Timeline for Two envelope (sub)-problem / related problem
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 28, 2016 at 19:56 | history | made wiki | Post Made Community Wiki by whuber♦ | ||
| Feb 5, 2016 at 12:29 | comment | added | John | By a chain I meant that the possible pairs are selected from a finite set of the form {(n, 2n), (2n, 4n), (4n, 8n), ... (2^(k-1)n, 2^kn} We could tell the player this or he could figure out that all fine sets are collections of such chains. Of course we wouldn't tell him what the value of n is as that would give too much information. My point is that this does not remove the paradox any more than telling him that the game is (X, 2X), if only he could accept this. | |
| Feb 5, 2016 at 11:10 | comment | added | John | What some mathematicians do is to say that we should take a different approach to resolving the paradox. This is what I am asking about in my sub puzzle. I am not convinced that their arguments are right or indeed relevant. Whether explicitly stated or not, the idea seems to be that the player should presume, on looking at an amount of money, that it is somehow more likely that the amount is the larger in the pair rather than the smaller. Or maybe that isn't the claim. But if it isn't it might be simpler to say that this whole line of argument is not relevant. | |
| Feb 5, 2016 at 11:05 | comment | added | John | When we know the amounts, or if we take an outsider's view, it is clear that there is no expectation of gain on swapping. If, e.g., the amounts are 100 and 200, then it is simply a matter of going up or down 100. Generally, label the amounts X and 2X where X is the smaller amount and it is once again clear. There are two amounts, not three (or four) and that's that: up or down X. Some philosophers say that the solution to the puzzle is getting the player to take this viewpoint and ignore everything else as illusory. I tend to agree with them. It's just very hard for the player to do this... | |
| Feb 5, 2016 at 3:08 | review | Late answers | |||
| Feb 5, 2016 at 3:18 | |||||
| Feb 5, 2016 at 2:52 | history | answered | delusionist | CC BY-SA 3.0 |