TimFreeman comments on St. Petersburg Mugging Implies You Have Bounded Utility - Less Wrong

10 Post author: TimFreeman 07 June 2011 03:06PM

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Comment author: TimFreeman 12 June 2011 03:34:07AM *  0 points [-]

See Alan Hajek's classic article "Waging War on Pascal's Wager."

That article is paywalled. It was published in 2003. Hajek's entry about Pascal's Wager in the Stanford Encylopedia of Philosophy is free and was substantively revised (hopefully by Hajek) in 2008, so there's a good chance the latter contains all the good ideas in the former and is easier to get to. The latter does mention the idea that utilities should be bounded, and many other things potentially wrong with Pascal's wager. There's no neat list of four items that looks like an obvious match to the title of the paywalled article.

Comment author: AlephNeil 12 June 2011 03:58:59AM 0 points [-]

You can find it here though.

Comment author: TimFreeman 16 June 2011 01:37:42PM 0 points [-]

Thanks for the pointer to a free version of Hajek's "Waging War on Pascal's Wager" paper. One of his alternative formulations uses surreal numbers for utilities, much to my surprise.

The main thrust is that either the utility of Heaven isn't the best possible thing, or it is the best possible thing and a mixed strategy of betting on heaven with probability p and betting on nothing with probability 1-p also gives infinite utility, for positive p. Thus, if Heaven is the best possible thing, Pascal's Wager doesn't rule out mixed strategies.

If someone could check my math here -- I don't think surreal numbers let you assign a utility to the St. Petersburg paradox. The expected utility received at each step is 1, so the total utility is 1 + 1 + 1 + ... . Suppose that sum is X. Then X + 1 = X. This is not true for any surreal number, right?