Article

Theory and Decision

, Volume 43, Issue 3, pp 253-277

First online:

Perspectives on a Pair of Envelopes

  • Piers RawlingAffiliated withPhilosophy Department, University of Missouri-St. Louis

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

The two envelopes problem has generated a significant number of publications (I have benefitted from reading many of them, only some of which I cite; see the epilogue for a historical note). Part of my purpose here is to provide a review of previous results (with somewhat simpler demonstrations). In addition, I hope to clear up what I see as some misconceptions concerning the problem. Within a countably additive probability framework, the problem illustrates a breakdown of dominance with respect to infinite partitions in circumstances of infinite expected utility. Within a probability framework that is only finitely additive, there are failures of dominance with respect to infinite partitions in circumstances of bounded utility with finitely many consequences (see the epilogue).

Pair of envelopes countable additivity principle of dominance finite additivity infinite partitions