Vorobyev, Oleg Yu. (2016): Blyth’s paradox «of three pies»: setwise vs. pairwise event preferences. Published in: Proceedings of the XV FAMEMS2016 Conference and the Workshop on Hilbert's sixth problem, Krasnoyarsk, Russia (30 September 2016): pp. 102108.

PDF
MPRA_paper_81897.pdf Download (188kB)  Preview 
Abstract
The pairwise independence of events does not entail their setwise independence (Bernstein’s example, 19101917). 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 wellknown to Yule2) by human ability to use triplewise and morewise preferences.
Item Type:  MPRA Paper 

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, MoscowLeningrad, 1946. [2] C.R. Blyth. On Simpson’s paradox and the surething 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 9785990335868, 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.unimuenchen.de/id/eprint/81897 