Transitivity of preferences is a fundamental principle shared by most major contemporary rational, prescriptive, and descriptive models of decision making. To have transitive preferences, a person, group, or society that prefers choice option x to y and y to z must prefer x to z. Any claim of empirical violations of transitivity by individual decision makers requires evidence beyond a reasonable doubt. We discuss why unambiguous evidence is currently lacking and how to clarify the issue. In counterpoint to Tversky's (1969) seminal "Intransitivity of Preferences," we reconsider his data as well as those from more than 20 other studies of intransitive human or animal decision makers. We challenge the standard operationalizations of transitive preferences and discuss pervasive methodological problems in the collection, modeling, and analysis of relevant empirical data. For example, violations of weak stochastic transitivity do not imply violations of transitivity of preference. Building on past multidisciplinary work, we use parsimonious mixture models, where the space of permissible preference states is the family of (transitive) strict linear orders. We show that the data from many of the available studies designed to elicit intransitive choice are consistent with transitive preferences.

Behavioral decision research compares theoretical constructs like preferences to behavior such as observed choices. Three fairly common links from constructs to behavior are (1) to tally, across participants and decision problems, the number of choices consistent with one predicted pattern of pairwise preferences; (2) to compare what most people choose in each decision problem against a predicted preference pattern; or (3) to enumerate the decision problems in which two experimental conditions generate a 1-sided significant difference in choice frequency 'consistent' with the theory. Although simple, these theoretical links are heuristics. They are subject to well-known reasoning fallacies, most notably the fallacy of sweeping generalization and the fallacy of composition. No amount of replication can alleviate these fallacies. On the contrary, reiterating logically inconsistent theoretical reasoning over and again across studies obfuscates science. As a case in point, we consider pairwise choices among simple lotteries and the hypotheses of overweighting or underweighting of small probabilities, as well as the description-experience gap. We discuss ways to avoid reasoning fallacies in bridging the conceptual gap between hypothetical constructs, such as, for example, "overweighting" to observable pairwise choice data. Although replication is invaluable, successful replication of hard-to-interpret results is not. Behavioral decision research stands to gain much theoretical and empirical clarity by spelling out precise and formally explicit theories of how hypothetical constructs translate into observable behavior. (PsycINFO Database Record

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.

Theories of rational choice often make the structural consistency assumption that every decision maker’s binary strict preference among choice alternatives forms a strict weak order. Likewise, the very concept of a utility function over lotteries in normative, prescriptive, and descriptive theory is mathematically equivalent to strict weak order preferences over those lotteries, while intransitive heuristic models violate such weak orders. Using new quantitative interdisciplinary methodologies we dissociate variability of choices from structural inconsistency of preferences. We show that laboratory choice behavior among stimuli of a classical “intransitivity” paradigm is, in fact, consistent with variable strict weak order preferences. We find that decision makers act in accordance with a restrictive mathematical model that, for the behavioral sciences, is extraordinarily parsimonious. Our findings suggest that the best place to invest future behavioral decision research is not in the development of new intransitive decision models, but rather in the specification of parsimonious models consistent with strict weak order(s), as well as heuristics and other process models that explain why preferences appear to be weakly ordered.

The goal of this paper is to make modeling and quantitative testing accessible to behavioral decision researchers interested in substantive questions. We provide a novel, rigorous, yet very general, quantitative diagnostic framework for testing theories of binary choice. This permits the nontechnical scholar to proceed far beyond traditionally rather superficial methods of analysis, and it permits the quantitatively savvy scholar to triage theoretical proposals before investing effort into complex and specialized quantitative analyses. Our theoretical framework links static algebraic decision theory with observed variability in behavioral binary choice data. The paper is supplemented with a custom-designed public-domain statistical analysis package, the QTest software. We illustrate our approach with a quantitative analysis using published laboratory data, including tests of novel versions of “Random Cumulative Prospect Theory.” A major asset of the approach is the potential to distinguish decision makers who have a fixed preference and commit errors in observed choices from decision makers who waver in their preferences.