Transitivity of preferences.

Abstract

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.

Economic irrationality is optimal during noisy decision making

“…Thus, when empirically obtained, such violations offer important theoretical constraints. Although WST violations have been reported in humans (11), recent research has shown that the vast majority of these putative violations were not statistically significant when a more appropriate statistical test is applied (20,22). It is thus an empirical question whether intransitivity, as predicted by our framework, will occur in human observers.…”

“…For w > 0, the alternative with two (out of three) winning attributes (A) will (on average) be chosen over an alternative that wins by a larger margin on a single attribute (B), because the input to the latter is more often dampened yielding a lower cumulative value. Thus, when the same three values are permuted circularly in three alternatives, the model predicts a violation of "weak stochastic transitivity" (WST) (11,20): A is chosen more often over B, B over C, and C over A (Fig. 1B; Table S2 for an illustration).…”

“…We could count in how many triplets per participant an intransitive circle was obtained. However, the statistical interpretation of this metric of intransitivity, based on pattern counting, is limited and controversial as explained elsewhere (20). Thus the design of experiment 1 was not suitable for rigorous examination of WST violations.]…”

“…1B, selective integration violates the principle of WST. The preference patterns in the cyclic trials in experiment 1 offer a widely used proxy for the degree of intransitivity; the conclusion that such patterns definitively violate WST can, however, be challenged in statistical grounds (20). [Cyclic trials were created using n different A, B, C triplets (Methods).…”

Monotonicity-based consensus states for the monometric rationalisation of ranking rules with application in decision making

“…which the votrix is monotone implies the property of strong stochastic transitivity [138]. A weaker property, usually referred to as weak stochastic transitivity, has also called the attention of researchers [136].…”