So in this case my question is why Kaj suggests his proposal instead of using bounded utility.

Two reasons.

First, like was mentioned elsewhere in the thread, bounded utility seems to produce unwanted effects, like we want utility to be linear in human lives and bounded utility seems to fail that.

Second, the way I arrived at this proposal was that RyanCarey asked me what's my approach for dealing with Pascal's Mugging. I replied that I just ignore probabilities that are small enough, which seems to be thing that most people do in practice. He objected that that seemed rather ad-hoc and wanted to have a more principled approach, so I started thinking about why exactly it would make sense to ignore sufficiently small probabilities, and came up with this as a somewhat principled answer.

Admittedly, as a principled answer to which probabilities are actually small enough to ignore, this isn't all that satisfying of an answer, since it still depends on a rather arbitrary parameter. But it still seemed to point to some hidden assumptions behind utility maximization as well as raising some very interesting questions about what it is that we actually care about.

If you have trouble finding the location, feel free to call me (Vadim) at 0542600919.

First, thanks for having this conversation with me. Before, I was very overconfident in my ability to explain this in a post.

In order for the local interpretation of Sleeping Beauty to work, it's true that the utility function has to assign utilities to impossible counterfactuals. I don't think this is a problem, but it does raise an interesting point.

Because only one action is actually taken, any consistent consequentialist decision theory that considers more than one action is a decision theory that has to assign utilities to impossible counterfactuals. But the counterfactuals you mention up are different: they have to be assigned a utility, but they never actually get considered by our decision theory because they're causally inaccessible - their utilities don't affect anything, in some logical-counterfactual or algorithmic-causal counterfactual sense.

In the utility functions I used as examples above (winning bets to maximize money, trying to watch a sports game on a specific day), the utility for these impossible counterfactuals is naturally specified because the utility function was specified as a sum of the utilities of local properties of the universe. This is what both allows local "consequences" in Savage's theorem, and specifies those causally-inaccessible utilities.

This raises the question of whether, if you were given only the total utilities of the causally accessible histories of the universe, it would be "okay" to choose the inaccessible utilities arbitrarily such that the utility could be expressed in terms of local properties. I think this idea might neglect the importance of causal information in deciding what to call an "event."

Different counterfactual games lead to different probability assignments.

Do you have some examples in mind? I've seen this claim before, but it's either relied on the assumption that probabilities can be recovered straightforwardly from the optimal action (not valid when the straightforward decision theory fails, e.g. absent-minded driver, Psy-kosh's non-anthropic problem), or that certain population-ethics preferences can be ignored without changing anything (highly dubious).

What makes something an "outcome" in Savage's theorem is simply that it follows a certain set of rules and relationships - the interpretation into the real world is left to the reader.

It's totally possible to regard the state of the entire universe as the "outcome" - in that case, the things that corresponds to the "actions" (the thing that the agent chooses between to get different "outcomes") are actually the strategies that the agent could follow. And the thing that the agent always acts as if it has probabilities over are the "events," which are the things outside the agent's control that determine the mapping from "actions" to "outcomes," and given this interpretation the day does not fulfill such a role - only the coin.

So in that sense, you're totally right. But this interpretation isn't unique.

It's also a valid interpretation to have the "outcome" be whether Sleeping Beauty wins, loses, or doesn't take an individual bet about what day it is (there is a preference ordering over these things), the "action" being accepting or rejecting the bet, and the "event" being which day it is (the outcome is a function of the chosen action and the event).

Here's the point: for all valid interpretations, a consistent Sleeping Beauty will act as if she has probabilities over the events. That's what makes Savage's theorem a theorem. What day it is is an event in a valid interpretation, therefore Sleeping Beauty acts as if it has a probability.

Side note: It is possible to make what day it is a non-"event," at least in the Savage sense. You just have to force the "outcomes" to be the outcome of a strategy. Suppose Sleeping Beauty instead just had to choose A or B on each day, and only gets a reward if her choices are AB or BA, but not AA or BB (or any case where the reward tensor is not a tensor sum of rewards for individual days). To play this game well, Savage's theorem does not say you have to act like you assign a probability to what day it is. The canonical example of this problem in anthropics is the absent-minded driver problem - compared to Sleeping Beauty, it is strictly trickier to talk about whether the absent-minded driver should have a probability that they're at the first intersection - argument in favor have to either resort to Cox's theorem (which I find more confusing), or engage in contortions about games that counterfactually could be constructed.

There is difference between "having an idea" and "solid theoretical foundations". Chemists before quantum mechanics had a lots of ideas. But they didn't have a solid theoretical foundation.

That's a bad example. You are essentially asking researchers to predict what they will discover 50 years down the road. A more appropriate example is a person thinking he has medical expertise after reading bodybuilding and nutrition blogs on the internet, vs a person who has gone through medical school and is an MD.

Short version: consider Savage's theorem (fulfilling the conditions by offering Sleeping Beauty a bet along with the question "what day is it?", or by having Sleeping Beauty want to watch a sports game on Monday specifically, etc.). Savages theorem requires your agent to have a preference ordering over outcomes, and have things it can do that lead to different outcomes depending on the state of the world (events), and it states that consistent agents have probabilities over the state of the world.

On both days, Sleeping Beauty satisfies these desiderata. She would prefer to win the bet (or watch the big game), and her actions lead to different outcomes depending on what day it is. She therefore assigns a probability to what day it is.

We do this too - it is physically possible that we've been duplicated, and yet we continue to assign probabilities to what day it is (or whether our favorite sports will be there when we turn on the TV) like normal people, rather than noticing that it is meaningless since we might be simultaneously in different days.

Man, that sleeping beauty digression at the end. I'm so easily aggroed.

I wonder if I should write up a rant or a better attempt at exposition, against this "clearly the problem is underdetermined" position. The correct answer is somewhat difficult and all expositions I've seen (or written!) so far have had big shortcomings. But even if one didn't know the right answer, one should readily conclude that a principled answer exists. We assign things probabilities for fairly deep reasons, reasons undisturbed by trifles like the existence of an amnesia pill.

That aside, good talk :)

I'll dig a little deeper but let me first ask these questions:

What do you define as a coincidence?

Where can I find an explanation of the N 2^{-(K + C)} weighting?

I did a considerable amount of software engineer recruiting during my career. I only called the references at an advanced stage, after an interview. It seems to me that calling references before an interview would take too much of their time (since if everyone did this they would be called very often) and too much of my time (since I think their input would rarely disqualify a candidate at this point). The interview played the most important role in my final decision, but when a reference mentioned something negative which resonated with something that concerned me after the interview, this was often a reason to reject.

I'm digging into this a little bit, but I'm not following your reasoning. UDT from what I see doesn't mandate the procedure you outline. (perhaps you can show an article where it does) I also don't see how which decision theory is best should play a strong role here.

But anyways I think the heart of your objection seems to be "Fragile universes will be strongly discounted in the expected utility because of the amount of coincidences required to create them". So I'll free admit to not understanding how this discounting process works, but I will note that current theoretical structures (standard model inflation cosmology/string theory) have a large amount of constants that are considered coincidences and also produce a large amount of universes like ours in terms of physical law but different in terms of outcome. I would also note that fragile universe "coincidences" don't seem to me to be more coincidental in character than the fact we happen to live on a planet suitable for life.

Lastly I would also note that at this point we don't have a good H1 or H2.