Wednesday, August 15, 2018

004 Lottery paradox

At least as of August 15, 2018, the Wikipedia entry on Henry Kyburg's The Lottery Paradox does not yet mention that a restatement of this paradox appears in Andrew Crumey's 1996 novel D'Alembert's Principle. 

https://en.wikipedia.org/wiki/Lottery_paradox

In Crumey's novel, it is attributed to a fictional philosopher of the Scottish Enlightenment -- one Magnus Ferguson -- who seeks to defeat D'Alembert's vision of an ordered and rational universe by reducing reality to the principles of chance and probability.

I find the statement of the paradox in the novel, by the way, more compelling and more obviously paradoxical than the Wikipedia description. To paraphrase from Crumey: imagine two scenarios: 1) a winning ticket is included in a thousand-ticket lottery; 2) a die is cast such that the number of possible outcomes is 1,000, and a gambler bets on one of these outcomes. In both scenarios, a participant in the game would have a 1/1000 chance of success. Yet -- scenario (1) guarantees a winner. Scenario (2) does not. So shouldn't the odds be better in scenario (1)?

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