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

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 |

Item ID: | 81897 |

Depositing User: | Prof Oleg Yu Vorobyev |

Date Deposited: | 13 Oct 2017 09:14 |

Last Modified: | 30 Sep 2019 18:23 |

References: | [1] S.N. Bernstein. Theory of Probability, 4th ed. Gostechizdat, Moscow-Leningrad, 1946. [2] C.R. Blyth. On Simpson’s paradox and the sure-thing principle. Journal of the American Statistical Association, 67(388):364–366, 1972. [3] R.P. Feynman. Simulating physics with computers. International Journal of Theoretical Physics, 21(6/7):467–488, 1982. [4] R.P. Feynman. Negative probability. in «Quantum implications»: Essays in honor of David Bohm, edited by B. J. Hiley and F. D. Peat, (Chap. 13):235–248, 1987. [5] M. Gardner. Time travel and other mathematical bewilderment. W.H.Freeman and Company, New York, 1968. [6] E.H. Simpson. The interpretation of interaction in contingency tables. Journal of the Royal Statistical Society, Seria B, (13):238–241, 1951. [7] O. Yu. Vorobyev. Mathematical metaphysics is a shadow of forthcoming mathematics. In. Proc. of the V FAM Conf. pages 15–23, 2001 (in Russian, abstract in English). [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. [10] G.U. Yule. Notes of the theory of association of attributes in statistics. Biometrika, (2):121–134, 1903. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/81897 |