Next Article in Journal
Detecting Chronotaxic Systems from Single-Variable Time Series with Separable Amplitude and Phase
Next Article in Special Issue
An Entropy-Based Approach to Path Analysis of Structural Generalized Linear Models: A Basic Idea
Previous Article in Journal
Information Geometry Formalism for the Spatially Homogeneous Boltzmann Equation
Previous Article in Special Issue
Collaborative Performance Research on Multi-level Hospital Management Based on Synergy Entropy-HoQ
Open AccessArticle

Intransitivity in Theory and in the Real World

School of Mechanical and Mining Engineering, The University of Queensland, Brisbane QLD 4072, Australia
Academic Editor: Ali E. Abbas
Entropy 2015, 17(6), 4364-4412;
Received: 30 March 2015 / Revised: 2 June 2015 / Accepted: 15 June 2015 / Published: 19 June 2015
(This article belongs to the Special Issue Entropy, Utility, and Logical Reasoning)
This work considers reasons for and implications of discarding the assumption of transitivity—the fundamental postulate in the utility theory of von Neumann and Morgenstern, the adiabatic accessibility principle of Caratheodory and most other theories related to preferences or competition. The examples of intransitivity are drawn from different fields, such as law, biology and economics. This work is intended as a common platform that allows us to discuss intransitivity in the context of different disciplines. The basic concepts and terms that are needed for consistent treatment of intransitivity in various applications are presented and analysed in a unified manner. The analysis points out conditions that necessitate appearance of intransitivity, such as multiplicity of preference criteria and imperfect (i.e., approximate) discrimination of different cases. The present work observes that with increasing presence and strength of intransitivity, thermodynamics gradually fades away leaving space for more general kinetic considerations. Intransitivity in competitive systems is linked to complex phenomena that would be difficult or impossible to explain on the basis of transitive assumptions. Human preferences that seem irrational from the perspective of the conventional utility theory, become perfectly logical in the intransitive and relativistic framework suggested here. The example of competitive simulations for the risk/benefit dilemma demonstrates the significance of intransitivity in cyclic behaviour and abrupt changes in the system. The evolutionary intransitivity parameter, which is introduced in the Appendix, is a general measure of intransitivity, which is particularly useful in evolving competitive systems. View Full-Text
Keywords: intransitivity; complex evolving systems; non-conventional thermodynamics; utility; behavioural economics; population dynamics intransitivity; complex evolving systems; non-conventional thermodynamics; utility; behavioural economics; population dynamics
MDPI and ACS Style

Klimenko, A.Y. Intransitivity in Theory and in the Real World. Entropy 2015, 17, 4364-4412.

Show more citation formats Show less citations formats

Article Access Map by Country/Region

Only visits after 24 November 2015 are recorded.
Search more from Scilit
Back to TopTop