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Perspective Article published: 13 December 2010 doi: 10.3389/fpsyg.2010.00148 Testing transitivity of preferences on two-alternative forced choice data Michel Regenwetter1*, Jason Dana 2 and Clintin P. Davis-Stober 3 1 Department of Psychology, University of Illinois at Urbana-Champaign, Champaign, IL, USA 2 Department of Psychology, University of Pennsylvania, Philadelphia, PA, USA 3 Department of Psychological Sciences, University of Missouri, Columbia, MO, USA Edited by: As Duncan Luce and other prominent scholars have pointed out on several occasions, testing Hans Colonius, Carl von Ossietzky algebraic models against empirical data raises difficult conceptual, mathematical, and statistical Universit?t Oldenburg, Germany challenges. Empirical data often result from statistical sampling processes, whereas algebraic Reviewed by: Jürgen Heller, Universit?t Tübingen, theories are nonprobabilistic. Many probabilistic specifications lead to statistical boundary Germany problems and are subject to nontrivial order constrained statistical inference. The present Reinhard Suck, University of paper discusses Luce’s challenge for a particularly prominent axiom: Transitivity. The axiom of Osnabrück, Germany transitivity is a central component in many algebraic theories of preference and choice. We Ulf B?ckenholt, Northwestern University, USA offer the currently most complete solution to the challenge in the case of transitivity of binary *Correspondence: preference on the theory side and two-alternative forced choice on the empirical side, explicitly Michel Regenwetter, Department of for up to five, and implicitly for up to seven, choi