to make them believe whatever makes them behave in a way that benefits you—or whatever makes them happy—then you can do that! There's no God to stop you. But in order to help you decide whether deceiving people is the right thing to do, it helps to notice that what you're doing is deceiving people.

It helps to notice what you're doing—if you're trying to be an agent that coherently steers the future in some direction. But who does that, really? Maybe you just want to feel good! And not even coherently steer the universe into configurations where you feel good, either!

Rational agents should want to have true beliefs: the map that reflects the territory, is the map that is useful for navigating the territory. But you don't—can't—have unmediated access to the world; you can only infer what the world is like from sensory data, and effectively live in your model of the world. Given the tricky indirection involved, it's not surprising that poorly-designed agents like humans sometimes get confused and "wirehead" themselves: if you don't notice the difference, it's tempting to fabricate a fake map that falsely portrays the territory as being good, instead of making a map that reflects the territory (which you can use to figure out how to improve the territory).

Similarly, if you don't notice the difference, it's tempting to choose language that makes the world sound good, than to have your language accurately describe the world (which description you can use to figure out how to make the world better).

Suppose I want people to think I'm funny. Funny is a value-laden concept in the specific lawful sense described earlier: non-human agents would have no motive to evaluate the particular fixed computation of humor. It's also a fuzzy concept: we don't have a simple test to precisely measure in standard units exactly how funny a joke is, but there's enough regularity in how people use the word "funny" for the word to be a useful communication signal. It's also a two-place concept: people have different senses of humor, so that what I consider funny isn't exactly the same as what you consider funny.

Given all these complications, one could imagine being tempted to think that humor is "subjective", and that therefore I can define it any way I want, and that therefore, if I feel sad about not being "funny", I can fix that by changing my definition of the word "funny" such that it includes my jokes. Because definitions can't be "false", right!? There's no rule of rationality prohibiting this boundary-redrawing project—and since I want so desperately to be "funny", there's every rule of human decency in favor of it, right?!

So, this obviously doesn't work. (Okay, it "works" if you deliberately choose to define the word "work" such that it works, but it doesn't actually work.) Yes requires the possibility of no: redefining X to make "Is it X?" come out true no matter what, loses the purpose of asking the question in the first place. The proposal to redefine the word "funny" came with the purported justification that words don't have intrinsic meanings, so it can't be "wrong" to redefine it. But precisely because words don't have intrinsic meanings, there's no reason to want to redefine an existing word, except to piggyback off the meaning people are already using that signal for.

(Note that this, in itself, isn't necessarily deceptive. Sometimes, coining new senses of a word that piggyback off an existing meaning can be a powerful tool for extending our vocabulary to cover new phenomena that we don't already have words for—as long as we're careful to specify which meaning is intended when it's not clear from context.)

It's not plausible to suppose that I want to be "funny" because I like five-letter words that start with the letter f; I want to be funny because of what that communication signal is already understood to refer to in common usage. The redefinition might (or might not) succeed at making me feel better about myself, but if it does, it only works by means of confusing me: using strategic equivocation to arbitrage the hedonic gap between my new definition, and the old definition (which I still mentally associate with the word).

If it does succeed at making me feel better about myself, is the redefinition "rational"? Happiness is good, right? Should not rationalists win?

I do not frame an answer: that would depend on how you draw the category boundaries of "rational", which is not an interesting question. (As it is written of a virtue which is nameless: if you speak overmuch of the Way, you will not attain it.)

What I can say, however, is that redefining the concept of humor is not a procedure that uses a map that reflects the territory to systematically achieve goals across a wide range of environments. If there's anything I can do to become funnier (like practicing telling jokes in a mirror, or studying great comedians to imitate their timing and delivery), I would seem less likely to notice and execute on such a plan after having sabotaged the concept I would need to notice the problem in the first place.

The map is not the territory ... but for real agents embedded in the physical universe, the map is part of the territory. This presents some complications to applications of our anti-wireheading moral. We don't want to wirehead ourselves by making the map look good at the expense of undermining our ability to navigate the territory—but there's no bright-line distinction demarcating which configurations of atoms are "the map". From the perspective of the eternal, it's all just territory.

In the previous post, we considered the case of an assembly line (well, sorting line) worker in the blegg–rube factory being excited about an ostensible promotion to the position of Vice President of Sorting—only to be aggrieved on finding out that it's a promotion literally in name only, with no changes in pay, authority, or work tasks.

If we interpret the title as part of "the map", a communication signal with the function of encoding information about the person's job, then we want to say that the new title is substantively misleading (even if it's not technically a "lie"): when you hear that someone's job is being a "Vice President", you predict that their work involves managing people and making high-level executive decisions for the firm. Your probability that the "Vice President" has to spend all day moving objects from a conveyor belt into one of two bins based on the object's color and shape (a task that should probably be automated), is lower than before you heard the person's title: hearing the title made you update in the wrong direction.

But if we interpret the title as part of "the territory", a feature of the job itself, rather than a communication signal about the job—then it's not misleading and can't be misleading. The job happens to be one that has the symbols "Vice President" printed on the accompanying business cards and employee roster, much like how bleggs are objects that happen to be blue. You can't say the blue is "lying"; that doesn't make any sense!

The function of words is to serve as signals for communication, so it seems safe to say that language should usually be construed as part of "the map". Changing names and only names, without altering the things that the names refer to, as in the phony "Vice President" example, is probably deceptive. But for other features associated with a category, it may not always be obvious when we should construe them as "map" rather than "territory": using a feature to infer category-membership is formally equivalent to regarding it as a signal sent by senders of that category. Is that man pretending to be a doctor, or does he just happen to be wearing a lab coat?

The concept we're groping towards, and hoping to formulate an elegant reduction of, is that of mimicry. Suppose there is some existing category of entity, an original, typified by some cluster of traits. A mimic is an entity optimized to approximately match the distribution of the original in many, but not all traits, thereby being part of the same cluster as the original in some subspace of the space the original category is defined in, but not the space as a whole. For example, if the vector \([4, 4, 4, 4, 4] \in \mathbb{R}^5\) is the original, then an optimization process trying to construct a mimic of it in the subspace spanned by \(x_1\), \(x_4\), and \(x_5\) might choose \([4, 0, 0, 4, 4]\): if you only look at the first, fourth, and fifth coordinates, then \([4, 4, 4, 4, 4]\) and \([4, 0, 0, 4, 4]\) "look the same"—they are the same in that subspace, but not the same if you include the second and third coordinates.

We can find examples in nature. Suppose one type of butterfly has evolved to be toxic to a type of predator, and also has distinctive wing markings that function as an honest warning signal to that predator: this butterfly is not good to eat. This provides an "opportunity" (in evolutionary time) for a second species of butterfly to develop similar wing markings, so that predators will confuse it for the first type of butterfly, despite the second butterfly not paying the metabolic cost of producing toxins. This kind of situation is called Batesian mimicry.

Is Batesian mimicry deceptive? (In our usual functionalist sense, which is obviously not a claim about butterfly psychology.) Is the second butterfly's very existence a kind of lie?

In some sense, yes! The mimic butterfly has been optimized by evolution to look like the first butterfly because of the fitness payoff of being categorized by the predator as the first, toxic, kind of butterfly. The "categorized by the predator as toxic" category is a natural, compact region in wing-marking-space, but "comes apart" into two clusters in the broader wing-markings–actual-toxicity space.

Furthermore, the evolutionary dynamics create an asymmetric relationship between the two categories, that isn't captured by just the two trait-clusters themselves. The reason for the mimic butterfly to have those particular wing-markings is in order to manipulate the predator's predictions of toxicity (which was learned from encounters with the original), so if the original's wing-markings were to change as a result of some new selection pressure, the mimic would be subjected to selection pressure to "keep up" by changing its wing-markings accordingly.

That's not true in the other direction: if the mimic's markings were to change, the original wouldn't "follow": the original would instead benefit from the probabilistic strength of its warning signal not being parasitically diluted by the mimic anymore. Thus, the asymmetric terminology of "original" and "mimic" is appropriate: it's not just that these two species happen to look like each other; one of them was there first, and the other looks like it.

Is mimicry always deceptive? Not necessarily—there might be some situations where the relevant set of variables are among those where the mimic matches the distribution of the original.

Suppose you and I are feeding some ducks in the park. I say, "I love feeding these ducks!"

You say, "Wrong! These aren't all ducks. This park is where a local inventor tests out his Anatid-oid robots that are designed to look and act like ducks. Therefore, you can't say, 'I love feeding these ducks'; you need to say 'I love feeding these ducks and Anatidoid robots'."

"Wow, they're so realistic!" I say. "I can't even tell which ones are really robots! In fact," I continue, "since I can't tell, I'm inclined to just keep calling them all ducks; it would be pretty awkward to refer to each one as a duck-or-Anatidoid-robot."

"But it is possible to tell," you claim. "For example, if you get really close to one of the Anatidoid robots, and there's not a lot of ambient noise, you can hear the gears inside, turning."

"Okay," I say, "but I can't hear the gears from here. Since I have no way of telling the difference between ducks and Anatidoid robots without doing the more expensive evidence-gathering of cornering one in a quiet place, it makes sense for me to talk and think about the robots as being a kind of duck."

"But that's a lie! Ducks and Anatidoid robots may look and act similarly, but they're actually very different! Ducks are made of flesh and blood inside and are fated to die, whereas Anatidoid robots have a plastic interior and are immortal. And the ducks digest and gain nutrients from the scraps of bread we're feeding them, whereas the Anatidoid robots merely store the bread in an internal compartment that later gets dumped as they recharge wirelessly in the inventor's lab."

"Sure," I agree. "And if I were interacting with these entities in a context where I wanted to minimize the expected squared error of my predictions about their internal makeup, energy sources, or ultimate fate, then I would want to make that distinction. But I just want to watch some cool ducks in the park, and in the context of that activity, I only need to minimize the expected squared error of my predictions about appearance and behavior."

This is the origin of the famous duck test: if it looks like a duck, and quacks like a duck, and you can model it as a duck without making any grievous prediction errors, then it makes sense to consider it a member of the category duck in the range of circumstances where your model continues to perform well.

The features for which mimics fail to match the original need not be hidden (like gear sounds that you can't hear in a noisy park) in order for mimics to not be deceptive; they only need to be irrelevant in the context the category is being used. Squirt guns aren't guns—and are usually manufactured in unrealistic colors specifically to prevent being confused with real guns—but in the context of a water fight, the utterance "Don't point that gun at me" (without the privative adjective squirt) is understood perfectly well.

Nondeceptive mimicry is fragile, however: it works in contexts where the all the relevant features are ones where the mimic matches the original. Mimics that don't match the distribution of the original along relevant features are deceptive in the sense that agents that observe the mimic and assign it to the same mental category as the original on the basis of the matching features, will use that categorization to make predictions about unobserved but nonmatching features, and be wrong. And they'll be wrong because the mimic is optimized to "look like" the original (to match on many observable features).

If different agents using a shared language disagree on what features are "relevant", they may have an incentive to fight about how scarce and valuable short codewords should be defined in their common language, in order to exert control over what inferences and decisions agents using that language can easily make and coordinate on.

Let's consider how this might apply to a real-world issue. From moral perspectives that place a lot of value on the welfare of nonhuman animals, factory farming is an ongoing moral catastrophe. Unfortunately (for the farmed animals), meat-eaters and the global agriculture industry they support aren't going to change their ways because of anyone's desperate cry at the horror of suffering or carefully-reasoned appeal to the global utilitarian calculus. Animal-rights advocates can sway behavior on the margin, but there's just too much biological and cultural inertia favoring the consumption of animal products for it to be feasible to outlaw factory farming the way chattel slavery was outlawed. It's not that humans hate farm animals; they're just ... made out of tissue that we can use for other things.

An alternative strategy for ending factory farming is to prioritize the development of artificial substitutes that mimic real meat, eggs, dairy, &c. along the consumption-relevant dimensions of taste, texture, nutrition, &c., but are produced in a lab or factory rather than from the tissues of sentient creatures. In the limit of arbitrarily capable physical manufacturing technology, carnivores and factory-farming opponents alike could both be satisfied: if two steaks are indistinguishable by any physical means whatsoever, then a meat-eater has no reason to care which one came from an actual cow's flesh, and which one was molecularly assembled by nanobots. Perhaps a Society of hunter–gatherers that attached cultural significance and ritual to the labor of killing one's own meal would have a reason to object, but modern folk for whom food comes from the supermarket have no basis within their experience to say that the nanoassembled steak isn't "real".

Unfortunately, we do not have arbitrarily capable physical manufacturing technology. Although progress continues, modern animal product substitutes are sufficiently unsuccessful mimics that they are usually not considered to belong to "the same" category as the original. Veggie burgers are not burgers in the sense that a customer who ordered "a burger" at a restaurant and was served a veggie burger would be likely to notice and complain—and in particular, would probably not be satisfied if the waiter were to reply, "Well, if you specifically wanted a burger made from cow flesh, you should have said that."

As technology to make plausible mimics/substitutes improves, however, different interest groups might face a temptation to fight over the meanings of words that was not present when the mimics weren't plausible enough for a dispute to arise. If you have the power of setting the default extension of a word that people are already using to communicate with, you can exert some amount of control over the decisions people make while trying to think using that word. Should the meaning change, then a restaurant customer who wants to make sure they receive a burger under the old definition now has to use more words, while those who don't have a strong preference or are too shy to complain will accept the restaurant's interpretation of the order.

Thus, if a fight breaks out about the meaning of the word meat, animal rights activists have a moral incentive to draw the category "boundaries" to include even substitutes that are very bad (on the empirical merits of successfully mimicking the original), whereas existing agricultural interests have a financial incentive to draw the "boundaries" to exclude even substitutes that are very good. (This kind of dispute is not hypothetical, and isn't necessarily limited to just words: in the late 19th century, dairy farmers pushed for laws that required margarine to be dyed pink to prevent consumers from confusing it for butter—the law effectively interpreting color as a communication signal, rather than a property of the good itself.)

If a fight breaks out about the meaning of the word meat, rationalists may not all take the same side, but we can at least strive for objectivity in describing the conflict—and in particular, to notice the difference between definitions motivated by describing reality, and definitions motivated by the positive or negative effects (such as profitably deceiving other agents) of choosing one description or another.

If some think that some meat substitute should be considered meat because the "taste" dimension is genuinely most relevant to the true meaning of meat, and some oddities in the texture don't matter, but others think vice versa, the philosophy articulated on this post has nothing to say to either side: the math of minimizing expected squared error by putting labels on clusters doesn't say which subspace to look for clusters in.

But if some think that some meat substitute should be considered meat because saving nonhuman animals from a life of torture is more important than conceptual parsimony ... I can't prove that that's not the right the answer to the decision problem of what verbal behavior to perform. The stakes are genuinely high.

What I can say is that the hidden Bayesian structure of language and cognition makes no reference to the stakes, and departing from the structure extracts a price that isn't up to us.

If, empirically, being generous about what counts as "meat" can prevent massive suffering (by altering the social defaults around consumption behavior), then maybe that's the right thing to do.

Similarly, if telling the public that masks don't work for preventing respiratory disease can preserve supplies for medical professionals who need them more, then maybe that's the right thing to do.

And if you live in an absurd thought experiment where saying "2 + 2 = 5" could save 3↑↑↑3 lives, maybe saying "2 + 2 = 5" is the right thing to do. But the empirical question of whether you happen to live in that particular thought experiment, doesn't change the laws that govern what you have when you take ●●-many plus another ●●-many, no matter what symbols are used to communicate this fact, and no matter the consequences for communicating it.

For these reasons it is written of the third virtue of lightness: you cannot make a true map of the category by drawing lines upon paper according to impulse; you must observe the joint distribution and draw lines on paper that correspond to what you see. If, seeing the category unclearly, you think that you can shift a boundary just a little to the right, just a little to the left, according to your caprice, this is just the same mistake.

And as it is written of a virtue which is nameless: perhaps your conception of rationality is that it is rational to believe the words of the Great Teacher, who lives in an area where claiming that the sky is blue would be political suicide.

And the Great Teacher says, "Some people I usually respect for their willingness to publicly die on a hill of facts, now seem to be talking as if color references are necessarily a factual statement about frequencies of light. But using language in a way you dislike, is not lying. You're not standing in defense of Truth if you insist on a word, brought explicitly into question, being used with some particular meaning." And you look up at the sky and see blue.

If you think: "It may look like the sky is blue, such that I'd ordinarily think that someone who said 'The sky is green' was being deceptive, but surely the Great Teacher wouldn't egregiously mislead people about the philosophy of language when being egregiously misleading happens to be politically convenient," you lose a chance to discover your mistake.

How will you discover your mistake? Not by comparing your description to itself.

But by comparing it to that which you did not name.

(Thanks to Jessica Taylor, Abram Demski, and Tsvi Benson-Tilson for discussion and feedback.)

(originally published at Less Wrong)

How is it possible to tell the truth?

I mean, sure, you can use your larynx to make sound waves in the air, or you can draw a sequence of symbols on paper, but sound waves and paper-markings can't be true, any more than a leaf or a rock can be "true". Why do you think you can tell the truth?

This is a pretty easy question. Words don't have intrinsic ontologically-basic meanings, but intelligent systems can learn associations between a symbol and things in the world. If I say "dog" and point to a dog a bunch of times, a child who didn't already know what the word "dog" meant, would soon get the idea and learn that the sound "dog" meant this-and-such kind of furry four-legged animal.

As a formal model of how this AI trick works, we can study sender–receiver games. Two agents, a "sender" and a "receiver", play a simple game: the sender observes one of several possible states of the world, and sends one of several possible signals—something that the sender can vary (like sound waves or paper-markings) in a way that the receiver can detect. The receiver observes the signal, and makes a prediction about the state of the world. If the agents both get rewarded when the receiver's prediction matches the sender's observation, a convention evolves that assigns common-usage meanings to the previously and otherwise arbitrary signals. True information is communicated; the signals become a shared map that reflects the territory.

This works because the sender and receiver have a common interest in getting the same, correct answer—in coordinating for the signals to mean something. If instead the sender got rewarded when the receiver made bad predictions, then if the receiver could use some correlation between the state of the world and the sender's signals in order to make better predictions, then the sender would have an incentive to change its signaling choices to destroy that correlation. No convention evolves, no information gets transferred. This case is not a matter of a map failing to reflect the territory. Rather, there just is no map.

How is it possible to lie?

This is ... a surprisingly less-easy question. The problem is that, in the formal framework of the sender–receiver game, the meaning of a signal is simply how it makes a receiver update its probabilities, which is determined by the conditions under which the signal is sent. If I say "dog" and four-fifths of the time I point to a dog, but one-fifth of the time I point to a tree, what should a child conclude? Does "dog" mean dog-with-probability-0.8-and-tree-with-probability-0.2, or does "dog" mean dog, and I'm just lying one time out of five? (Or does "dog" mean tree, and I'm lying four times out of five?!) Our sender–receiver game model would seem to favor the first interpretation.

Signals convey information. What could make a signal, information, deceptive?

Traditionally, deception has been regarded as intentionally causing someone to have a false belief. As Bayesians and reductionists, however, we endeavor to pry open anthropomorphic black boxes like "intent" and "belief." As a first attempt at making sense of deceptive signaling, let's generalize "causing someone to have a false belief" to "causing the receiver to update its probability distribution to be less accurate (operationalized as the logarithm of the probability it assigns to the true state)", and generalize "intentionally" to "benefiting the sender (operationalized by the rewards in the sender–receiver game)".

One might ask: why require the sender to benefit in order for a signal to count as deceptive? Why isn't "made the receiver update in the wrong direction" enough?

The answer is that we're seeking an account of communication that systematically makes receivers update in the wrong direction—signals that we can think of as having been optimized for making the receiver make wrong predictions, rather than accidentally happening to mislead on this particular occasion. The "rewards" in this model should be interpreted mechanistically, not necessarily mentalistically: it's just that things that get "rewarded" more, happen more often. That's all—and that's enough to shape the evolution of how the system processes information. There need not be any conscious mind that "feels happy" about getting rewarded (although that would do the trick).

Let's test out our proposed definition of deception on a concrete example. Consider a firefly of the fictional species P. rey exploring a new area in the forest. Suppose there are three possibilities for what this area could contain. With probability 1/3, the area contains another P. rey firefly of the opposite sex, available for mating. With probability 1/6, the area contains a firefly of a different species, P. redator, which eats P. rey fireflies. With probability 1/2, the area contains nothing of interest.

A potential mate in the area can flash the P. rey mating signal to let the approaching P. rey know it's there. Fireflies evolved their eponymous ability to emit light specifically for this kind of sexual communication—potential mates have a common interest in making their presence known to each other. Upon receiving the mating signal, the approaching P. rey can eliminate the predator-here and nothing-here states, and update its what's-in-this-area probability distribution from {\(\frac{1}{3}\) mate, \(\frac{1}{6}\) predator, \(\frac{1}{2}\) nothing} to {\(1\) mate}. True information is communicated.

Until "one day" (in evolutionary time), a mutant P. redator emits flashes that imitate the P. rey mating signal, thereby luring an approaching P. rey, who becomes an easy meal for the P. redator. This meets our criteria for deceptive signaling: the P. rey receiver updates in the wrong direction (revising its probability of a P. redator being present downwards from \(\frac{1}{6}\) to 0, even though a P. redator is in fact present), and the P. redator sender benefits (becoming more likely to survive and reproduce, thereby spreading the mutant alleles that predisposed it to emit P. rey-mating-signal-like flashes, thereby ensuring that this scenario will systematically recur in future generations, even if the first time was an accident because fireflies aren't that smart).

Or rather, this meets our criteria for deceptive signaling at first. If the P. rey population counteradapts to make correct Bayesian updates in the new world containing deceptive P. redators, then in the new equilibrium, seeing the mating signal causes a P. rey to update its what's-in-this-area probability distribution from {\(\frac{1}{3}\) mate, \(\frac{1}{6}\) predator, \(\frac{1}{2}\) nothing} to {\(\frac{2}{3}\) mate, \(\frac{1}{3}\) predator}. But now the counteradapted P. rey is not updating in the wrong direction. If both mates and predators send the same signal, than the likelihood ratio between them is one; the observation doesn't favor one hypothesis more than the other.

So ... is the P. redator's use of the mating signal no longer deceptive after it's been "priced in" to the new equilibrium? Should we stop calling the flashes the "P. rey mating signal" and start calling it the "P. rey mating and/or P. redator prey-luring signal"? Do we agree with the executive in Moral Mazes who said, "We lie all the time, but if everyone knows that we're lying, is a lie really a lie?"

Some authors are willing to bite this bullet in order to preserve our tidy formal definition of deception. (Don Fallis and Peter J. Lewis write: "Although we agree [...] that it seems deceptive, we contend that the mating signal sent by a [predator] is not actually misleading or deceptive [...] not all sneaky behavior (such as failing to reveal the whole truth) counts as deception".)

Personally, I don't care much about having tidy formal definitions of English words; I want to understand the general laws governing the construction and perversion of shared maps, even if a detailed understanding requires revising or splitting some of our intuitive concepts. (Cailin O'Connor writes: "In the case of deception, though, part of the issue seems to be that we generally ground judgments of what is deceptive in terms of human behavior. It may be that there is no neat, unitary concept underlying these judgments.")

Whether you choose to describe it with the signal/word "deceptive", "sneaky", Täuschung, הונאה, 欺瞞, or something else, something about P. redator's signal usage has the optimizing-for-the-inaccuracy-of-shared-maps property. There is a fundamental asymmetry underlying why we want to talk about a mating signal rather than a 2/3-mating-1/3-prey-luring signal, even if the latter is a better description of the information it conveys.

Brian Skyrms and Jeffrey A. Barrett have an explanation in light of the observation that our sender–receiver framework is a sequential game: first, the sender makes an observation (or equivalently, Nature chooses the type of sender—mate, predator, or null in the story about fireflies), then the sender chooses a signal, then the receiver chooses an action. We can separate out the propositional content of signals from their informational content by taking the propositional meaning to be defined in the subgame where the sender and receiver have a common interest—the branches of the game tree where the players are trying to communicate.

Thus, we see that deception is "ontologically parasitic" in sense that holes are. You can't have a hole without some material for it to be a hole in; you can't have a lie without some shared map for it to be a lie in. And a sufficiently deceptive map, like a sufficiently holey material, collapses into noise and dust.

Bibliography

I changed the species names in the standard story about fireflies because I can never remember which of Photuris and Photinus is which.

Fallis, Don and Lewis, Peter J., "Toward a Formal Analysis of Deceptive Signaling"

O'Connor, Cailin, Games in the Philosophy of Biology, §5.5, "Deception"

Skyrms, Brian, Signals: Evolution, Learning, and Information, Ch. 6, "Deception"

Skyrms, Brian and Barrett, Jeffrey A., "Propositional Content in Signals"

(originally published at Less Wrong)

The explaining-away effect (or, collider bias; or, Berkson's paradox) is a statistical phenomenon in which statistically independent causes with a common effect become anticorrelated when conditioning on the effect.

In the language of d-separation, if you have a causal graph X → Z ← Y, then conditioning on Z unblocks the path between X and Y.

Daphne Koller and Nir Friedman give an example of reasoning about disease etiology: if you have a sore throat and cough, and aren't sure whether you have the flu or mono, you should be relieved to find out it's "just" a flu, because that decreases the probability that you have mono. You could be inflected with both the influenza and mononucleosis viruses, but if the flu is completely sufficient to explain your symptoms, there's no additional reason to expect mono.¹

Judea Pearl gives an example of reasoning about a burglar alarm: if your neighbor calls you at your dayjob to tell you that your burglar alarm went off, it could be because of a burglary, or it could have been a false-positive due to a small earthquake. There could have been both an earthquake and a burglary, but if you get news of an earthquake, you'll stop worrying so much that your stuff got stolen, because the earthquake alone was sufficient to explain the alarm.²

Here's another example: if someone you're arguing with is wrong, it could be either because they're just too stupid to get the right answer, or it could be because they're being dishonest—or some combintation of the two, but more of one means that less of the other is required to explain the observation of the person being wrong. As a causal graph—³

Notably, the decomposition still works whether you count subconscious motivated reasoning as "stupidity" or "dishonesty". (Needless to say, it's also symmetrical across persons—if you're wrong, it could be because you're stupid or are being dishonest.)

(originally published at Less Wrong)

Reply to: Meta-Honesty: Firming Up Honesty Around Its Edge-Cases

Eliezer Yudkowsky, listing advantages of a "wizard's oath" ethical code of "Don't say things that are literally false", writes—

Repeatedly asking yourself of every sentence you say aloud to another person, "Is this statement actually and literally true?", helps you build a skill for navigating out of your internal smog of not-quite-truths.

I mean, that's one hypothesis about the psychological effects of adopting the wizard's code.

A potential problem with this is that human natural language contains a lot of ambiguity. Words can be used in many ways depending on context. Even the specification "literally" in "literally false" is less useful than it initially appears when you consider that the way people ordinarily speak when they're being truthful is actually pretty dense with metaphors that we typically don't notice as metaphors because they're common enough to be recognized legitimate uses that all fluent speakers will understand.

For example, if I want to convey the meaning that our study group has covered a lot of material in today's session, and I say, "Look how far we've come today!" it would be pretty weird if you were to object, "Liar! We've been in this room the whole time and haven't physically moved at all!" because in this case, it really is obvious to all ordinary English speakers that that's not what I meant by "how far we've come."

Other times, the "intended"¹ interpretation of a statement is not only not obvious, but speakers can even mislead by motivatedly equivocating between different definitions of words: the immortal Scott Alexander has written a lot about this phenomenon under the labels "motte-and-bailey doctrine" (as coined by Nicholas Shackel) and "the noncentral fallacy".

For example, Zvi Mowshowitz has written about how the claim that "everybody knows" something² is often used to establish fictitious social proof, or silence those attempting to tell the thing to people who really don't know, but it feels weird (to my intuition, at least) to call it a "lie", because the speaker can just say, "Okay, you're right that not literally³ everyone knows; I meant that most people know but was using a common hyperbolic turn-of-phrase and I reasonably expected you to figure that out."

So the question "Is this statement actually and literally true?" is itself potentially ambiguous. It could mean either—

• "Is this statement actually and literally true as the audience will interpret it?"; or,
• "Does this statement permit an interpretation under which it is actually and literally true?"

But while the former is complicated and hard to establish, the latter is ... not necessarily that strict of a constraint in most circumstances?

Think about it. When's the last time you needed to consciously tell a bald-faced, unambiguous lie?—something that could realistically be outright proven false in front of your peers, rather than dismissed with a "reasonable" amount of language-lawyering. (Whether "Fine" is a lie in response to "How are you?" depends on exactly what "Fine" is understood to mean in this context. "Being acceptable, adequate, passable, or satisfactory"—to what standard?)

Maybe I'm unusually honest—or possibly unusually bad at remembering when I've lied!?—but I'm not sure I even remember the last time I told an outright unambiguous lie. The kind of situation where I would need to do that just doesn't come up that often.

Now ask yourself how often your speech has been partially optimized for any function other than providing listeners with information that will help them better anticipate their experiences. The answer is, "Every time you open your mouth"⁴—and if you disagree, then you're lying. (Even if you only say true things, you're more likely to pick true things that make you look good, rather than your most embarrassing secrets. That's optimization.)

In the study of AI alignment, it's a truism that failures of alignment can't be fixed by deontological "patches". If your AI is exhibiting weird and extreme behavior (with respect to what you really wanted, if not what you actually programmed), then adding a penalty term to exclude that specific behavior will just result in the AI executing the "nearest unblocked" strategy, which will probably also be undesirable: if you prevent your happiness-maximizing AI from administering heroin to humans, it'll start administering cocaine; if you hardcode a list of banned happiness-producing drugs, it'll start researching new drugs, or just pay humans to take heroin, &c.

Humans are also intelligent agents. (Um, sort of.) If you don't genuinely have the intent to inform your audience, but consider yourself ethically bound to be honest, but your conception of honesty is simply "not lying", you'll naturally gravitate towards the nearest unblocked cognitive algorithm of deception.⁵

So another hypothesis about the psychological effects of adopting the wizard's code is that—however noble your initial conscious intent was—in the face of sufficiently strong incentives to deceive, you just end up accidentally training yourself to get really good at misleading people with a variety of not-technically-lying rhetorical tactics (motte-and-baileys, false implicatures, stonewalling, selective reporting, clever rationalized arguments, gerrymandered category boundaries, &c.), all the while congratulating yourself on how "honest" you are for never, ever emitting any "literally" "false" individual sentences.

Ayn Rand's novel Atlas Shrugged⁶ portrays a world of crony capitalism in which politicians and businessmen claiming to act for the "common good" (and not consciously lying) are actually using force and fraud to temporarily enrich themselves while destroying the credit-assignment mechanisms Society needs to coordinate production.⁷

In one scene, Eddie Willers (right-hand man to our railroad executive heroine Dagny Taggart) expresses horror that the government's official scientific authority, the State Science Institute, has issued a hit piece denouncing the new alloy, Rearden Metal, with which our protagonists have been planning to use to build a critical railroad line. (In actuality, we later find out, the Institute leaders want to spare themselves the embarrassment—and therefore potential loss of legislative funding—of the innovative new alloy having been invented by private industry rather than the Institute's own metallurgy department.)

"The State Science Institute," he said quietly, when they were alone in her office, "has issued a statement warning people against the use of Rearden Metal." He added, "It was on the radio. It's in the afternoon papers."

"What did they say?"

"Dagny, they didn't say it! ... They haven't really said it, yet it's there—and it—isn't. That's what's monstrous about it."

[...] He pointed to the newspaper he had left on her desk. "They haven't said that Rearden Metal is bad. They haven't said it's unsafe. What they've done is ..." His hands spread and dropped in a gesture of futility.

She saw at a glance what they had done. She saw the sentences: "It may be possible that after a period of heavy usage, a sudden fissure may appear, though the length of this period cannot be predicted. ... The possibility of a molecular reaction, at present unknown, cannot be entirely discounted. ... Although the tensile strength of the metal is obviously demonstrable, certain questions in regard to its behavior under unusual stress are not to be ruled out. ... Although there is no evidence to support the contention that the use of the metal should be prohibited, a further study of its properties would be of value."

"We can't fight it. It can't be answered," Eddie was saying slowly. "We can't demand a retraction. We can't show them our tests or prove anything. They've said nothing. They haven't said a thing that could be refuted and embarrass them professionally. It's the job of a coward. You'd expect it from some con-man or blackmailer. But, Dagny! It's the State Science Institute!"

I think Eddie is right to feel horrified and betrayed here. At the same time, it's notable that with respect to wizard's code, no lying has taken place.

I like to imagine the statement having been drafted by an idealistic young scientist in the moral maze of Dr. Floyd Ferris's office at the State Science Institute. Our scientist knows that his boss, Dr. Ferris, expects a statement that will make Rearden Metal look bad; the negative consequences to the scientist's career for failing to produce such a statement will be severe. (Dr. Ferris didn't say that, but he didn't have to.) But the lab results on Rearden Metal came back with flying colors—by every available test, the alloy is superior to steel along every dimension.

Pity the dilemma of our poor scientist! On the one hand, scientific integrity. On the other hand, the incentives.

He decides to follow a rule that he thinks will preserve his "inner agreement with truth which allows ready recognition": after every sentence he types into his report, he will ask himself, "Is this statement actually and literally true?" For that is his mastery.

Thus, his writing process goes like this—

"It may be possible after a period of heavy usage, a sudden fissure may appear." Is this statement actually and literally true? Yes! It may be possible!

"The possibility of a molecular reaction, at present unknown, cannot be entirely discounted." Is this statement actually and literally true? Yes! The possibility of a molecular reaction, at present unknown, cannot be entirely discounted. Okay, so there's not enough evidence to single out that possibility as worth paying attention to. But there's still a chance, right?

"Although the tensile strength of the metal is obviously demonstrable, certain questions in regard to its behavior under unusual stress are not to be ruled out." Is this statement actually and literally true? Yes! The lab tests demonstrated the metal's unprecedented tensile strength. But certain questions in regard to its behavior under unusual stress are not to be ruled out—the probability isn't zero.

And so on. You see the problem. Perhaps a member of the general public who knew about the corruption at the State Science Institute could read the report and infer the existence of hidden evidence: "Wow, even when trying their hardest to trash Rearden Metal, this is the worst they could come up with? Rearden Metal must be pretty great!"

But they won't. An institution that proclaims to be dedicated to "science" is asking for a very high level of trust—and in the absence of a trustworthy auditor, they might get it. Science is complicated enough and natural language is ambiguous enough, that that kind of trust that can be betrayed without lying.

I want to emphasize that I'm not saying the report-drafting scientist in the scenario I've been discussing is a "bad person." (As it is written, almost no one is evil; almost everything is broken.) Under more favorable conditions—in a world where metallurgists had the academic freedom to speak the truth as they see it (even if their voice trembles) without being threatened with ostracism and starvation—the sort of person who finds the wizard's oath appealing, wouldn't even be tempted to engage in these kinds of not-technically-lying shenanigans. But the point of the wizard's oath is to constrain you, to have a simple bright-line rule to force you to be truthful, even when other people are making that genuinely difficult. Yudkowsky's meta-honesty proposal is a clever attempt to strengthen the foundations of this ethic by formulating a more complicated theory that can account for the edge-cases under which even unusually honest people typically agree that lying is okay, usually due to extraordinary coercion by an adversary, as with the proverbial murderer or Gestapo officer at the door.

And yet it's precisely in adversarial situations that the wizard's oath is most constraining (and thus, arguably, most useful). You probably don't need special ethical inhibitions to tell the truth to your friends, because you should expect to benefit from friendly agents having more accurate beliefs.

But an enemy who wants to use information to hurt you is most constrained if the worst they can do is selectively report harmful-to-you true things, rather than just making things up—and therefore, by symmetry, if you want to use information to hurt an enemy, you are most constrained if the worst you can do is selectively report harmful-to-the-enemy true things, rather that just making things up.

Thus, while the study of how to minimize information transfer to an adversary under the constraint of not lying is certainly interesting, I argue that this "firming up" is of limited practical utility given the ubiquity of other kinds of deception. A theory of under what conditions conscious explicit unambiguous outright lies are acceptable doesn't help very much with combating intellectual dishonesty—and I fear that intellectual dishonesty, plus sufficient intelligence, is enough to destroy the world all on its own, without the help of conscious explicit unambiguous outright lies.

Unfortunately, I do not, at present, have a superior alternative ethical theory of honesty to offer. I don't know how to unravel the web of deceit, rationalization, excuses, disinformation, bad faith, fake news, phoniness, gaslighting, and fraud that threatens to consume us all. But one thing I'm pretty sure won't help much is clever logic puzzles about implausibly sophisticated Nazis.

(Thanks to Michael Vassar for feedback on an earlier draft.)

(originally published at Less Wrong)

I want you to imagine a world consisting of a sequence of independent and identically distributed random variables \(X_i\), and two computer programs.

The first program is called Reporter. As input, it accepts a bunch of the random variables \(X_i\). As output, it returns a list of sets whose elements belong to the domain of the \(X_i\).

The second program is called Audience. As input, it accepts the output of Reporter. As output, it returns a probability distribution.

Suppose the \(X_i\) are drawn from the following distribution:

We can model drawing a sample from this distribution using this function in the Python programming language:

import random

def x():
    r = random.random()
    if 0 <= r < 1/2:
        return 1
    elif 1/2 <= r < 3/4:
        return 2
    elif 3/4 <= r < 15/16:
        return 3
    else:
        return 4

For compatibility, we can imagine that Reporter and Audience are also written in Python. This is just for demonstration in the blog post that I'm writing—the real Reporter and Audience (out there in the world I'm asking you to imagine) might be much more complicated programs written for some kind of alien computer the likes of which we have not yet dreamt! But I like Python, and for the moment, we can pretend.

So pretend that Audience looks like this (where the dictionary, or hashmap, that gets returned represents a probability distribution, with the keys being random-variable outcomes and the values being probabilities):

from collections import Counter

def audience(report):
    a = Counter()
    for sight in report:
        for possibility in sight:
            a[possibility] += 1/len(sight)            
    d = sum(a_j - len(a) for a_j in a.values())
    return {x: (a_i - 1)/d for x, a_i in a.items()}

Let's consider multiple possibilities for the form that Reporter could take. A particularly simple implementation of Reporter (call it reporter_0) might look like this:

def reporter_0(xs):
    output = []
    for x in xs:
        output.append({x})
    return output

The pairing of audience and reporter_0 has a Very Interesting Property! When we call our Audience on the output of this Reporter, the probability distribution that Audience returns is very similar to the distribution that our random variables are from!¹

>>> audience(reporter_0([x() for _ in range(100000)]))
{1: 0.5003300528084493, 2: 0.2502900464074252, 3: 0.1873799807969275, 4: 0.062119939190270444}

# Compare to P(X) expressed as a Python dictionary—
>>> {1: 1/2, 2: 1/4, 3: 3/16, 4: 1/16}
{1: 0.5, 2: 0.25, 3: 0.1875, 4: 0.0625}

Weird, right?!

Of course, there are other possible implementations of Reporter. For example, this choice of Reporter (reporter_1) does not result in the Very Interesting Property—

def reporter_1(xs):
    output = []
    for _ in range(len(xs)):
        output.append({4})
    return output

It instead induces Audience to output a very different (and rather boring) distribution. It doesn't even matter how the \(X_i\) turned up; the result will always be the same:

>>> audience(reporter_1([x() for _ in range(100000)]))
{4: 1.0}

We could go on imagining other versions of Reporter, like this one (reporter_2)—

def reporter_2(xs):
    output = []
    for x in xs:
        if x == 4 or random.random() < 0.2:
            output.append({x})
        else:
            continue
    return output

While the distribution that reporter_2 makes Audience output isn't as boring as the one we saw for reporter_1, it still doesn't result in the Very Interesting Property of matching the distribution of the \(X_i\). It comes closer than reporter_1 did—notice how the ratios of probabilities assigned to the first three outcomes is similar to that of the original distribution—but it's assigning way too much probability-mass to the outcome "4":

>>> audience(reporter_2([x() for _ in range(100000)]))
{1: 0.3971289947471831, 2: 0.20309555314968522, 3: 0.14860259032038173, 4: 0.2516540358474678}

So far, all of the Reporters we've imagined are still only putting one element in the inner sets of the list-of-sets that they return. But we could imagine reporter_3—

def reporter_3(xs):
    output = []
    for x in xs:
        if x == 1 or x == 4:
            output.append({1, 4})
        else:
            output.append({x})
    return output

Unlike reporter_2 (which typically returned a list with fewer elements than it received as input), the list returned by reporter_3 has exactly as many elements as the list it took in. Yet this Reporter still prompts Audience to return a distribution with too many "4"s—and unlike reporter_2, it doesn't even get the ratio of the other outcomes right, yielding disproportionately fewer "1"s compared to "2"s and "3"s than the original distribution—

>>> audience(reporter_3([x() for _ in range(100000)]))
{1: 0.2808949431909106, 2: 0.24795967354776766, 3: 0.19037045927348376, 4: 0.2808949431909106}

Again, I've presented Audience and various possible Reporters as simple Python programs for illustration and simplicity, but the same input-output relationships could be embodied as part of a more complicated system—perhaps an entire conscious mind which could talk.

So now imagine our Audience as a person with her own hopes and fears and ambitions ... ambitions whose ultimate fulfillment will require dedication, bravery—and meticulously careful planning based on an accurate estimate of \(P(X)\), with almost no room for error.

So, too, imagine each of our possible Reporters as a person: loyal, responsible—and, entirely coincidentally, the supplier of a good that Audience's careful plans call for in proportion to the value of \(P(X = 4)\).

When the expected frequency of "4"s fails to appear, Audience's lifework is in ruins. All of her training, all of her carefully calibrated plans, all the interminable hours of hard labor, were for nothing. She confronts Reporter in a furor of rage and grief.

"You lied," she says through tears of betrayal, "I trusted you and you lied to me!"

The Reporter whose behavior corresponds to reporter_2 replies, "How dare you accuse me of lying?! Sure, I'm not a perfect program free from all bias, but everything I said was true—every outcome I reported corresponded to one of the \(X_i\). You can't call that misleading!"

He is perfectly sincere. Nothing in his consciousness reflects intent to deceive Audience, any more than an eight-line Python program could be said to have such "intent." (Does a for loop "intend" anything? Does a conditional "care"? Of course not!)

The Reporter whose behavior corresponds to reporter_3 replies, "Lying?! I told you the truth, the whole truth, and nothing but the truth: everything I saw, I reported. When I said an outcome was a oneorfour, it actually was a oneorfour. Perhaps you have a different category system, such that what I think of as a 'oneorfour', appears to you to be any of several completely different outcomes, which you think my 'oneorfour' concept is conflating. If those outcomes had wildly different probabilities, if one was much more common than fou—I mean, than the other—then you'd have no way of knowing that from my report. But using language in a way you dislike, is not lying. I can define a word any way I want!"

He, too, is perfectly sincere.

Commentary

Much has been written on this website about reducing mental notions of "truth", "evidence", &c. to the nonmental. One need not grapple with tendentious mysteries of "mind" or "consciousness", when so much more can be accomplished by considering systematic cause-and-effect processes that result in the states of one physical system becoming correlated with the states of another—a "map" that reflects a "territory."

The same methodology that was essential for studying truthseeking, is equally essential for studying the propagation of falsehood. If true "beliefs" are models that make accurate predictions, then deception would presumably be communication that systematically results in less accurate predictions (by a listener applying the same inference algorithms that would result in more accurate predictions when applied to direct observations or "honest" reports).

In a peaceful world where most falsehood was due to random mistakes, there would be little to be gained by studying processes that systematically create erroneous maps. In a world of conflict, where there are forces trying to slash your tires, one would do well do study these—algorithms of deception!

(originally published at Less Wrong)

In "Against Lie Inflation", the immortal Scott Alexander argues that the word "lie" should be reserved for knowingly-made false statements, and not used in an expanded sense that includes unconscious motivated reasoning. Alexander argues that the expanded sense draws the category boundaries of "lying" too widely in a way that would make the word less useful. The hypothesis that predicts everything predicts nothing: in order for "Kevin lied" to mean something, some possible states-of-affairs need to be identified as not lying, so that the statement "Kevin lied" can correspond to redistributing conserved probability mass away from "not lying" states-of-affairs onto "lying" states-of-affairs.

All of this is entirely correct. But Jessica Taylor (whose post "The AI Timelines Scam" inspired "Against Lie Inflation") wasn't arguing that everything is lying; she was just using a more permissive conception of lying than the one Alexander prefers, such that Alexander didn't think that Taylor's definition could stably and consistently identify non-lies.

Concerning Alexander's arguments against the expanded definition, I find I have one strong objection (that appeal-to-consequences is an invalid form of reasoning for optimal-categorization questions for essentially the same reason as it is for questions of simple fact), and one more speculative objection (that our intuitive "folk theory" of lying may actually be empirically mistaken). Let me explain.

(A small clarification: for myself, I notice that I also tend to frown on the expanded sense of "lying". But the reasons for frowning matter! People who superficially agree on a conclusion but for different reasons, are not really on the same page!)

Appeals to Consequences Are Invalid

There is no method of reasoning more common, and yet none more blamable, than, in philosophical disputes, to endeavor the refutation of any hypothesis, by a pretense of its dangerous consequences[.]

—David Hume

Alexander contrasts the imagined consequences of the expanded definition of "lying" becoming more widely accepted, to a world that uses the restricted definition:

[E]veryone is much angrier. In the restricted-definition world, a few people write posts suggesting that there may be biases affecting the situation. In the expanded-definition world, those same people write posts accusing the other side of being liars perpetrating a fraud. I am willing to listen to people suggesting I might be biased, but if someone calls me a liar I'm going to be pretty angry and go into defensive mode. I'll be less likely to hear them out and adjust my beliefs, and more likely to try to attack them.

But this is an appeal to consequences. Appeals to consequences are invalid because they represent a map–territory confusion, an attempt to optimize our description of reality at the expense of our ability to describe reality accurately (which we need in order to actually optimize reality).

(Again, the appeal is still invalid even if the conclusion—in this case, that unconscious rationalization shouldn't count as "lying"—might be true for other reasons.)

Some aspiring epistemic rationalists like to call this the "Litany of Tarski". If Elijah is lying (with respect to whatever the optimal category boundary for "lying" turns out to be according to our standard Bayesian philosophy of language), then I desire to believe that Elijah is lying (with respect to the optimal category boundary according to ... &c.). If Elijah is not lying (with respect to ... &c.), then I desire to believe that Elijah is not lying.

If the one comes to me and says, "Elijah is not lying; to support this claim, I offer this-and-such evidence of his sincerity," then this is right and proper, and I am eager to examine the evidence presented.

If the one comes to me and says, "You should choose to define lying such that Elijah is not lying, because if you said that he was lying, then he might feel angry and defensive," this is insane. The map is not the territory! If Elijah's behavior is, in fact, deceptive—if he says things that cause people who trust him to be worse at anticipating their experiences when he reasonably could have avoided this—I can't make his behavior not-deceptive by changing the meanings of words.

Now, I agree that it might very well empirically be the case that if I say that Elijah is lying (where Elijah can hear me), he might get angry and defensive, which could have a variety of negative social consequences. But that's not an argument for changing the definition of lying; that's an argument that I have an incentive to lie about whether I think Elijah is lying! (Though Glomarizing about whether I think he's lying might be an even better play.)

Alexander is concerned that people might strategically equivocate between different definitions of "lying" as an unjust social attack against the innocent, using the classic motte-and-bailey maneuver: first, argue that someone is "lying (expanded definition)" (the motte), then switch to treating them as if they were guilty of "lying (restricted definition)" (the bailey) and hope no one notices.

So, I agree that this is a very real problem. But it's worth noting that the problem of equivocation between different category boundaries associated with the same word applies symmetrically: if it's possible to use an expanded definition of a socially-disapproved category as the motte and a restricted definition as the bailey in an unjust attack against the innocent, then it's also possible to use an expanded definition as the bailey and a restricted definition as the motte in an unjust defense of the guilty. Alexander writes:

The whole reason that rebranding lesser sins as "lying" is tempting is because everyone knows "lying" refers to something very bad.

Right—and conversely, because everyone knows that "lying" refers to something very bad, it's tempting to rebrand lies as lesser sins. Ruby Bloom explains what this looks like in the wild:

I worked in a workplace where lying was commonplace, conscious, and system 2. Clients asking if we could do something were told "yes, we've already got that feature (we hadn't) and we already have several clients successfully using that (we hadn't)." Others were invited to be part an "existing beta program" alongside others just like them (in fact, they would have been the very first). When I objected, I was told "no one wants to be the first, so you have to say that."

[...] I think they lie to themselves that they're not lying (so that if you search their thoughts, they never think "I'm lying")[.]

If your interest in the philosophy of language is primarily to avoid being blamed for things—perhaps because you perceive that you live in a Hobbesian dystopia where the primary function of words is to elicit actions, where the denotative structure of language was eroded by political processes long ago, and all that's left is a standardized list of approved attacks—in that case, it makes perfect sense to worry about "lie inflation" but not about "lie deflation." If describing something as "lying" is primarily a weapon, then applying extra scrutiny to uses of that weapon is a wise arms-restriction treaty.

But if your interest in the philosophy of language is to improve and refine the uniquely human power of vibratory telepathy—to construct shared maps that reflect the territory—if you're interested in revealing what kinds of deception are actually happening, and why—

(in short, if you are an aspiring epistemic rationalist)

—then the asymmetrical fear of false-positive identifications of "lying" but not false-negatives—along with the focus on "bad actors", "stigmatization", "attacks", &c.—just looks weird. What does that have to do with maximizing the probability you assign to the right answer??

The Optimal Categorization Depends on the Actual Psychology of Deception

Deception
My life seems like it's nothing but
Deception
A big charade

I never meant to lie to you
I swear it
I never meant to play those games

—"Deception" by Jem and the Holograms

Even if the fear of rhetorical warfare isn't a legitimate reason to avoid calling things lies (at least privately), we're still left with the main objection that "lying" is a different thing from "rationalizing" or "being biased". Everyone is biased in some way or another, but to lie is "[t]o give false information intentionally with intent to deceive." Sometimes it might make sense to use the word "lie" in a noncentral sense, as when we speak of "lying to oneself" or say "Oops, I lied" in reaction to being corrected. But it's important that these senses be explicitly acknowledged as noncentral and not conflated with the central case of knowingly speaking falsehood with intent to deceive—as Alexander says, conflating the two can only be to the benefit of actual liars.

Why would anyone disagree with this obvious ordinary view, if they weren't trying to get away with the sneaky motte-and-bailey social attack that Alexander is so worried about?

Perhaps because the ordinary view relies an implied theory of human psychology that we have reason to believe is false? What if conscious intent to deceive is typically absent in the most common cases of people saying things that (they would be capable of realizing upon being pressed) they know not to be true? Alexander writes—

So how will people decide where to draw the line [if egregious motivated reasoning can count as "lying"]? My guess is: in a place drawn by bias and motivated reasoning, same way they decide everything else. The outgroup will be lying liars, and the ingroup will be decent people with ordinary human failings.

But if the word "lying" is to actually mean something rather than just being a weapon, then the ingroup and the outgroup can't both be right. If symmetry considerations make us doubt that one group is really that much more honest than the other, that would seem to imply that either both groups are composed of decent people with ordinary human failings, or that both groups are composed of lying liars. The first description certainly sounds nicer, but as aspiring epistemic rationalists, we're not allowed to care about which descriptions sound nice; we're only allowed to care about which descriptions match reality.

And if all of the concepts available to us in our native language fail to match reality in different ways, then we have a tough problem that may require us to innovate.

The philosopher Roderick T. Long writes—

Suppose I were to invent a new word, "zaxlebax," and define it as "a metallic sphere, like the Washington Monument." That's the definition—"a metallic sphere, like the Washington Monument." In short, I build my ill-chosen example into the definition. Now some linguistic subgroup might start using the term "zaxlebax" as though it just meant "metallic sphere," or as though it just meant "something of the same kind as the Washington Monument." And that's fine. But my definition incorporates both, and thus conceals the false assumption that the Washington Monument is a metallic sphere; any attempt to use the term "zaxlebax," meaning what I mean by it, involves the user in this false assumption.

If self-deception is as ubiquitous in human life as authors such as Robin Hanson argue (and if you're reading this blog, this should not be a new idea to you!), then the ordinary concept of "lying" may actually be analogous to Long's "zaxlebax": the standard intensional definition ("speaking falsehood with conscious intent to deceive"/"a metallic sphere") fails to match the most common extensional examples that we want to use the word for ("people motivatedly saying convenient things without bothering to check whether they're true"/"the Washington Monument").

Arguing for this empirical thesis about human psychology is beyond the scope of this post. But if we live in a sufficiently Hansonian world where the ordinary meaning of "lying" fails to carve reality at the joints, then authors are faced with a tough choice: either be involved in the false assumptions of the standard believed-to-be-central intensional definition, or be deprived of the use of common expressive vocabulary. As Ben Hoffman points out in the comments to "Against Lie Inflation", an earlier Scott Alexander didn't seem shy about calling people liars in his classic 2014 post "In Favor of Niceness, Community, and Civilization"—

Politicians lie, but not too much. Take the top story on Politifact Fact Check today. Some Republican claimed his supposedly-maverick Democratic opponent actually voted with Obama's economic policies 97 percent of the time. Fact Check explains that the statistic used was actually for all votes, not just economic votes, and that members of Congress typically have to have >90% agreement with their president because of the way partisan politics work. So it's a lie, and is properly listed as one. [bolding mine —ZMD] But it's a lie based on slightly misinterpreting a real statistic. He didn't just totally make up a number. He didn't even just make up something else, like "My opponent personally helped design most of Obama's legislation".

Was the politician consciously lying? Or did he (or his staffer) arrive at the misinterpretation via unconscious motivated reasoning and then just not bother to scrupulously check whether the interpretation was true? And how could Alexander know?

Given my current beliefs about the psychology of deception, I find myself inclined to reach for words like "motivated", "misleading", "distorted", &c., and am more likely to frown at uses of "lie", "fraud", "scam", &c. where intent is hard to establish. But even while frowning internally, I want to avoid tone-policing people whose word-choice procedures are calibrated differently from mine when I think I understand the structure-in-the-world they're trying to point to. Insisting on replacing the six instances of the phrase "malicious lies" in "Niceness, Community, and Civilization" with "maliciously-motivated false belief" would just be worse writing.

And I definitely don't want to excuse motivated reasoning as a mere ordinary human failing for which someone can't be blamed! One of the key features that distinguishes motivated reasoning from simple mistakes is the way that the former responds to incentives (such as being blamed). If the elephant in your brain thinks it can get away with lying just by keeping conscious-you in the dark, it should think again!

(originally published at Less Wrong)

If you ever find yourself saying, "Even if Hypothesis H is true, it doesn't have any decision-relevant implications," you are rationalizing! The fact that H is interesting enough for you to be considering the question at all (it's not some arbitrary trivium like the 1923th binary digit of π, or the low temperature in São Paulo on September 17, 1978) means that it must have some relevance to the things you care about. It is vanishingly improbable that your optimal decisions are going to be the same in worlds where H is true and worlds where H is false. The fact that you're tempted to say they're the same is probably because some part of you is afraid of some of the imagined consequences of H being true. But H is already true or already false! If you happen to live in a world where H is true, and you make decisions as if you lived in a world where H is false, you are thereby missing out on all the extra utility you would get if you made the H-optimal decisions instead! If you can figure out exactly what you're afraid of, maybe that will help you work out what the H-optimal decisions are. Then you'll be a better position to successfully notice which world you actually live in.

I had always thought Twilight Sparkle was the pony that best exemplified the spirit of epistemic rationality. If anypony should possess the truth, it must be the ones with high p (p being the letter used to represent the pony intelligence factor first proposed by Charles Spearpony and whose existence was confirmed by later psychometric research by such ponies as Arthur Jenfoal) who devote their lives to tireless scholarship!

After this year, however, I think I'm going to have to go with Applejack. Sometimes, all a pony needs to do to possess the truth is simply to stop lying.

Just—stop fucking lying!

Growing up in an ostensibly reform-Jewish household that didn't even take that seriously, atheism was easy for me, so I don't know how hard deconversion is, how much it hurts, or how much of one's entire conception of self is trashed in the process and can't be recovered.

As an atheist, it's tempting to say, "Look, it's not that bad: God doesn't exist exist, but you can still go to church and praise God and stuff if you want; it's just that there are benefits to being honest about what you're actually doing and why."

Somehow, I suspect that this is not a very convincing sell.

Applications to other topics are—as always—left as an exercise to the reader.