It’s unclear what people mean when saying they’re reporting a probability according to their inside view model(s). We’ll look through what this could mean and why most interpretations are problematic. Note that we’re not making claims about which communication norms are socially conducive to nice dialogue. We’re hoping to clarify...
The Sleeping Beauty problem is a classic conundrum in the philosophy of self-locating uncertainty. From Elga (2000): > Sleeping Beauty. Some researchers are going to put you to sleep. During the two days that your sleep will last, they will briefly wake you up either once or twice, depending on...
The 'individual rationality condition' is about the payoffs in equilibrium, not about the strategies. It says that the equilibrium payoff profile must yield to each player at least their minmax payoff. Here, the minmax payoff for a given player is -99.3 (which comes from the player best responding with 30 forever to everyone else setting their dials to 100 forever). The equilibrium payoff is -99 (which comes from everyone setting their dials to 99 forever). Since -99 > -99.3, the individual rationality condition of the Folk Theorem is satisfied.
Because the meaning of statements does not, in general, consist entirely in observations/anticipated experiences, and it makes sense for people to have various attitudes (centrally, beliefs and desires) towards propositions that refer to unobservable-in-principle things.
Accepting that beliefs should pay rent in anticipated experience does not mean accepting that the meaning of sentences are determined entirely by observables/anticipated experiences. We can have that the meanings of sentences are the propositions they express, and the truth-conditions of propositions are generally states-of-affairs-in-the-world and not just observations/anticipated experiences. Eliezer himself puts it nicely here: "The meaning of a statement is not the future experimental predictions that it brings about, nor isomorphic up to those predictions [...]... (read 371 more words →)
It’s unclear what people mean when saying they’re reporting a probability according to their inside view model(s). We’ll look through what this could mean and why most interpretations are problematic. Note that we’re not making claims about which communication norms are socially conducive to nice dialogue. We’re hoping to clarify some object-level claims about what kinds of probability assignments make sense, conceptually. These things might overlap.
Consider the following hypothetical exchange:
Person 1: “I assign 90% probability to X”
Person 2: “That’s such a confident view considering you might be wrong”
Person 1: “I’m reporting my inside view credence according to my model(s)”
This response looks coherent at first glance. But it’s unclear what Person 1 is actually saying.... (read 804 more words →)
Same as Sylvester, though my credence in consciousness-collapse interpretations of quantum mechanics has moved from 0.00001 to 0.000001.
Yeah great point, thanks. We tried but couldn't really get a set-up where she just learns a phenomenal fact. If you have a way of having the only difference in the 'Tails, Tuesday' case be that Mary learns a phenomenal fact, we will edit it in!
The Sleeping Beauty problem is a classic conundrum in the philosophy of self-locating uncertainty. From Elga (2000):
Sleeping Beauty. Some researchers are going to put you to sleep. During the two days that your sleep will last, they will briefly wake you up either once or twice, depending on the toss of a fair coin (Heads: once; Tails: twice). After each waking, they will put you back to sleep with a drug that makes you forget that waking. When you are first awakened, to what degree ought you believe that the outcome of the coin toss is Heads?
Here are some variants of the problem, not to be taken all too seriously.
... (read 2375 more words →)Sleeping Logic-1. Some
Thanks, the clarification of UDT vs. "updateless" is helpful.
But now I'm a bit confused as to why you would still regard UDT as "EU maximisation, where the thing you're choosing is policies". If I have a preference ordering over lotteries that violates independence, the vNM theorem implies that I cannot be represented as maximising EU.
In fact, after reading Vladimir_Nesov's comment, it doesn't even seem fully accurate to view UDT taking in a preference ordering over lotteries. Here's the way I'm thinking of UDT: your prior over possible worlds uniquely determines the probabilities of a single lottery L, and selecting a global policy is equivalent to choosing the outcomes of this lottery L.... (read more)
Okay this is very clarifying, thanks!
If the preference ordering over lotteries violates independence, then it will not be representable as maximising EU with respect to the probabilities in the lotteries (by the vNM theorem). Do you think it's a mistake then to think of UDT as "EU maximisation, where the thing you're choosing is policies"? If so, I believe this is the most common way UDT is framed in LW discussions, and so this would be a pretty important point for you to make more visibly (unless you've already made this point before in a post, in which case I'd love to read it).
Yeah by "having a utility function" I just mean "being representable as trying to maximise expected utility".
Ah okay, interesting. Do you think that updateless agents need not accept any separability axiom at all? And if not, what justifies using the EU framework for discussing UDT agents?
In many discussions on LW about UDT, it seems that a starting point is that agent is maximising some notion of expected utility, and the updatelessness comes in via the EU formula iterating over policies rather than actions. But if we give up on some separability axiom, it seems that this EU starting point is not warranted, since every major EU representation theorem needs some version of separability.
Don't updateless agents with suitably coherent preferences still have utility functions?
Oh yeah, the Folk Theorem is totally consistent with the Nash equilibrium of the repeated game here being 'everyone plays 30 forever', since the payoff profile '-30 for everyone' is feasible and individually-rational. In fact, this is the unique NE of the stage game and also the unique subgame-perfect NE of any finitely repeated version of the game.
To sustain '-30 for everyone forever', I don't even need a punishment for off-equilibrium deviations. The strategy for everyone can just be 'unconditionally play 30 forever' and there is no profitable unilateral deviation for anyone here.
The relevant Folk Theorem here just says that any feasible and individually-rational payoff profile in the stage game (i.e. setting dials at a given time) is a Nash equilibrium payoff profile in the infinitely repeated game. Here, that's everything in the interval [-99.3, -30] for a given player. The theorem itself doesn't really help constrain our expectations about which of the possible Nash equilibria will in fact be played in the game.