David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
You are given a choice between two envelopes. You are told, reliably, that each envelope has some money in it—some whole number of dollars, say—and that one envelope contains twice as much money as the other. You don’t know which has the higher amount and which has the lower. You choose one, but are given the opportunity to switch to the other. Here is an argument that it is rationally preferable to switch: Let x be the quantity of money in your chosen envelope. Then the quantity in the other is either 1/2x or 2x, and these possibilities are equally likely. So the expected utility of switching is 1/2(1/2x) + 1/2(2x) = 1.25x, whereas that for sticking is only x. So it is rationally preferable to switch. There is clearly something wrong with this argument. For one thing, it is obvious that neither choice is rationally preferable to the other: it’s a tossup. For another, if you switched on the basis of this reasoning, then the same argument could immediately be given for switching back; and so on, indefinitely. For another, there is a parallel argument for the rational preferability of sticking, in terms of the quantity y in the other envelope. But the problem is to provide an adequate account of how the argument goes wrong. This is the two envelope paradox. In an earlier paper Horgan 2000) I offered a diagnosis of the paradox. I argued that the flaw in the argument is considerably more subtle and interesting than is usually believed, and that an adequate diagnosis reveals important morals about both probability and the foundations of decision theory. One moral is that there is a kind of expected utility, not previously noticed as far as I know, that I call nonstandard expected utility. I proposed a general normative principle governing the proper application of nonstandard expected utility in rational decisionmaking. But this principle is inadequate in several respects, some of which I acknowledged in note added in press and some of which I have meanwhile discovered..
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Olav Gjelsvik (2002). Paradox Lost, but in Which Envelope? Croatian Journal of Philosophy 2 (3):353-362.
Gary Malinas (2003). Two Envelope Problems and the Roles of Ignorance. Acta Analytica 18 (1-2):217-225.
Michael Clark & Nicholas Shackel (2000). The Two-Envelope Paradox. Mind 109 (435):415--442.
Terry Horgan (2000). The Two-Envelope Paradox, Nonstandard Expected Utility, and the Intensionality of Probability. Noûs 34 (4):578–603.
Paul Syverson (2010). Opening Two Envelopes. Acta Analytica 25 (4):479-498.
W. Schaafsma, B. P. Kooi & C. Albers (2005). Trying to Resolve the Two-Envelope Problem. Synthese 145 (1):89-109.
Casper J. Albers, Barteld P. Kooi & Willem Schaafsma (2005). Trying to Resolve the Two-Envelope Problem. Synthese 145 (1):89 - 109.
Christopher J. G. Meacham & Jonathan Weisberg (2003). Clark and Shackel on the Two-Envelope Paradox. Mind 112 (448):685-689.
Added to index2009-05-10
Total downloads69 ( #22,455 of 1,099,942 )
Recent downloads (6 months)4 ( #90,387 of 1,099,942 )
How can I increase my downloads?