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Feb 28, 2016 at 19:56 history made wiki Post Made Community Wiki by whuber
Feb 4, 2016 at 0:04 comment added John To generalise (i): any finite collection of envelopes can be viewed as a collection of separate chains. A single pair is also a chain - a special case of a chain of length two. So thinking about finite collections reduces to thinking about a chain which in turn reduces to thinking about a single pair.
Feb 3, 2016 at 23:22 comment added John (ii) You write: 'Notice that if you correctly guess the range of starting values used, you can then correctly decide whether or not to trade.' It seems to me that some mathematical arguments about prior probabilities effectively say that on opening the first envelope the amount inside allows the player to make a judgement about the prior probabilities. This is what I am not sure about, and what I was getting at in the original post.
Feb 3, 2016 at 23:17 comment added John (i) consider a chain of pairs in which every amount appears twice, once as the smaller amount in the pair, once as the larger amount in the pair. Except that is, that two amounts appear only once - the smallest in the chain and the largest. On every value except the extremes he should swap (expectation of gain). For one extreme he should stick (certain loss on swapping), for one he should swap (certain gain). If the player is looking at, say, £100 and is told it is an extreme, what should he do? 50% chance it is the smallest, 50% chance it is the largest. We're back to the single envelope case
Feb 3, 2016 at 23:05 comment added John Very nicely put, and I agree with most of your arguments. Perhaps I should add that I also agree with you that in general there is no expectation of gain on swapping. But (i) I'm not sure the reasoning above quite deals with the paradox from the player's perspective, or it deals with it no better than arguments about how to think about a single pair do, and (ii) my point in presenting the (sub)-problem is to ask whether mathematical arguments about prior probabilities are relevant. More on both to follow...
Feb 2, 2016 at 18:52 review Late answers
Feb 2, 2016 at 19:13
Feb 2, 2016 at 18:36 history answered delusionist CC BY-SA 3.0