Representativeness and conjoint probability.

Abstract

People commonly violate a basic rule of probability, judging a conjunction of events to be more probable than at least 1 of its component events. Many manifestations of this conjunction fallacy have been ascribed to people's reliance on the representativeness heuristic for judging probability. Some conjunction fallacies, however, have been ascribed to the incorrect rules people use to combine probabilities. In 2 experiments, representativeness was pitted against probability combination to determine the contributions of each to the fallacy. Even for exemplar representativeness problems, the fallacy stemmed primarily from the application of incorrect combination rules. Representativeness seemed to be involved only insofar as it influenced the probabilities of a conjunction's component events. Implications of these findings are discussed for the representativeness account of judgmental errors and the relation between similarity and probability.

Compositional Anomalies in the Semantics of Evidence

“…Gavanski and Roskos-Ewoldsen (1991) did not test (41) directly, although it is a testable condition, but rather they tested a consequence of (41), namely, that the average number of conjunction errors should be about the same for related and unrelated conjunctions. Gavanski and Roskos-Ewoldsen (1991) found no significant differences in the frequency of conjunction errors produced by related and unrelated conjunctions. The statistics reported in their study do not permit one to evaluate the power of their tests, but the fact that the null result was found in experiments with samples of 180 and 153 subjects, respectively, suggests that statistical power was sufficient to detect differences of moderate size.…”

“…Perhaps the similarity of the results for related and unrelated events is merely a coincidence resulting from a particular choice of propositions. Gavanski and Roskos-Ewoldsen (1991) provided evidence against this objection, as well as a sharper test of the generality of probability combination models. They selected propositions A 1 , A 2 , B 1 , and B 2 such that A 1 and A 2 pertained to the same issue, and B 1 and B 2 pertained to some other issue.…”

“…Next, we turn to an alternative theory of conjunction errors according to which these errors result from the application of improper mental rules when combining the probabilities of individual propositions (Gavanski and Roskos-Ewoldsen, 1991;Yates and Carlson, 1986). We review arguments for this theory, and then present new experimental results that cannot be explained by the improper rules hypothesized by Yates and Carlson (1986) and Gavanski and Roskos-Ewoldsen (1991). In the following section, we turn to compositional anomalies in counterfactual reasoning.…”

"Falácia da conjunção": definição e variáveis de controle

“…as regras estatísticas e leis de probabilidade (e.g., Gavanski & Roskos-Ewoldsen, 1991;Stolarz-Fantino, Fantino & Kulik, 1996;Tversky & Kahneman, 1983;Wolford, Taylor & Beck, 1990). Os julgamentos intuitivos da probabilidade de um evento composto são baseados em heurísticas da representatividade, as quais negligenciam considerações outras que não aquelas relacionadas com a similaridade entre um exemplo e um modelo.…”

“…Nos dois casos, a identificação da regra que controlou o julgamento da probabilidade do composto é baseada na comparação entre as probabilidades do composto e de seus constituintes. Controle pela soma das probabilidades dos constituintes é inferido quando a probabilidade estimada do composto é maior do que a probabilidade de ambos os eventos constituintes (e.g., Fantino & Savastano, 1996;Gavanski & Roskos-Ewoldsen, 1991;Rodrigues, 2005). Por outro lado, controle pela média das probabilidades dos constituintes é sugerido quando a probabilidade estimada do composto é maior do que a probabilidade do evento constituinte menos provável e menor do que aquela do evento constituinte mais provável (e.g., Fantino, Kulik, Stolarz-Fantino & Wright, 1997;Gavanski & Roskos-Ewoldsen, 1991;Shanteau, 1975;Zizzo, StolarzFantino, Wen & Fantino, 2000).…”