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Entropy 2015, 17(3), 968-983;

Do Transitive Preferences Always Result in Indifferent Divisions?

Institute of Mathematics, University of Bialystok, Ciołkowskiego 1M, Pl-15245 Białystok, Poland
Institute of Physics, University of Silesia, Uniwersytecka 4, Pl-40007 Katowice, Poland
Author to whom correspondence should be addressed.
Academic Editors: Demosthenes Ellinas, Giorgio Kaniadakis, Jiannis Pachos and Antonio M. Scarfone
Received: 9 January 2015 / Revised: 7 February 2015 / Accepted: 17 February 2015 / Published: 2 March 2015
(This article belongs to the Special Issue Quantum Computation and Information: Multi-Particle Aspects)
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The transitivity of preferences is one of the basic assumptions used in the theory of games and decisions. It is often equated with the rationality of choice and is considered useful in building rankings. Intransitive preferences are considered paradoxical and undesirable. This problem is discussed by many social and natural scientists. A simple model of a sequential game in which two players choose one of the two elements in each iteration is discussed in this paper. The players make their decisions in different contexts defined by the rules of the game. It appears that the optimal strategy of one of the players can only be intransitive (the so-called relevant intransitive strategy)! On the other hand, the optimal strategy for the second player can be either transitive or intransitive. A quantum model of the game using pure one-qubit strategies is considered. In this model, an increase in the importance of intransitive strategies is observed: there is a certain course of the game where intransitive strategies are the only optimal strategies for both players. The study of decision-making models using quantum information theory tools may shed some new light on the understanding of mechanisms that drive the formation of types of preferences. View Full-Text
Keywords: relevant intransitive strategies; quantum strategy; quantum modeling; decision-making relevant intransitive strategies; quantum strategy; quantum modeling; decision-making
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Makowski, M.; Piotrowski, E.W.; Sładkowski, J. Do Transitive Preferences Always Result in Indifferent Divisions? Entropy 2015, 17, 968-983.

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