Introduction

This post introduces updatelessness to readers who are familiar with evidential and causal decision theory (EDT and CDT). Roughly, an updateless agent follows the policy that she would have wanted to commit to before learning which situation she is in, even if a different action seems best after she updates on her observations. I start with examples in which an agent would like to commit in advance to a policy that she will later want to deviate from. I use these examples to introduce pseudo-updateless agents like son-of-EDT and son-of-CDT, which follow policies they previously committed to. Then I describe full updatelessness, which requires no prior commitment and so applies even to situations that the agent is born into. After that, I give an argument for updatelessness based on an example in which combining EDT with updating leads to a clearly wrong choice. Finally, I describe different ways of thinking about updatelessness philosophically, distinguish between action and policy updatelessness, and briefly comment on logical updatelessness.

Motivating examples

Consider the following two scenarios:

Parfit's Hitchhiker (quoted from Parfit’s Reasons and Persons)

Parfit's Hitchhiker

Suppose that I am driving at midnight through some desert. My car breaks down. You are a stranger, and the only other driver near. I manage to stop you, and I offer you a great reward if you rescue me. I cannot reward you now, but I promise to do so when we reach my home. Suppose next that I am transparent, unable to deceive others. I cannot lie convincingly. Either a blush, or my tone of voice, always gives me away. Suppose, finally, that I know myself to be never self-denying. If you drive me to my home, it would be worse for me if I gave you the promised reward. Since I know that I never do what will be worse for me, I know that I shall break my promise. Given my inability to lie convincingly, you know this too. You do not believe my promise, and therefore leave me stranded in the desert. [...] It would have been better for me if I had been trustworthy, disposed to keep my promises even when doing so would be worse for me. You would then have rescued me.

The problem in this situation is that from my perspective while I am stranded in the desert, the optimal policy is to make the promise and then actually give the reward, but from the perspective of my (hypothetical) future self who has already arrived in the city, the optimal action is to break the promise. If I could, I would ensure that my future self sticks to the policy that is optimal from my current (stranded) point of view.

Transparent Newcomb's Problem (per the LessWrong wiki, with some changes)

Omega is about to play the following game with you:
It puts two boxes in front of you, Box A and Box B.
Box A is transparent and contains $1,000.
Box B is also transparent and contains either $1,000,000 or $0.
You can either take both boxes ("two-box"), or take only Box B ("one-box").
Before the game, Omega puts $1,000,000 into Box B if and only if it predicts that you would one-box when faced with a visibly full Box B.
Omega has played this game thousands of times and has been right 99% of the time.

The problem is that once you can see the two transparent boxes, the action that seems best is to take both boxes. However, from your perspective before you play the game, the best policy seems to be to one-box upon seeing a full Box B, because then Omega predicts that you will one-box and puts $1,000,000 into Box B. If you could commit to this policy, you would clearly like to do so. (Strictly speaking, for CDT agents this depends on when and how Omega makes its prediction, as I discuss in the next section.)

Pseudo-updateless behavior through commitment

In this section, I present a stepping stone to understanding full updatelessness: pseudo-updateless behavior through commitment.

Imagine Alice knows that she is about to face Transparent Newcomb's Problem. Suppose that, unlike in the standard version of this problem, she can commit in advance to taking only one box. If she does commit, then once she actually sees the transparent boxes, she sticks to the policy that's optimal from the point of view she had before seeing them. In contrast, an agent without a commitment takes whatever action seems best once she has seen the two boxes. The same applies to Parfit's Hitchhiker: if Alice is stranded in the desert and can commit to paying the driver, she does so and sticks to this commitment once she arrives in the city.

Alice can go a step further and reason: "Hm. I happen to know that I'm going to face Transparent Newcomb's Problem. But maybe I will end up in situations that are similar, but not identical, to Transparent Newcomb's Problem—situations in which I will wish I had committed to a certain policy now. In those situations, it won't help me to commit to one-boxing specifically in Transparent Newcomb’s Problem. I should think of all hypothetical scenarios, figure out what's optimal to commit to now, and commit. That is, I should commit to the policy that is optimal from my current point of view."

By policy, I mean a complete mapping from inputs to outputs (the agent's actions). An input is the agent's entire information state, i.e., all her observations, including her internal observations like her beliefs and memories.

Committing in exactly the way described is usually intractable, since the space of possible inputs is too large to think through. Instead, a realistic agent will have to do something like the following:

Let t_0 be the time at which the agent commits to the following procedure. At any later decision point, she uses the beliefs she had at t_0 to answer the question: "Which action in response to my current input would I have wanted to commit to at t_0, before I knew that I would actually receive this input?" (Recall that her input includes her current beliefs and her memories of what has happened since t_0.) She then takes this action. Don't worry if this explanation feels too abstract or is hard to follow: The next section works through examples of how to apply this reasoning, which should make it clearer.

The terms "son-of-EDT" and "son-of-CDT" refer to EDT and CDT agents that have committed in exactly this way. Note that son-of-EDT and son-of-CDT differ. For example, in Transparent Newcomb's Problem, CDT agents want to commit to one-boxing only if the commitment causes Omega to predict that they will one-box. In particular, since causation only goes forward in time, CDT agents only want to commit to one-boxing if they can do so before Omega makes its prediction. (This is a necessary condition but not a sufficient one. For example, if Omega predicts their choice from their genes rather than by scanning their brains after they commit, committing early doesn't cause Omega to predict that they will one-box.)

EDT agents, on the other hand, want to commit to one-boxing whenever committing gives them sufficient evidence that Omega predicts that they will one-box. They want to commit even if Omega has already made its prediction, as long as they don't know what Omega predicted. (Relatedly, EDT agents that can't commit would sometimes like to avoid learning things. For example, suppose that Omega instead predicts whether the agent will actually one-box. Then an EDT agent would, if she could, close her eyes to avoid seeing the boxes. With her eyes closed, she faces the standard Newcomb's Problem, in which EDT agents one-box, so Omega predicts this and fills Box B.)

Some people refer to agents that have committed in this way as updateless. Others, including me, use the term only for the more radical version that I introduce later. One reason I don't call this updatelessness is that EDT and CDT uncontroversially recommend making this kind of commitment if an agent can commit, so one might more properly think of it as a normal part of these theories. For the rest of this post, I will call this type of agent pseudo-updateless.

Further examples of pseudo-updateless behavior through commitment

In this section, I go through some examples to illustrate how a pseudo-updateless agent acts. Feel free to skip this section if you're already familiar with this topic. In these examples, I generally assume that predictions are made in such a way that any prior commitment by the agent causally influences the prediction, so I don't need to distinguish between son-of-EDT and son-of-CDT.

Counterfactual mugging (per the LessWrong wiki, with slight changes)

Omega, a perfect predictor, flips a coin. If it comes up heads, Omega asks you for $100. If it comes up tails, Omega pays you $10,000 if and only if it predicts that you would have paid if it had come up heads. Omega approaches you and tells you the coin came up heads. Should you pay?

Before being asked to pay, the agent doesn't know whether the coin will come up heads or tails, and she considers both outcomes equally likely. From that perspective, it is clearly optimal to commit to paying when asked, so that Omega predicts this policy and pays the agent if the coin comes up tails. (Committing to pay is worth 0.5 × −$100 + 0.5 × $10,000 = $4,950 in expectation, whereas committing to refuse is worth $0.) Hence, the pseudo-updateless agent pays when approached.

Uncommitted CDT and EDT agents both refuse to pay, since they update on learning that the coin came up heads, in which case paying is a pure loss of $100.

Evidential blackmail/XOR blackmail (quoted from Levinstein and Soares, 2017)

An agent has been alerted to a rumor that her house has a terrible termite infestation, which would cost her $1,000,000 in damages. She does not know whether this rumor is true. A greedy and accurate predictor with a strong reputation for honesty has learned whether or not it’s true, and drafts a letter:
"I know whether or not you have termites, and I have sent you this letter if and only if exactly one of the following is true: (i) the rumor is false, and you are going to pay me $1,000 upon receiving this letter; or (ii) the rumor is true, and you will not pay me upon receiving this letter."
The predictor then predicts what the agent would do upon receiving the letter, and sends the agent the letter if and only if exactly one of (i) or (ii) is true. Thus, the claim made by the letter is true. Assume the agent receives the letter. Should she pay up?

An uncommitted EDT agent pays in this situation. The agent knows that she is in one of the two situations circled in blue above, but she doesn't know which one. Paying gives her evidence that she is in the left branch, where she has no termites and the predictor predicted that she would pay, so she pays.

However, if the agent had known in advance that she would face this scenario, she would have committed not to pay. Why? Her choice of policy doesn't affect whether she has termites. It only affects whether the greedy predictor sends her a letter and whether she pays upon receiving one. If she commits not to pay, the predictor only sends her a letter if she has termites, and she never pays. If she instead commits to pay, the predictor only sends her a letter if she doesn't have termites, and she then pays $1,000. So, compared to committing not to pay, committing to pay costs her $1,000 × (1 − p(termites)) in expectation. The same goes for not committing at all, since an uncommitted EDT agent pays upon receiving the letter.

From her perspective before receiving the letter, the best policy to commit to is to never pay. So the pseudo-updateless agent doesn't pay. Unlike the uncommitted EDT agent, she doesn't condition on having received the letter when deciding whether to pay.

Handling totally mundane situations in a totally mundane way

Contrast the examples with the following case:

Hummus vs. avocado (quoted from MacAskill, 2019)

Suppose I’m choosing between an avocado sandwich and a hummus sandwich, and my prior was that I prefer avocado, but I’ve since tasted them both and gotten evidence that I prefer hummus. [... U]ncontroversially, I should choose the hummus sandwich, because I prefer hummus to avocado.

Let's say the agent commits to pseudo-updatelessness on Sunday. On Monday, she learns that she prefers hummus over avocado. On Tuesday, she has to choose between a hummus and an avocado sandwich. If the agent learns on Sunday that she will be in this situation on Tuesday, what policy does she want to commit to? Clearly, she just wants to commit to eating whichever of the two she discovers she prefers. So the agent does the normal thing and chooses hummus.

Pseudo-updateless agents behave like updateful agents (i.e., agents that take whatever action is optimal from their current perspective) in most mundane situations. That's because the optimal policy to commit to in advance is usually to just do what's optimal in the situation. When that's not the case, it's because something special is happening—namely, one's policy on one observation changes either a) what happens if you instead have another observation or b) the probability of each observation. For example, in Transparent Newcomb's Problem, which policy an agent commits to changes whether she observes a full or an empty Box B; in XOR blackmail, an agent's policy changes the probability of observing a letter; in counterfactual mugging, an agent's policy changes what happens if the coin comes up the other way. In hummus vs. avocado, nothing like that is going on. In general, when the output of your policy on a particular observation affects things only through the action you actually take in the world given that observation, updatelessness is not relevant. (Note, however, that "special" situations might be commonplace if you take things like Evidential Cooperation in Large Worlds seriously.)

Full updatelessness: Going beyond commitment

In this section, I describe how fully updateless agents behave in different thought experiments where intuitions about the right choice may differ. In the next section, I give arguments for updatelessness. Note that for my analysis of what updateless agents do, it doesn't really matter whether they use EDT or something with logical counterfactuals like FDT. The results are the same.

Introductory examples

So far, I have only discussed pseudo-updatelessness, which arises naturally as a strategy for dealing with uncertainty when commitment is possible. In the above cases, pseudo-updateless agents follow the so-called ex ante optimal policy, i.e., the policy that is optimal from the agent's perspective before she learns which situation she is in. I call this perspective the ex ante perspective. Note that an ex ante optimal policy always exists regardless of whether one has actually committed. In other words, the ex ante optimal policy is the policy that one would have committed to if one could have.

A fully updateless agent always follows the ex ante optimal policy, even if she didn't previously commit. So in Parfit's Hitchhiker, the updateless agent pays even if she didn't make any commitment beforehand and in Transparent Newcomb's Problem without prior commitment, she one-boxes. (Note that, as I discuss in the "cases that you are born into" section, there isn't really a fully updateless version of traditional CDT.)

I can easily modify the previous examples so that the agent faces the choice without having committed to anything:

Optional example: Parfit's Hitchhiker but you're already in the city

You are in a desert city. Next to you is a stranger who just saved your life by driving you to the city after your car broke down in the desert. The stranger now reveals that, before saving you, they predicted whether you would pay them $10,000 upon arriving in the city. Since the stranger predicted you would, they saved you. Upon hearing this, you remember news stories about a famous selfish psychologist who could predict people's behavior with extreme accuracy. You realize the stranger is that psychologist. Before finding yourself in this situation, you were mostly just thoughtlessly dawdling around in life, so you never committed to any kind of pseudo-updatelessness. Do you pay the stranger?

From your perspective in the city, it's optimal not to pay the stranger. That's the updateful choice. However, the ex ante optimal policy, i.e., the policy that's best to commit to from the (imaginary) perspective before the stranger picked you up, is still to pay once you are in the city. So updateless agents pay in this scenario.

Optional example: Transparent Newcomb's Problem without preparation

Consider Transparent Newcomb's Problem again, but this time you face it without having committed to anything:

Box A is transparent and contains $1,000. Box B is also transparent and contains $1,000,000. You can either take both boxes ("two-box"), or take only Box B ("one-box"). You know that Omega put money into Box B if and only if Omega predicted that you would one-box in this situation. Before finding yourself in this situation, you were mostly just thoughtlessly dawdling around in life, so you never committed to any kind of pseudo-updatelessness. Do you one-box or two-box?

From the perspective before the game, the optimal policy to commit to is to one-box. Since you didn't commit in this version, only fully updateless agents one-box.

Cases that you are born into

So far, I have relied on what an agent would have liked to commit to before the start of a decision scenario, had she thought about it. This gets tricky when the agent is born into a decision situation. In those cases, the agent can't derive the updateless choice by asking what policy her past self would have wanted to commit to, because she didn't exist before the decision situation. Instead, the agent has to take a hypothetical perspective from before she existed and use her prior beliefs (i.e., her beliefs before updating on any observations). Then, figuring out the optimal action works just as in the commitment cases.

Note that there is no fully updateless version of traditional CDT for cases that you are born into. CDT evaluates an option by the causal consequences of intervening to bring it about. For updatelessness, the natural intervention is to make the agent commit to a policy in advance. But "If I had committed to a given policy before I was born, what would be the causal consequences?" is either not a well-formed question or the answer is straightforwardly "nothing". In general, before you are born, you're not causally upstream of anything. So at most, applying updatelessness to CDT amounts to asking which policy she would have wanted to commit to at some earlier time in her life, which is how son-of-CDT reasons. Decision theories like FDT try to salvage this by introducing the notion of logical causation, which is beyond the scope of this post. In the cases below, these theories behave the same as updateless EDT. The rest of this post therefore focuses on EDT.

In toy decision problems, one generally imagines that the agent just has correct beliefs about how the problem works, and so the ex ante perspective and the associated prior are well-defined. But in real life, one has to determine one's prior somehow. How to do this is a difficult question. In some cases, a particular prior seems very natural. For example, it's natural to think that one's prior for a coin landing heads should be 50%. In other situations, like Evidential blackmail/XOR blackmail below, the choice of prior doesn't matter (as long as the agent is confident that she actually is facing Evidential blackmail/XOR blackmail). But in yet other situations, priors are both very important and less straightforward. Discussing priors is unfortunately out of scope for this post.

Counterfactual mugging that you have been born into (per Fallenstein, 2014b, with changes)

A million years ago, Omega flipped a coin. If it came up heads, Omega would leave the sky blue and ask you for $100 a million years later. If it came up tails, Omega would turn the sky green and pay you $10,000 a million years later if and only if Omega predicted that you would have paid it if the coin had come up heads and the sky had been blue. Now, Omega approaches you and tells you the coin came up heads. Should you pay?

Of course, you and everyone else have always known that the sky is blue. At no point in time could you have thought, "Oh, the sky color is 50/50. I should commit to paying in the cases where the sky is blue, so that I get paid in cases where the sky is green. That way, I'll get $4,950 in expectation." You were never uncertain about the color of the sky.

But intuitively, from the ex ante perspective (before the coin was flipped), you would like to have the policy of paying if the coin came up heads, so that you get $10,000 if it came up tails. So, paying would be the updateless thing to do.

Evidential blackmail/XOR blackmail that you have been born into (based on Fallenstein, 2014b, with some changes)

Suppose that you wake up with a letter in front of your face. The letter explains that Omega just created you. It also asks you to watch Omega's favorite movie with Omega. Unfortunately, you hate this movie so much that you'd quite literally rather never have existed than suffer through it even once. The letter further explains that one of two things has happened: Either (1) humanity has undergone a positive intelligence explosion, and Omega has predicted that you will watch the movie; or (2) humanity has wiped itself out, and Omega has predicted that you will not watch the movie. In any other scenario, Omega wouldn't have created you. You care far more about humanity's fate than about avoiding the movie. Should you watch the movie?

Updateful EDT watches the movie in this scenario, since watching is evidence that humanity has undergone a positive intelligence explosion. However, from the ex ante perspective, the optimal policy is not to watch the movie: Your choice of policy doesn't actually influence whether humanity is flourishing or wiped out (and remember you'd rather never have existed than watch the horrid movie). It only changes the conditional probabilities of being created. So updateless agents don't watch the movie.

Arguments for updatelessness

So far in the discussion of full updatelessness, I have gone through a few examples where updateful and updateless behavior come apart and where it's perhaps a matter of intuition or subjective taste which behavior is preferable. I now turn to an example where combining EDT with updating leads to choices that seem more clearly wrong.

Optional example: EDT with certain ways of updating double-counts

Paul Christiano offers a scenario in which combining EDT with common ways of updating (i.e., theories of anthropics) gives the intuitively wrong answer. This is not actually a case where updatelessness is necessary, since combining EDT with a specific updateful theory of anthropics, called minimal reference class SSA (mrcSSA), gets this right. I still go through it here because mrcSSA is in some sense less updateful than other theories of anthropics, so the example conveys some intuition in favor of updating less. So for the discussion of Christiano's example, when I talk about "updateful EDT", I mean EDT combined with an anthropic theory other than mrcSSA, and "updateless EDT" means either truly updateless EDT or EDT combined with mrcSSA. You don't need to know anything about anthropics to understand this section, and I won't discuss anthropics further. The next section EDT with updating neglects counterfactual worlds introduces a thought experiment that requires updatelessness proper.

Calculator bet (per Christiano, 2021, with minor edits)

I am offered the opportunity to bet on a mathematical statement X to which I initially assign 50% probability (perhaps X = the parity of the 1,000,000th digit of pi is even). I have access to a calculator that is 99% reliable, i.e. it corrupts the answer 1% of the time at random. The calculator says that X is true. With what probability should I be willing to wager?

The answer clearly seems to be 99%. However, in some settings, updateful EDT is willing to bet at much higher than 99:1 odds.

Calculator bet continued (roughly based on Christiano, 2021)

Assume that you live in a large universe or multiverse that contains 100 copies of you. (If that's too fantastic for you, you can instead assume that you get woken up a hundred times and always forget your previous awakenings.) Your calculator says that the 1,000,000th digit of pi is even. Your calculator is 99% reliable, and its mistakes are independent of those of your copies' calculators, which are also 99% reliable. You are now offered the following bet: If the 1,000,000th digit of pi is in fact even (E), you get $1. If it is odd (O), you lose $1,000. You care about the total sum of money across all copies of you. You know that you were only offered this bet because your calculator outputted E: There would have been no bet offer otherwise.

Clearly, taking the bet loses you money in expectation. Its ex ante value is 0.5 × 99 × $1 − 0.5 × 1 × $1,000 = −$450.50, summed across all copies.

Updateful EDT takes the bet.

Upon observing that the calculator says E, an updateful EDT agent updates to 99% credence that she is in the world where E is true. Further, in the E-world, an expected 99 copies of the EDT agent observe the calculator output E. The EDT agent therefore reasons: "If I am in the E-world, my action gives me evidence about what all 99 copies of me who see E do. Taking the bet means all 99 copies of me take the bet, gaining me 99 × $1 = $99." So, the value of taking the bet in the E-world is $99.

Meanwhile, in the O-world, only one copy of the EDT agent observes the calculator output E in expectation. The EDT agent therefore reasons: "If I am in the O-world, only one copy of me sees E. So, if I take the bet, only one copy of me (me) takes the bet, losing me 1 × $1,000 = $1,000." So, the value of taking the bet in the O-world is −$1,000.

Since the EDT agent has 99% credence that she is in the E-world and 1% credence that she is in the O-world, the expected value of taking the bet is 0.99 × $99 − 0.01 × $1,000 = $88.01. This is positive, so the updateful EDT agent accepts the bet.

Intuitively, what goes wrong here is that the EDT agent double-counts the factor of 99. It shows up once in the 99:1 odds that the EDT agent is in the E-world and again in the 99× payoff in the E-world, which contains 99 times as many copies of the agent who observe E (and hence take the bet).

Updateless EDT solves this problem by acting on the prior odds of E and O, 1:1, rather than on the updated odds of 99:1. With the prior odds, taking the bet has an expected value of 0.5 × $99 − 0.5 × $1,000 = −$450.50, so updateless EDT declines the bet. (This is the same ex ante calculation as at the beginning of the section.)

EDT with updating neglects counterfactual worlds

In this example, EDT agents have to be truly updateless to not get the intuitively wrong result.

White-Black-Grey Sleeping Beauty variant (per Conitzer, 2015)

[Sleeping Beauty is put to sleep, and] will be awoken twice, once on Monday and once on Tuesday. [W]hen she is awoken on Tuesday, she has no memory of the previous awakening. The only information available to her upon awakening (besides the information that was available to her at the start of the experiment) is the color of the room in which she is awoken. Two distinct fair coins are tossed to determine the color of the room in which she is awoken on each of the two days. Coin 1 has a white side and a black side; this coin will be used to determine the color of the room in which she is awoken on Monday. Coin 2 has a grey side and a side with the word “opposite” written on it; this coin will be used to determine the color of the room in which she is awoken on Tuesday, where Opposite indicates that the color of the room should be the opposite of what it was on Monday. That is, if the first coin comes up White and the second coin comes up Opposite, then she will be awoken in the black room on Tuesday, and vice versa.

Table of resulting possibilities adapted from Conitzer, 2015

[...]
Beauty will be offered the following bet [...] each time that Beauty awakens in the white or the black room, but never in the grey room. Thus, it will be offered once overall if coin 2 comes up Grey, but twice overall if coin 2 comes up Opposite. It costs 24 and pays out 33 if coin 2 comes up Opposite.

If Beauty takes the bet upon awakening in a white room, she probably also takes the bet upon awakening in a black room, since the situations are completely symmetric and she knows this. So, her choice of policy is effectively between "never take the bet" and "always take the bet when it is offered to me". Never taking the bet neither costs nor wins Beauty any money. Consider the value of always taking the bet from the ex ante perspective.

The coins come up WG, WO, BG, and BO with probability 1/4 each. (For example, WG means that coin 1 comes up White and coin 2 comes up Grey.) In WG worlds, Beauty takes the bet once and loses, costing her $24. In WO worlds, Beauty takes the bet twice and wins, costing her $24 twice and winning her $33 twice, for a total profit of $18. BG is the same as WG, and BO is the same as WO. So overall, Beauty has a 1/2 chance of losing $24 and a 1/2 chance of gaining $18, for an expected value of 1/2 × −$24 + 1/2 × $18 = −$3. Clearly, this is a bad bet to take.

However, if Beauty is an updateful EDT agent, she will end up taking the bet and hence lose money in expectation. Let's analyze the situation from Beauty's perspective just after she has awoken in a white room. (The analysis is the same if she awakens in a black room.)

Having woken up in a white room, Beauty updates on this observation and rules out the world where the coins came up BG, since in that world she never wakes up in a white room. Hence, Beauty redistributes her credences across the remaining three possible worlds: 1/3 credence in WG, 1/3 credence in WO, and 1/3 credence in BO.

In WG, taking the bet will cost her $24 and gain her nothing.
In WO, taking the bet will cost her $24, but she will also gain $33, netting her $9. Further, taking the bet means that Beauty's future instance, who will wake up in the black room, will also take the bet, netting her a further $9. So, taking the bet has a total value of $18. (Remember that Beauty is an EDT agent, so her choice gives her evidence about what her future instance does.)
BO is just like WO (except that Beauty's choice gives her evidence about what her past instance did, instead of what her future instance will do), so taking the bet in BO also gains her $18.

So, once Beauty has awoken in a white room, the expected value of the bet is 1/3 × −$24 + 1/3 × $18 + 1/3 × $18 = $4, so she takes the bet. Clearly, something has gone wrong.

Intuitively, the problem with updating in this case is that Beauty ignores what her behavior tells her about her counterfactual behavior in the BG world.

Taking the bet when awakening in a white room means that she would also take the bet when awakening in the black room in BG worlds, which would lose her $24. But this ex ante possibility never enters her calculation. So, when deciding whether to take the bet, Beauty systematically leaves out one of the ex ante possible coin combinations in which she loses.

In some sense, the problem is that Beauty updates on the fact that she, the agent observing a white room, exists. If she did not update on the fact that at least one instance of her awakens in a white room, Beauty would avoid this problem.

How to think about updatelessness philosophically

So far, I've just described what updateless behavior is (following the ex ante optimal policy) and why it seems to give the correct results. But what kind of reasoning actually leads an agent to act updatelessly?

One option is to think of updatelessness as a raw fact about an agent's decision procedure. That is, every time the agent faces a decision, she computes the ex ante optimal policy and follows it, and that's the end of the story.

Another perspective views updatelessness as caring about what happens to counterfactual versions of yourself. Paul Christiano (2021) describes this, although one could also read his description as an extension of a commitment-based motivation.

A third perspective is that, to the extent you are correlated with something (for example, the counterfactual version of you that makes a different observation, or Omega's actual prediction of what you would do when making a different observation), you should be uncertain about whether you are that something. Cooper, Oesterheld, and Conitzer (2024) give an account of this, justify its plausibility, and describe how it leads to updateless behavior.

Below, I describe another possible answer: updatelessness as a consequence of l-zombie anthropics.

Updatelessness through l-zombie anthropics

Alternatively, one can implement updateless EDT by combining EDT with a particular theory of anthropics (i.e., a theory of how to change your beliefs based on empirical observations), called l-zombie anthropics.

An agent that adopts l-zombie anthropics acts as if she could be a logical zombie (l-zombie) version of herself. An l-zombie is a logically possible agent that does not actually exist or, as Fallenstein (2014b) puts it, "a mathematically possible conscious experience that isn't physically instantiated and therefore isn't actually consciously experienced". L-zombies were first introduced in Fallenstein (2014a). (It's possible that all mathematically possible agents exist, in which case l-zombies don't exist. This view yields the same behavior as l-zombie anthropics.)

What does this imply for an agent's credence over what kind of world she's in? If she follows l-zombie anthropics, she excludes from consideration all worlds in which she's logically impossible. The agent has a prior over the worlds in which she is logically possible. This includes worlds where she is logically possible but does not exist. She then never updates this prior on any empirical evidence, including the observation that she exists.

Intuitively, this sounds crazy, and you might think: "Wait, if I don't update on the fact that I exist and that, say, there is a laptop in front of me, how do I even act? Do I have to take some completely crazy action that would be best on average across all the worlds where I'm logically possible, regardless of what I observe?"

Luckily, EDT with l-zombie anthropics behaves completely normally in everyday situations. In the laptop example, for instance, it acts exactly like an agent who updates her beliefs upon seeing the laptop:

Let's define situation s: The agent actually exists and has a laptop in front of her. Let's suppose that the correct action in this situation is action a: to intently continue reading this post.

An agent with l-zombie anthropics never updates her beliefs about which world she is in, so she can't choose action a (keep reading) on the grounds that she is in situation s. However, an EDT agent with l-zombie anthropics can reason as follows: "If I do a in reaction to some input i, then all agents like me will do a in reaction to that same input i. Let's call my current input I(s): It's the input that I get if I'm actually in s. I can't tell whether I am actually in situation s or just an l-zombie with the input I(s). But I do know that if I do a, then the version of me that's actually in situation s will also do a, and that's good. The worlds in which I'm merely an l-zombie and not in situation s don't matter for this particular decision, so I should just do a." In other words: If you're an l-zombie, it usually doesn't matter what you do anyway. So you should usually behave as if you're not an l-zombie. Of course, this is different in cases like XOR blackmail that you are born into: Here, the behavior of your l-zombie version matters, since it determines whether you come to exist.

Further considerations

Action vs. policy updatelessness

So far, the examples have been agnostic about the distinction between action and policy updatelessness. Action updatelessness corresponds to Wei Dai's UDT 1.0 (2009), while policy updatelessness corresponds to Wei Dai's UDT 1.1 (2010). The two can come apart in cases like the following:

Bomb installation with imperfect recall

Boom & Bust Corp. offers to pay you $10 if you allow it to install a 48-hour time bomb in your house. Boom & Bust also tells you that, regardless of your choice, it will approach you again the next day and offer to remove any bombs from your house for $50. You know that when you wake up tomorrow morning, you will have forgotten whether you chose to accept Boom & Bust's offer. (You will still remember that it approached you with this offer, though.) Should you take the $10 and allow Boom & Bust to install a bomb in your house? And when you wake up without knowing whether you took the money, should you pay Boom & Bust $50 to remove any potential bombs?

Policy updatelessness recommends following the policy that is ex ante optimal on the assumption that every instance of the agent follows it. This means that in Bomb installation, the policy-updateless agent neither takes the $10 nor pays the $50.

Action updatelessness evaluates each decision on its own and calculates the optimal action based on the agent's credences about how her other instances act. Hence, the behavior of an action-updateless agent in Bomb installation depends on her credences. (Note that her own action might well influence her credences about what her other instance does. For example, the agent might think that her decision is correlated with (or logically causes) her other instance's decision.)

For example, suppose the agent is asked to pay $50 to remove any bombs from her house. If the action-updateless agent is pretty sure, but not 100% confident, that she turned down the $10 the day before, she might pay the $50 just in case. (Let's assume she also knows this is a one-time situation and that Boom & Bust Corp. won't start pulling this kind of thing every week from now on.) Of course, the agent in the first instance might be confident that her future self will reason this way. Then she might as well take the $10 and let Boom & Bust Corp. install the bomb, since she expects her future self to pay for its removal anyway.

The policy-updateless agent, on the other hand, always follows the ex ante optimal policy and assumes that all her instances do the same: She neither takes the $10 nor pays the $50.

As an aside: Although Wei Dai introduced policy updatelessness as an improvement over action updatelessness, I currently favor action updatelessness. But that discussion is beyond the scope of this post.

Logical updatelessness

I don't discuss logical updatelessness at length in this post. Briefly: Lukas Finnveden (2026) presents a Dutch book against logically updateful EDT agents, which is similar to Conitzer's 2015 White-Black-Grey Sleeping Beauty variant. Many of the arguments for empirical updatelessness seem to apply to logical updatelessness as well. Unfortunately, logical updatelessness is a big bullet to bite, because it likely leads to nonsensical behavior. Caspar Oesterheld discusses the unappealing properties of logical updatelessness in this unfinished draft.

Acknowledgments

I would like to thank Emery Cooper and Caspar Oesterheld for helpful comments and discussion.