A Review of the Lottery Paradox

In William Harper & Gregory Wheeler, Probability and Inference: Essays in Honour of Henry E. Kyburg, Jr. College Publications (2007)
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Abstract

Henry Kyburg’s lottery paradox (1961, p. 197) arises from considering a fair 1000 ticket lottery that has exactly one winning ticket. If this much is known about the execution of the lottery it is therefore rational to accept that one ticket will win. Suppose that an event is very likely if the probability of its occurring is greater than 0.99. On these grounds it is presumed rational to accept the proposition that ticket 1 of the lottery will not win. Since the lottery is fair, it is rational to accept that ticket 2 won’t win either—indeed, it is rational to accept for any individual ticket i of the lottery that ticket i will not win. However, accepting that ticket 1 won’t win, accepting that ticket 2 won’t win, . . . , and accepting that ticket 1000 won’t win entails that it is rational to accept that no ticket will win, which entails that it is rational to accept the contradictory proposition that one ticket wins and no ticket wins

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Gregory Wheeler
Frankfurt School Of Finance And Management

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References found in this work

Can we do without pragmatic encroachment.Brian Weatherson - 2005 - Philosophical Perspectives 19 (1):417–443.
The Epistemology of Belief and the Epistemology of Degrees of Belief.Richard Foley - 1992 - American Philosophical Quarterly 29 (2):111 - 124.
A logic for default reasoning.Ray Reiter - 1980 - Artificial Intelligence 13 (1-2):81-137.

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