Human agents happen to judge that a conjunction of two terms is more probable than one of the terms, in contradiction with the rules of classical probabilities—this is the conjunction fallacy. One of the most discussed accounts of this fallacy is currently the quantum-like explanation, which relies on models exploiting the mathematics of quantum mechanics. The aim of this paper is to investigate the empirical adequacy of major quantum-like models which represent beliefs with quantum states. We first argue that they (...) can be tested in three different ways, in a question order effect configuration which is different from the traditional conjunction fallacy experiment. We then carry out our proposed experiment, with varied methodologies from experimental economics. The experimental results we get are at odds with the predictions of the quantum-like models. This strongly suggests that this quantum-like account of the conjunction fallacy fails. Future possible research paths are discussed. (shrink)

The conjunction fallacy is the well-documented empirical finding that subjects sometimes rate a conjunction A&B as more probable than one of its conjuncts, A. Most explanations appeal in some way to the fact that B has a high probability. But Tentori et al. (2013) have recently challenged such approaches, reporting experiments which find that (1) when B is confirmed by relevant evidence despite having low probability, the fallacy is common, and (2) when B has a high probability but has not (...) been confirmed by relevant evidence, the fallacy is less common. They conclude that degree of confirmation, rather than probability, is the central determinant of the conjunction fallacy. In this paper, we address a confound in these experiments: Tentori et al. (2013) failed to control for the fact that their (1)-situations make B conversationally relevant, while their (2)-situations do not. Hence their results are consistent with the hypothesis that con- versationally relevant high probability is an important driver of the conjunction fallacy. Inspired by recent theoretical work that appeals to conversational relevance to explain the conjunction fallacy, we report on two experiments that control for this issue by making B relevant without changing its degree of probability or confirmation. We find that doing so increases the rate of the fallacy in (2)-situations, and leads to comparable fallacy-rates as (1)-situations. This suggests that (non-probabilistic) conversational relevance indeed plays a role in the conjunction fallacy, and paves the way toward further work on the interplay between relevance and confirmation. (shrink)

Bayesianism provides a rich theoretical framework, which lends itself rather naturally to the explication of various “contrastive” and “non-contrastive” concepts. In this (brief) discussion, I will focus on issues involving “contrastivism”, as they arise in some of the recent philosophy of science, epistemology, and cognitive science literature surrounding Bayesian confirmation theory.

ABSTRACTProbability judgements entail a conjunction fallacy if a conjunction is estimated to be more probable than one of its conjuncts. In the context of predication of alternative logical hypothesis, Bayesian logic provides a formalisation of pattern probabilities that renders a class of pattern-based CFs rational. BL predicts a complete system of other logical inclusion fallacies. A first test of this prediction is investigated here, using transparent tasks with clear set inclusions, varying in observed frequencies only. Experiment 1 uses data where (...) BL makes dominant predictions; Experiment 2's predictions were less clear, and we additionally investigated judgements about the second-most probable hypotheses. The results corroborated a pattern-probability account and cannot be easily explained by other theories of CFs. IFs were not limited to conjunctions, but rather occurred systematically for several logical connectives. Thus, pattern-based prob... (shrink)

This essay addresses the methodology of philosophy of science and illustrates how formal and empirical methods can be fruitfully combined. Special emphasis is given to the application of experimental methods to confirmation theory and to recent work on the conjunction fallacy, a key topic in the rationality debate arising from research in cognitive psychology. Several other issue can be studied in this way. In the concluding section, a brief outline is provided of three further examples.

In a series of three behavioral experiments, we found a systematic distortion of probability judgments concerning elementary visual stimuli. Participants were briefly shown a set of figures that had two features (e.g., a geometric shape and a color) with two possible values each (e.g., triangle or circle and black or white). A figure was then drawn, and participants were informed about the value of one of its features (e.g., that the figure was a “circle”) and had to predict the value (...) of the other feature (e.g., whether the figure was “black” or “white”). We repeated this procedure for various sets of figures and, by varying the statistical association between features in the sets, we manipulated the probability of a feature given the evidence of another (e.g., the posterior probability of hypothesis “black” given the evidence “circle”) as well as the support provided by a feature to another (e.g., the impact, or confirmation, of evidence “circle” on the hypothesis “black”). Results indicated that participants’ judgments were deeply affected by impact, although they only should have depended on the probability distributions over the features, and that the dissociation between evidential impact and posterior probability increased the number of errors. The implications of these findings for lower and higher level cognitive models are discussed. (shrink)

Inductive reasoning requires exploiting links between evidence and hypotheses. This can be done focusing either on the posterior probability of the hypothesis when updated on the new evidence or on the impact of the new evidence on the credibility of the hypothesis. But are these two cognitive representations equally reliable? This study investigates this question by comparing probability and impact judgments on the same experimental materials. The results indicate that impact judgments are more consistent in time and more accurate than (...) probability judgments. Impact judgments also predict the direction of errors in probability judgments. These findings suggest that human inductive reasoning relies more on estimating evidential impact than on posterior probability. (shrink)