The underinformative formulation of conditional probability

Abstract

The phenomenon of base-rate neglect has elicited much debate. One arena of debate concerns how people make judgments under conditions of uncertainty. Another more controversial arena concerns human rationality. In this target article, we attempt to unpack the perspectives in the literature on both kinds of issues and evaluate their ability to explain existing data and their conceptual coherence. From this evaluation we conclude that the best account of the data should be framed in terms of a dualprocess model of judgment, which attributes base-rate neglect to associative judgment strategies that fail to adequately represent the set structure of the problem. Base-rate neglect is reduced when problems are presented in a format that affords accurate representation in terms of nested sets of individuals.

A New Test for Rationality: Contributions and Outstanding Issues

“…However, now this perspective is at the center of a debate. The psychology of thinking, by adopting a depsychologized standard, leaves outside some important psychological characteristics, such as sensitivity to context, content, implicit presuppositions, and conversational rules, which instead to be considered as causes of biases have to be considered fundamental adaptive factors (at least as well as the formal reasoning capacity), the bases of an "interactional intelligence" Hilton, 1995;Macchi, 1995Macchi, , 2000Macchi & Bagassi, 2007, 2014, 2015Macchi, Bagassi, & Passerini, 2006;Passerini, Macchi, & Bagassi, 2012;Politzer & Macchi, 2000). From this perspective many factors that were formerly seen as biases or shortcuts appear as legitimate inferences and rational procedures (see, for instance, the experiments on the "postal employee" reported in Bagassi & Macchi, 2016;Mosconi, 2016;Mosconi & D'Urso, 1975;Sperber, Cara, & Girotto, 1995).…”

Statistical formats to optimize evidence-based decision making: A behavioral approach

“…The psychological research on judgments under uncertainty typically asks subjects to solve a statistical problem and compares decisions between two choices with different wordings. However, as Girotto and Gonzalez (2007) point out, standard word problems are not the best instruments to test general hypotheses about the nature of human judgment (Macchi 2000;Macchi and Bagassi 2007;Macchi and Mosconi 1998). Brase (2002) simply and directly evaluates whether-apart from simplifying statistical inference tasks-simple frequencies defined on small reference groups are clearer than other formats.…”

Words, numbers, warnings, tips, but still low risk perception

“…We explored confusion in inversed conditional probabilities, the low awareness of the importance to define the base line in understanding percentages and the right denominators for frequency etc. (Barbey and Sloman 2007 ; Macchi 1995 , 2000 ; Macchi and Bagassi 2007 ), and how we formulate probabilistic judgments about low probability events (Koehler and Macchi 2004 ; Macchi et al 1999 ). And we find again these phenomena in the difficulty in representing the trend of, for instance, Covid-19 contagion, based on probability of contagion and mortality.…”