tag:blogger.com,1999:blog-3891434218564545511.post7757358419044319449..comments2017-05-24T14:50:15.143-05:00Comments on Alexander Pruss's Blog: More on St PetersburgAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-3891434218564545511.post-90077152300686164612017-05-16T08:48:15.742-05:002017-05-16T08:48:15.742-05:00Actually, my weakening of the axiom doesn't se...Actually, my weakening of the axiom doesn't seem enough to generate the paradox. One really does seem to need the fuller and crazy Archimedean axiom. But one would need to be crazy to submit to a week of torture for a one in googolplex chance of some fixed finite good. Alexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-88631265249388159242017-05-16T08:05:18.427-05:002017-05-16T08:05:18.427-05:00In the real world nobody is an Archimedean; that i...In the real world nobody is an Archimedean; that is certainly the principle to reject. Lots of people will spend a dollar on a lottery ticket. Nobody will spend all their assets on lottery tickets, no matter what the expected payoff is, so long as the chance of receiving it is low. Heath Whitehttp://www.blogger.com/profile/13535886546816778688noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-30709179063308573422017-05-15T11:18:43.332-05:002017-05-15T11:18:43.332-05:00Probably, but only if you have a convex sum operat...Probably, but only if you have a convex sum operation that allows one to combine countably infinitely many gambles.<br /><br />Yes, these are very different Archimedean axioms. The vN-M axioms can all be satisfied even if there is a maximum utility. The axiom I give, of course, cannot.Alexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-19988372283138394862017-05-14T17:42:59.975-05:002017-05-14T17:42:59.975-05:00I think you could make this work without numerical...I think you could make this work without numerical utility, using only (complete) preferences.<br /><br />Note that Archimedianism is very different from the von Neumann – Morgenstern Archimedian axiom.IanShttp://www.blogger.com/profile/00111583711680190175noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-14649229437425506622017-05-14T08:39:29.312-05:002017-05-14T08:39:29.312-05:00A slight weakening of the axiom: There is a positi...A slight weakening of the axiom: There is a positive utility U0 such that for any finite utility U < U0 and non-zero probability ϵ > 0, there is a finite utility V such that a gamble that offers a probability ϵ of getting V is always better than a certainty of U.Alexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-45231911444597955932017-05-13T14:17:36.829-05:002017-05-13T14:17:36.829-05:00Alex,
I'd like to raise the issue of existen...Alex, <br /><br />I'd like to raise the issue of existence in your argument and computing power: <br /><br />Your argument seems to assume that for every n, there is Vn such that probability of Vn is 1/2^n. <br /><br />However, human brains - or human brains + computers, etc., or the brains of aliens, etc. - are not able to compute 1/2^n (for example) for arbitrary n. We understand a symbol "n", but we would not be able to assign probabilities in such manner in the real world (even if it's metaphysically possible, it's not within our power). For every agent with finite computing power (or any finite number of cooperating agents, each with finite computing power), and for all but finitely many values of n (there doesn't have to be a precise number for any agent, since it may change with the circumstances), 1/(2^n) is comprehension-transcendent, and there is no way for the agent to attribute the require probability to make choices on that basis.<br /><br />A similar difficulty results from the assumption that for any n, there are n units of utility.Angra Mainyuhttp://www.blogger.com/profile/16342860692268708455noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-40489783465937227272017-05-13T08:34:25.221-05:002017-05-13T08:34:25.221-05:00I agree. We can easily see this by example: let pr...I agree. We can easily see this by example: let probability ϵ be 1 in a googolplex. And let U be anything good you please. No reasonable human being would choose the bet, regardless of what V is (in fact even if V were actually infinite.) <br /><br />What this really comes down to is saying that human beings care about things to a finite degree since they are themselves finite. The Archimedean postulate basically says that we can care infinitely about something, but this is false.entirelyuselesshttps://entirelyuseless.wordpress.com/noreply@blogger.com