= 27d567bc2d48d9f40e9ccc20ea370b15)
Sniffnoy comments on A summary of Savage's foundations for probability and utility. - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (88)
Great summary!
P7 looks self-evident to me. I'm less comfortable with the P6. Unbounded utility depends on P6 requiring a partition into an arbitrarily large number of parts - is this used in the proof of bounded utility? In general, I don't think Archimedian axioms are safe given our current level of understanding of Pascal's mugger-like problems.
EDIT: P7 doesn't look as self-evident anymore. Consider the St. Petersburg lottery. Any particular payout from buying a ticket for $2 is worse than the expected value of buying a ticket for $1, but obviously it is preferable to buy the ticket for $1. Again, I don't think we can judge this given our current level of understanding of Pascal's mugger-like problems.
This strikes me as very similar to Fishburn's proof that P7 implies utility is bounded. (Maybe it's essentially the same? Need to read more carefully; point is, his proof also works by comparing two St. Petersburg lotteries.). Of course, we only get the problem if we imagine that the St. Petersburg lottery is for utility, rather than for money with decreasing marginal (and in this theory, ultimately bounded) utility...
Yes, this is Fishburn's proof, just as a modus tollens rather than a modus ponens.