Testing Transitivity of Preferences on Two-Alternative Forced Choice Data

Frontiers in Psychology

Michel Regenwetter¹ 

关键词: axiom testing;    random utility;    rationalizability;    transitivity;    triangle inequality;    utility theory;    stochastic transitivity;   

DOI  :  10.3389/fpsyg.2010.00148

学科分类：心理学（综合）

来源: Frontiers

【 摘 要 】

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.

【 授权许可】

CC BY