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Blyth’s paradox «of three pies»: setwise vs. pairwise event preferences

Vorobyev, Oleg Yu. (2016): Blyth’s paradox «of three pies»: setwise vs. pairwise event preferences. Published in: Proceedings of the XV FAMEMS-2016 Conference and the Workshop on Hilbert's sixth problem, Krasnoyarsk, Russia (30 September 2016): pp. 102-108.

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The pairwise independence of events does not entail their setwise independence (Bernstein’s example, 1910-1917). The probability distributions of all pairs of events do not determine the probability distribution of the whole set of events (the triangular room paradox of negative probabilities of events [8, 9, 2001]). The pairwise preferences of events do not determine their setwise preferences (Blyth’s paradox, 1972). The eventological theory of setwise event preferences, proposed in [8, 2007], gives an event justification and extension of the classical theory of preferences and explains Blyth’s paradox «of three pies»1 (that was already well-known to Yule2) by human ability to use triplewise and morewise preferences.

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