Timeline for Two envelope (sub)-problem / related problem
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Feb 28, 2016 at 19:56 | history | made wiki | Post Made Community Wiki by whuber♦ | ||
| Feb 10, 2016 at 21:35 | comment | added | delusionist | When those boundaries, which are the highest and lowest amount in that particular game, are taken into consideration, the FPL breaks down. | |
| Feb 10, 2016 at 21:35 | comment | added | delusionist | The FPL seems true because our minds travel into unbounded universes when considering whether or not twice or half an amount could exist. In that unbounded universe, both amounts exist, equally. But an actual game lives in a finite universe, and it is on the boundaries of that finite universe that the FPL breaks down. It isn’t natural to think about those boundaries when thinking through the logic as most people do. But those boundaries must be taken into consideration when calculating the odds of some strategy in any particular game. | |
| Feb 10, 2016 at 21:31 | comment | added | delusionist | Sorry, forgot this: (Note: I’ll call this: “When I see an amount, the other envelope will contain twice my amount half the time and half my amount half the time,” the “Faulty Paradox Logic,” or FPL. That way, I don’t have to type it out so many times. ☺) | |
| Feb 10, 2016 at 21:25 | comment | added | delusionist | The FPL implies a game that doesn’t happen. This is why it is both clever and misleading. It implies that some amount, and no other amount, will be repeatedly drawn. That doesn’t happen. It seems like it should be able to happen, but it can’t happen on average. You might think that if you look at any particular amount individually, the FPL will be true. Although it will be true in some games, it won’t be true in other games. Twice or half of any particular amount will happen in some games, but won’t happen in other games. The FPL must be true in every game for every amount. It isn’t. | |
| Feb 10, 2016 at 19:07 | comment | added | delusionist | So, the logic above shows why the logic that leads to the paradox is faulty and should not be used. Without that logic, no paradox arises. The logic above does this for any number of pairs, including one. | |
| Feb 10, 2016 at 18:58 | comment | added | delusionist | I agree with everything you said above. The paradox related to only one pair in isolation is resolved with the above logic. The paradox related to multiple pairs is also resolved. In other words, the above logic resolves the paradox regardless of the number of envelope pairs used in any game. | |
| Feb 9, 2016 at 11:37 | comment | added | John | You suggest this: 'I’ll define a trial as each time 2 envelopes are filled and one is chosen. I’ll define a game as any finite number of trials. This assumes that every game ends. No game goes on indefinitely.' If a game is any finite number of trials, I choose the specific case of n=1, i.e. one trial. The game is made up of one trial. So, it reduces to consideration of a single pair in isolation. | |
| Feb 9, 2016 at 11:32 | comment | added | John | Yes, I agree with this. It does however lead to the following conclusion: consideration of possible amounts or sets of possible amounts is irrelevant to the resolution of the paradox. Above, you have assessed the situation after the event, so once the game has finished. From this perspective, it doesn't matter where the amounts could have come from or where they did come from. All that matters is the amounts that were in the pairs of envelopes on the table during the game. Next, I suggest that this is no different to the treatment of a single pair considered in isolation... | |
| Feb 9, 2016 at 7:19 | review | Late answers | |||
| Feb 9, 2016 at 7:22 | |||||
| Feb 9, 2016 at 7:01 | history | answered | delusionist | CC BY-SA 3.0 |