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McEs, A Hacker Life
Sunday, November 15, 2009
 On Unexpected Hanging Paradox and applications in law enforcement

[Note: this post has nothing to do with the ongoing executions in Iran.]

Unexpected hanging paradox is a well-known alleged logical paradox about a prisoner's response to an unusual death sentence. To quote Wikipedia, here is the statement of the paradox:
A judge tells a condemned prisoner that he will be hanged at noon on one weekday in the following week but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day. Having reflected on his sentence, the prisoner draws the conclusion that he will escape from the hanging. His reasoning is in several parts. He begins by concluding that the "surprise hanging" can't be on a Friday, as if he hasn't been hanged by Thursday, there is only one day left - and so it won't be a surprise if he's hanged on a Friday. Since the judge's sentence stipulated that the hanging would be a surprise to him, he concludes it cannot occur on Friday. He then reasons that the surprise hanging cannot be on Thursday either, because Friday has already been eliminated and if he hasn't been hanged by Wednesday night, the hanging must occur on Thursday, making a Thursday hanging not a surprise either. By similar reasoning he concludes that the hanging can also not occur on Wednesday, Tuesday or Monday. Joyfully he retires to his cell confident that the hanging will not occur at all. The next week, the executioner knocks on the prisoner's door at noon on Wednesday — which, despite all the above, will still be an utter surprise to him. Everything the judge said has come true.

This has intrigued me again and again and I could never come to peace with it. While researching this recently I came across this paper which is a non-exhaustive survey of various tries to model the paradox. Great read.

Today I came across a blog post by Ed Felten called Targeted Copyright Enforcement: Deterring Many Users with a Few Lawsuits. While I find it very disturbing that a scientist like Ed Felten may be helping RIAA better screw people by their copyvio lawsuits, the puzzle and the solution provided are well worth a read. Not irrelevant to the Hanging Paradox, though in this case the reasoning may actually work.

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