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Probability, Choice, and Reason
Published in Technometrics, 2022
Stan Lipovetsky
Chapter 3, “Probability and Choice,” presents problems which do not have a unique agreed solution or with a surprising solution. It considers William Newcomb’s paradox discussed in decision theory as a choice between reason unsupported by evidence, and evidence unsupported by reason; the Sleeping Beauty problem; the God’s Coin Toss problem with the self-sampling and self-indication assumptions; the Doomsday Argument of the human race extinction, related also to the Lindy effect; the problem of when to stop looking and start choosing, aka the Secretary problem; why we more often are in the slower lane problem, related to the observer selection effect; Blaise Pascal’s Wager problem of preference to believe in God, and the related climate change and mugging problems; J.M. Keynes’ Beauty Contest, or money market problem; and the famous Benford’s Law, helping to identify the fraud series of numbers.