Timeline for Endless controversy about the correctness of significant papers
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Feb 6, 2023 at 14:29 | comment | added | usul | Terry (and Winkler) focus on probability. But the decision-theory aspect of the paradox is important. E.g. (Conitzer 2015) shows how evidentiary decisionmaking arguments that are used to justify a belief of 1/3 are vulnerable to Dutch books in some variants of the paradox. I think it is about justifying "locally correct" beliefs that are also globally consistent (or at least not exploitable). [It is easier to tell sleeping beauty how to gamble optimally than to tell her how to form beliefs such that she gambles optimally.] | |
| Dec 31, 2018 at 22:50 | comment | added | Terry Tao | The paradox arises because the problem involves two random variables: C, the result of the coin toss, and D, the current day of the week). Since SB will exist (but not necessarily be conscious) for both Monday and Tuesday, the prior distribution of (C,D) is equally distributed among all four possibilities (Heads,Monday), (Heads,Tuesday), (Tails,Monday), (Tails,Tuesday). Thus the prior probability of heads is 1/2. But when SB learns that she is conscious today, she now knows that (Heads,Tuesday) is eliminated, and the posterior probability of heads is now 1/3. | |
| Oct 13, 2017 at 9:45 | comment | added | Robert Frost | So it's a paradox of whether accuracy of probability is measured per coin toss or per "ask". | |
| Oct 13, 2017 at 9:43 | comment | added | Robert Frost | @GerryMyerson The paradox is solved thus: She knows in advance that she will be double-sampling from the tails. Therefore the strategy to take over multiple samples, in order to maximise accuracy, is one third. But if you were to ask her this question: "when we ask you what the coin turned up, please bear in mind that if it transpires that we have asked you twice about the same coin toss then your two answers will only be given the same weight as the one answer you give in relation to some coin toss about which you are only asked once" then she should answer half. | |
| Oct 11, 2017 at 0:50 | comment | added | Gerry Myerson | @Philip, if you have a conclusive argument to settle Sleeping Beauty, I would encourage you to publish it. | |
| Oct 10, 2017 at 22:58 | comment | added | Philip Oakley | @GerryMyerson, The similarity with Monty Hall (a game show host) is the misdirection of the audience and the contestants as to what the over all scenario is. Both cases have a three (boxes/sleeps) versus two (still-closed-boxes/sides-of-a-coin) confusion of human comprehension. If one states the problem too carefully, then neither are a problem! | |
| Oct 10, 2017 at 21:56 | comment | added | Gerry Myerson | @Philip, I think a difference is that once one states Monty Hall carefully there is one answer that is clearly correct, whereas there seems to be genuine controversy about Sleeping Beauty. | |
| Oct 10, 2017 at 14:32 | comment | added | Philip Oakley | The Sleeping Beauty problem looks to hav a lot of similarities to the Monty-Hall problem, but done in reverse, with a slightly different twist as to what one needs to (not) know to change a 1/3 probability into a 1/2 probability, and vice versa | |
| Oct 6, 2017 at 3:07 | comment | added | Gerry Myerson | @Timothy, maybe so, though it has been the subject of an article in the Math Intelligencer (J S Rosenthal, A mathematical analysis of the Sleeping Beauty problem, 31 (2009) 32-37) and Winkler's essay in the Monthly. | |
| Oct 5, 2017 at 23:09 | comment | added | Timothy Chow | This seems to me to be a philosophical controversy rather than a mathematical one. | |
| Oct 5, 2017 at 22:21 | comment | added | kjetil b halvorsen | Sleeping beauty paradox discussed at Cross Validated: stats.stackexchange.com/questions/41208/… | |
| S Oct 5, 2017 at 21:30 | history | answered | Gerry Myerson | CC BY-SA 3.0 | |
| S Oct 5, 2017 at 21:30 | history | made wiki | Post Made Community Wiki by Gerry Myerson |