Talk:Unexpected hanging paradox

The View from 30,000 feet

The "paradox" here is because two contradictory things are asserted. Both can't be true. Here is a "resolution", light on "rigor" but heavy on "intuition".

By "complete information" I mean anything that the prisoner knows will happen with probability 1.

Thing 1: The prisoner has "complete information" about being hanged. When the prisoner is told "you will be hanged sometime next week", he has "complete information".

Thing 2: The prisoner does not have "complete information" about being hanged. When the prisoner is told "you will not know whether you will be hanged today", he does not have "complete information".

I don't have "complete information" if I will win the lotto today, even though it is possible I will. There is a small probability (say 1 in a billion trillion) I will suddenly have an urge to buy a lotto ticket that will win, but I do not know anything with probability 1. Similarly telling the prisoner "you may or may not hang today" implied lack of "complete information".

The "solution" for the paradox is that you can't both have and not have "complete information".

If you define the "events" rigorously using probability (measure theory etc.), define rigorously what it means to be "surprised" etc. etc. etc., any paradox goes away.

JS (talk) 19:04, 10 January 2014 (UTC)

WP:TPG: "Article talk pages should not be used by editors as platforms for their personal views on a subject." If you want to suggest changes to the article, please state what should be changed, and which reliable sources support the change. Paradoctor (talk) 19:07, 10 January 2014 (UTC)

this article should be deleted for lack of notability of the subject matter

This so-called paradox is not well known enough to warrant having its own article. Tweedledee2011 (talk) 01:02, 11 January 2014 (UTC)

WP:AfD, though you might want to check the weather report first, it might WP:Snow. Or read the article. Paradoctor (talk) 02:34, 11 January 2014 (UTC)

Lame Duck

I can't believe people are arguing this at all.

This "logic problem" is about as idiotic as the "arrow moves half the distance" problem. Anyone with half a brain realizes that there is no paradox, they just might not be able to articulate exactly why.

This problem breaks down the minute the timeframe is longer than 2 days. It's always a surprise except on the last day. This is exactly a case of the gambler's fallacy. Nothing more. Odds don't change due to expectations. If the Judge draws a random lot to choose the day (which is implied) then any expectations the prisoner makes are pure fantasy. He will be surprised by the day, in fact, he makes himself more surprised by the very concept of believing he can outwit the judge.

Think about it.

Lajekahr 15:15, 12 May 2007 (UTC)

Of course paradoxes do not exist, not in mathematics at least, but the point is to find situations which would be very hard to believe to not be paradoxical. The Unexpected Hanging Paradox is an excellent example in my opinion. To solve a "paradox" means to find an error in it. The point is not to decide whether the prisoner can outwit the judge, but to find where the prisoner made a mistake. By the way, the case of 2 days is no different from the case of 5 days, if the prisoner is to be hanged on the first. People are arguing, i think, because there are many possible solutions, but the explanation Lajekahr has given is not a complete solution. Do you think the prisoner made a mistake when he concluded that he would not be hanged on Thursday, but with Friday his conclusion was valid? Think about it. --Cokaban (talk) 15:30, 8 December 2007 (UTC)

I don't understand why this is considered a paradox at all. If he's alive on Thursday night, he would have to be hanged Friday, which means he expects it, which means it can't be the day. If he's alive Wednesday night, then the day can't be Thursday, because if it wasn't Thursday, it would have to be Friday, which he would expect, etc. However, on Monday morning, how does he know if it's going to be Monday, or Tuesday? Can't be Thursday because at 12:01 PM on Wednesday he would KNOW it's Thursday because it can't be Friday. If he's alive on Monday night, it could be Tuesday or Wednesday, which means they could kill him Monday and he would be surprised. — Preceding unsigned comment added by 207.199.253.60 (talk) 19:43, 18 February 2014 (UTC)

Simple refutation

"You will be hanged tomorrow, but you do not know that"

Shouldn't this one read ".., but you will not know that"? --User:unmanaged — Preceding undated comment added 10:36, 19 November 2014‎

The Selfish Gene

Richard Dawkins brings up this very subject, although not by this name, and with regard to a different scenario, in The Selfish Gene. He talks about it in the context of the prisoner's dilemma, though in an iterated fashion, but where the number of rounds is unknown to either adversary, because of course if either of them knew that the game was going to end in a predictable number of rounds, the only rational thing to do, assuming the other person is also rational, is to defect.[1] The shadow of the future must be long in order for both adversaries to cooperate. Perhaps this would make an interesting addition to the page?24.6.187.181 (talk) 18:08, 7 April 2015 (UTC)

This is not a paradox at all

This paradox should be deleted as it arises because of the false assertion that on Thursday one minute past noon you are still alive. Only then you can say that on Friday you can’t be hung and build on the argument backwards till Monday…