Context dependent probabilistic choice models based on measures of binary advantage

Abstract Rotondo has developed a constant utility generalization of Luce's choice model that can handle various examples that contradict the choice model. This paper axiomatizes a generalization of Rotondo's model and discusses unidimensional and multidimensional versions of that generalization; several additional incomplete characterizations of the model are also presented. The class of random advantage models , which generalizes the classical random utility family, is presented and related to the generalized Rotondo model.

[1]  D. Wise,et al.  A CONDITIONAL PROBIT MODEL FOR QUALITATIVE CHOICE: DISCRETE DECISIONS RECOGNIZING INTERDEPENDENCE AND HETEROGENEOUS PREFERENCES' , 1978 .

[2]  A. A. J. Marley,et al.  Some Probabilistic Models of Simple Choice and Ranking , 1968 .

[3]  R. D. Bock,et al.  Multivariate Statistical Methods in Behavioral Research , 1978 .

[4]  D. J. Strauss,et al.  Some results on random utility models , 1979 .

[5]  R. Duncan Luce,et al.  Individual Choice Behavior , 1959 .

[6]  A. A. J. Marley,et al.  Aggregation theorems and multidimensional stochastic choice models , 1991 .

[7]  Daniel N. Osherson,et al.  An advantage model of choice , 1989 .

[8]  A. A. J. Marley,et al.  A random utility family that includes many of the ‘classical’ models and has closed form choice probabilities and choice reaction times , 1989 .

[9]  R. Luce,et al.  The Choice Axiom after Twenty Years , 1977 .

[10]  A. Tversky.  Choice by elimination , 1972 .

[11]  J. Yellott.  The relationship between Luce's Choice Axiom, Thurstone's Theory of Comparative Judgment, and the double exponential distribution , 1977 .

[12]  David W. Strauss.  Choice by features: An extension of Luce's choice model to account for similarities , 1981 .

[13]  J. Aczél.  On weighted synthesis of judgements , 1984 .

[14]  Eugene Galanter,et al.  Handbook of mathematical psychology: I. , 1963 .

[15]  László Lovász,et al.  Submodular functions and convexity , 1982, ISMP.

[16]  Peter C. Fishburn,et al.  Nonlinear preference and utility theory , 1988 .

[17]  Jean-Claude Falmagne,et al.  On a recurrent misuse of a classical functional equation result , 1981 .

[18]  Jaap Van Brakel,et al.  Foundations of measurement , 1983 .

[19]  Peter C. Fishburn,et al.  Binary choice probabilities between gambles: Interlocking expected utility models ☆ , 1976 .

[20]  Daniel McFadden,et al.  Modelling the Choice of Residential Location , 1977 .

[21]  Richard R. Batsell,et al.  A New Class of Market Share Models , 1985 .

[22]  A. Marley.  Multivariate stochastic processes compatible with “aspect” models of similarity and choice , 1981 .

[23]  K. Small.  A Discrete Choice Model for Ordered Alternatives , 1987 .

[24]  A. Tversky.  Elimination by aspects: A theory of choice. , 1972 .