Commentary: “Neural signatures of intransitive preferences”

Kalenscher et al. (2010) explored the neural signatures of intransitive preferences. This endeavor is of great interest because transitivity of preferences has long been considered a key feature of rationality. The success of this approach hinges upon appropriate methods for identifying decision makers with intransitive preferences. The authors invented a descriptive numerical “index of intransitivity” (henceforth labeled K. Index) that we argue is not grounded in a quantitative model of choice behavior. We revisit the authors’ original data and reclassify the participants using two well-known and well-established quantitative criteria for transitive preferences, the random preference model of transitive linear orders (Block and Marschak, 1960; Becker et al., 1963) and weak stochastic transitivity (Block and Marschak, 1960; Tversky, 1969; Iverson and Falmagne, 1985). These two models of transitive preferences embody two different ways to capture uncertainty/variability of behavior formally. According to the random preference model, preferences are probabilistic, while responses are deterministic (error-free). According to weak stochastic transitivity, preferences are deterministic and responses are probabilistic (noisy). Suitable statistical tests for these models have only recently become broadly available. Similar to the seminal study of Tversky (1969), Kalenscher et al.’s task consisted of twoalternative forced choices among binary lotteries, with reward size and probability of a reward trading off against each other. Using a set of five lotteries, the data of interest consist of 200 responses per person, 20 repetitions for each of the 10 pairs of lotteries. Eighteen of their 30 participants scored a K. Index > 0.3 and were classified as intransitive. The authors motivated the K. Index as a means to evaluate weak stochastic transitivity. Economists and psychologists have studied the conceptual challenges of taking a deterministic axiom like transitivity and expanding it into a probability model to incorporate the inherent uncertainty in human behavior (Luce, 1959; Block and Marschak, 1960; Luce and Narens, 1994; Loomes and Sugden, 1995; Hey, 2005). Equally importantly, recent work has provided the statistical tools needed to evaluate such models (Myung et al., 2005; Davis-Stober, 2009; Cavagnaro and Davis-Stober, 2014; Regenwetter et al., 2014). Regenwetter et al. (2010, 2011a) gave an in-depth critique of the literature on testing transitivity of preferences. These papers contributed three main points relevant to this discussion: