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A Two-interval Forced-choice Task for Multisensory Comparisons
Published on: November 9, 2018
Testing transitivity of preferences on two-alternative forced choice data.
Michel Regenwetter1, Jason Dana, Clintin P Davis-Stober
1Department of Psychology, University of Illinois at Urbana-Champaign Champaign, IL, USA.
Frontiers in Psychology
|August 12, 2011
Summary
This study addresses challenges in testing algebraic choice models with empirical data, offering a robust solution for assessing transitivity in preferences. It recommends abandoning weak stochastic transitivity for modeling individual preferences.
Area of Science:
- Decision Sciences
- Mathematical Psychology
- Statistics
Background:
- Testing algebraic choice models against empirical data presents significant conceptual, mathematical, and statistical challenges.
- Empirical data are inherently probabilistic, while algebraic theories are typically nonprobabilistic, leading to complex statistical inference problems.
- Duncan Luce highlighted the difficulties in reconciling these theoretical and empirical frameworks, particularly concerning axioms like transitivity.
Purpose of the Study:
- To address Duncan Luce's challenge regarding the empirical testing of the transitivity axiom in algebraic preference and choice theories.
- To provide a comprehensive solution for evaluating the transitivity of binary preferences using two-alternative forced choice data.
- To clarify the relationship between the proposed solution and weak stochastic transitivity, offering a recommendation for their use.
Main Methods:
- Developed a theoretical framework for assessing the transitivity of binary preferences.
- Utilized two-alternative forced choice (TAFC) data as the empirical basis for testing.
- Provided explicit solutions for up to five choice alternatives and implicit solutions for up to seven.
Main Results:
- Presented the most complete solution to date for testing the transitivity axiom within the specified theoretical and empirical constraints.
- Analyzed the mathematical and statistical properties of the proposed solution.
- Demonstrated the relationship between the proposed transitivity test and weak stochastic transitivity.
Conclusions:
- The proposed method offers a robust approach to empirically validating the transitivity axiom in choice theory.
- Weak stochastic transitivity is found to be an inadequate model for representing transitive individual preferences.
- The study recommends abandoning weak stochastic transitivity in favor of more appropriate models for individual choice.
Keywords:
axiom testingrandom utilityrationalizabilitystochastic transitivitytransitivitytriangle inequalityutility theoryMore Related Videos
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