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.

Abstract

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Eventology, event, probability, preference, pairwise event preferences, setwise event preferences, theory of setwise event preferences.
• Subjects: A - General Economics and Teaching > A1 - General Economics; A - General Economics and Teaching > A1 - General Economics > A14 - Sociology of Economics; C - Mathematical and Quantitative Methods > C0 - General; C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C46 - Specific Distributions ; Specific Statistics; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C65 - Miscellaneous Mathematical Tools; Z - Other Special Topics > Z1 - Cultural Economics ; Economic Sociology ; Economic Anthropology; Z - Other Special Topics > Z1 - Cultural Economics ; Economic Sociology ; Economic Anthropology > Z13 - Economic Sociology ; Economic Anthropology ; Social and Economic Stratification

References

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[8] O. Yu. Vorobyev. Eventology. Siberian Federal University, Krasnoyarsk, Russia, 2007, 435p., https://www.academia.edu/179393/.

[9] O. Yu. Vorobyev. Triangle room paradox of negative probabilities of events. In. Proc. of the XIV Intern. FAMEMS Conf. on Financial and Actuarial Mathematics and Eventology of Multivariate Statistics & the Workshop on Hilbert’s Sixth Problem, Krasnoyarsk, SFU (Oleg Vorobyev ed.):100–103, 2016; ISBN 978-5-9903358-6-8, https://www.academia.edu/32419497.

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