Testing transitivity of preferences on two-alternative forced choice data

As Duncan Luce and other prominent scholars have pointed out on several occasions, testing algebraic models against empirical data raises difficult conceptual, mathematical, and statistical challenges. Empirical data often result from statistical sampling processes, whereas algebraic theories are no...

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Published inFrontiers in psychology Vol. 1; p. 148
Main Authors Regenwetter, Michel, Dana, Jason, Davis-Stober, Clintin P
Format Journal Article
LanguageEnglish
Published Switzerland Frontiers Research Foundation 01.01.2010
Frontiers Media S.A
Subjects
Axiom Testing
Psychology
random utility
Rationalizability
Stochastic Transitivity
Transitivity
Triangle Inequality
axiom testing
rationalizability
random utility
transitivity
triangle inequality
stochastic transitivity
utility theory
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Summary:As Duncan Luce and other prominent scholars have pointed out on several occasions, testing algebraic models against empirical data raises difficult conceptual, mathematical, and statistical challenges. Empirical data often result from statistical sampling processes, whereas algebraic theories are nonprobabilistic. Many probabilistic specifications lead to statistical boundary problems and are subject to nontrivial order constrained statistical inference. The present paper discusses Luce's challenge for a particularly prominent axiom: Transitivity. The axiom of transitivity is a central component in many algebraic theories of preference and choice. We offer the currently most complete solution to the challenge in the case of transitivity of binary preference on the theory side and two-alternative forced choice on the empirical side, explicitly for up to five, and implicitly for up to seven, choice alternatives. We also discuss the relationship between our proposed solution and weak stochastic transitivity. We recommend to abandon the latter as a model of transitive individual preferences.
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Reviewed by: Jürgen Heller, Universität Tübingen, Germany; Reinhard Suck, University of Osnabrück, Germany; Ulf Böckenholt, Northwestern University, USA
Edited by: Hans Colonius, Carl von Ossietzky Universität Oldenburg, Germany
This article was submitted to Frontiers in Quantitative Psychology and Measurement, a specialty of Frontiers in Psychology.
ISSN:1664-1078
1664-1078
DOI:10.3389/fpsyg.2010.00148