There are a number of problems with that:
1) You don't specify whether the bet is offered to all my copies or just to one of them, or if to just one of them, whether it is guaranteed to be the one in the Milky Way. Or if the one in the Milky Way knows he is in the Milky Way when taking the bet, and so on.
Suppose I am offered the bet before knowing whether I am in Andromeda or Milky Way. What odds should I accept on the coin toss: 50/50? Suppose I am then told I am in the Milky Way... what odds should I now accept on the coin-toss: still 50/50? If you say 50/50 in both cases then you are a "double-halfer" (in the terminology of Sleeping Beauty problems) and you can be Dutch-booked. If you answer other than 50/50 in one case or the other, then you are saying there are circumstances where you'd bet at odds different (probably very different) from the physical odds of a fair coin toss and without any context, that sounds rather crazy. So whatever you say, there is a bullet to bite.
2) I am, by the way, quite aware of the literature on Anthropic Decision Theory (especially Stuart Armstrong's paper) and since my utility function is roughly the average utility for my future copies (rather than total utility) I feel inclined to bet with the SSA odds. Yes, this will lead to the "me" in the Milky Way making a loss in the case of "H" but at that stage he counts for only a tiny slither of my utility function, so I think I'll take the risk and eat the loss. If I modify my reasoning now then there are other bets which will lead to a bigger expected loss (or even a guaranteed loss if I can be Dutch-booked).
Remember though that I only assigned 90% probability to the original hypothesis. Part of the remaining 10% uncertainty is that I am not fully confident that SSA odds are the right ones to use. So the anthropic mugger might not be able to make $500 off me (I'm likely to refuse the 1000:1 bet), but he probably could make $5 off me.
3) As in many such problems, you oversimplify by specifying in advance that the coin is fair, which then leads to the crazy-sounding betting odds (and the need to bite a bullet somewhere). But in the real world case, the coin has unknown bias (as we don't know the size of the future filter). This means we have to try to estimate the bias (size of filter) based on the totality of our evidence.
Suppose I'm doubtful about the fair coin hypothesis and have two other hypotheses: heavy bias towards heads or heavy bias towards tails. Then it seems very reasonable that under the "bias towards heads" hypothesis I would expect to be in Andromeda, and if I discover I am not, that counts as evidence for the "bias towards tails" hypothesis. So as I now suspect bias in one particular direction, why still bet on 50/50 odds?
1) You don't specify whether the bet is offered to all my copies or just to one of them, or if to just one of them, whether it is guaranteed to be the one in the Milky Way. Or if the one in the Milky Way knows he is in the Milky Way when taking the bet, and so on.
I meant that the bet is offered to the copy in the Milky Way and that he knows he is in the Milky Way. This is the right analogy with the "large civilizations" problem since we know we're in a small civilization.
...Suppose I am offered the bet before knowing whether I am in Andromeda o
The 'Irrationality Game' posts in discussion came before my time here, but I had a very good time reading the bits written in the comments section. I also had a number of thoughts I would've liked to post and get feedback on, but I knew that being buried in such old threads not much would come of it. So I asked around and feedback from people has suggested that they would be open to a reboot!
I hereby again quote the original rules:
I would suggest placing *related* propositions in the same comment, but wildly different ones might deserve separate comments for keeping threads separate.
Make sure you put "Irrationality Game" as the first two words of a post containing a proposition to be voted upon in the game's format.
Here we go!
EDIT: It was pointed out in the meta-thread below that this could be done with polls rather than karma so as to discourage playing-to-win and getting around the hiding of downvoted comments. If anyone resurrects this game in the future, please do so under that system If you wish to test a poll format in this thread feel free to do so, but continue voting as normal for those that are not in poll format.