Abstract

Various proposals have been made for solving The Two Envelope Problem. But even though the problem itself is easily stated and quite simple, the proposedsolutions have not been. Some involve calculus, some involve considerations about infinite values, and some are complicated in other ways. Moreover, there is not yet any one solution that is widely accepted as correct. In addition to being notable for its simplicity and its lack of a generally agreed-upon solution, The Two Envelope Problem is also notable because it demonstrates that something that has been taken to be a fundamental principle of decision theory is false. The main purpose of this paper is to propose and defend a simple solution to The Two Envelope Problem. But I also want to make a start on the project of figuring out how the relevant fundamental principle of decision theory should be revised.