Some algebraic characterizations of preference structures

Abstract In decision theory several preference structures are used for modeling coherence and rational behavior. In this paper we establish, from an algebraic approach, characterizations of some general properties involving preference and indifference relations, as well as the more common preference structures used in the literature.

[1]  Philippe Vincke,et al.  Semiorders - Properties, Representations, Applications , 1997, Theory and decision library: series B.

[2]  R. Luce Semiorders and a Theory of Utility Discrimination , 1956 .

[3]  A. Sen,et al.  Collective Choice and Social Welfare , 2017 .

[4]  K. May Intransitivity, Utility, and the Aggregation of Preference Patterns , 1954 .

[5]  Peter C. Fisi-Iburn Nontransitive preferences in decision theory , 1991 .

[6]  Alexis Tsoukiàs,et al.  Preference Modelling , 2004, Preferences.

[7]  P. Benson,et al.  Remark , 1994 .

[8]  A. Tversky Intransitivity of preferences. , 1969 .

[9]  Hugo Sonnenschein,et al.  THE RELATIONSHIP BETWEEN TRANSITIVE PREFERENCE AND THE STRUCTURE OF THE CHOICE SPACE , 1965 .

[10]  J. Chipman The Foundations of Utility , 1960 .

[11]  K. Suzumura Rational Choice, Collective Decision And Social Welfare (位相幾何学と経済学) , 1980 .

[12]  Robert A. Pollak,et al.  Collective rationality and dictatorship: The scope of the arrow theorem , 1979 .

[13]  J. H. Blau,et al.  Semiorders and collective choice , 1979 .

[14]  H. D. Swart,et al.  Towards an axiomatization of orderings , 1992 .

[15]  A. Chateauneuf Continuous representation of a preference relation on a connected topological space , 1987 .

[16]  Patrick Suppes,et al.  Foundational aspects of theories of measurement , 1958, Journal of Symbolic Logic.

[17]  P. Acker Transitivity revisited , 1990 .

[18]  A. Sen,et al.  Social Choice Theory: A Re-Examination , 1977 .

[19]  P. Fishburn Intransitive indifference with unequal indifference intervals , 1970 .

[20]  Amartya Sen,et al.  Quasi-Transitivity, Rational Choice and Collective Decisions , 1969 .