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Free to choose. A different answer to a known puzzle

Nalebuff (Journal of Economic Perspectives, 1(2), 157–63, 1987) proposes a puzzle and a standard solution to the mentioned puzzle based on Bayes theorem. After giving the standard solution to this problem, Professor Nalebuff asked: ‘Since many if not most individuals choose to stay with their original choice, does this suggest we should look for alternatives to Bayes rule?’ In this paper a right answer to that question is proportionated.