The conjunction fallacy: A test of averaging hypotheses

Biased Estimates of Environmental Impact in the Negative Footprint Illusion: The Nature of Individual Variation

People consistently act in ways that harm the environment, even when believing their actions are environmentally friendly. A case in point is a biased judgment termed the negative footprint illusion, which arises when people believe that the addition of "eco-friendly" items (e.g., environmentally certified houses) to conventional items (e.g., standard houses), reduces the total carbon footprint of the whole item-set, whereas the carbon footprint is, in fact, increased because eco-friendly items still contribute to the overall carbon footprint. Previous research suggests this illusion is the manifestation of an "averaging-bias." We present two studies that explore whether people's susceptibility to the negative footprint illusion is associated with individual differences in: (i) environment-specific reasoning dispositions measured in terms of compensatory green beliefs and environmental concerns; or (ii) general analytic reasoning dispositions measured in terms of actively open-minded thinking, avoidance of impulsivity and reflective reasoning (indexed using the Cognitive Reflection Test; CRT). A negative footprint illusion was demonstrated when participants rated the carbon footprint of conventional buildings combined with eco-friendly buildings (Study 1 and 2) and conventional cars combined with eco-friendly cars (Study 2). However, the illusion was not identified in participants' ratings of the carbon footprint of apples (Study 1 and 2). In Studies 1 and 2, environment-specific dispositions were found to be unrelated to the negative footprint illusion. Regarding reflective thinking dispositions, reduced susceptibility to the negative footprint illusion was only associated with actively open-minded thinking measured on a 7-item scale (Study 1) and 17-item scale (Study 2). Our findings provide partial support for the existence of a negative footprint illusion and reveal a role of individual variation in reflective reasoning dispositions in accounting for a limited element of differential susceptibility to this illusion.

Quantum Cognition

Uncertainty is an intrinsic part of life; most events, affairs, and questions are uncertain. A key problem in behavioral sciences is how the mind copes with uncertain information. Quantum probability theory offers a set of principles for inference, which align well with intuition about psychological processes in certain cases: cases when it appears that inference is contextual, the mental state changes as a result of previous judgments, or there is interference between different possibilities. We motivate the use of quantum theory in cognition and its key characteristics. For each of these characteristics, we review relevant quantum cognitive models and empirical support. The scope of quantum cognitive models encompasses fallacies in decision-making (such as the conjunction fallacy or the disjunction effect), question order effects, conceptual combination, evidence accumulation, perception, over-/underdistribution effects in memory, and more. Quantum models often formalize psychological ideas previously expressed in heuristic terms, allow unified explanations of previously disparate findings, and have led to several surprising, novel predictions. We also cast a critical eye on quantum models and consider some of their shortcomings and issues regarding their further development. Expected final online publication date for the Annual Review of Psychology, Volume 73 is January 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Random variation and systematic biases in probability estimation

A number of recent theories have suggested that the various systematic biases and fallacies seen in people's probabilistic reasoning may arise purely as a consequence of random variation in the reasoning process. The underlying argument, in these theories, is that random variation has systematic regressive effects, so producing the observed patterns of bias. These theories typically take this random variation as a given, and assume that the degree of random variation in probabilistic reasoning is sufficiently large to account for observed patterns of fallacy and bias; there has been very little research directly examining the character of random variation in people's probabilistic judgement. We describe 4 experiments investigating the degree, level, and characteristic properties of random variation in people's probability judgement. We show that the degree of variance is easily large enough to account for the occurrence of two central fallacies in probabilistic reasoning (the conjunction fallacy and the disjunction fallacy), and that level of variance is a reliable predictor of the occurrence of these fallacies. We also show that random variance in people's probabilistic judgement follows a particular mathematical model from frequentist probability theory: the binomial proportion distribution. This result supports a model in which people reason about probabilities in a way that follows frequentist probability theory but is subject to random variation or noise.

Sampling as a resource-rational constraint

Resource rationality is useful for choosing between models with the same cognitive constraints but cannot settle fundamental disagreements about what those constraints are. We argue that sampling is an especially compelling constraint, as optimizing accumulation of evidence or hypotheses minimizes the cost of time, and there are well-established models for doing so which have had tremendous success explaining human behavior.

On cognitive preferences and the plausibility of rule-based models

It is conventional wisdom in machine learning and data mining that logical models such as rule sets are more interpretable than other models, and that among such rule-based models, simpler models are more interpretable than more complex ones. In this position paper, we question this latter assumption by focusing on one particular aspect of interpretability, namely the plausibility of models. Roughly speaking, we equate the plausibility of a model with the likeliness that a user accepts it as an explanation for a prediction. In particular, we argue that—all other things being equal—longer explanations may be more convincing than shorter ones, and that the predominant bias for shorter models, which is typically necessary for learning powerful discriminative models, may not be suitable when it comes to user acceptance of the learned models. To that end, we first recapitulate evidence for and against this postulate, and then report the results of an evaluation in a crowdsourcing study based on about 3000 judgments. The results do not reveal a strong preference for simple rules, whereas we can observe a weak preference for longer rules in some domains. We then relate these results to well-known cognitive biases such as the conjunction fallacy, the representative heuristic, or the recognition heuristic, and investigate their relation to rule length and plausibility.

Parallel Interactive Processing as a Way to Understand Complex Information Processing: The Conjunction Fallacy and Other Examples

Parallel interactive processing (PIP) represents an approach in which specific context generates interactive relationships between general attributes. This article summarizes previous research that demonstrates how such relationships influence inference making in categorization. This is followed by evidence that the approach can be extended to other areas of cognition, including probability judgments. PIP was successful in fitting data that revealed the prevalence of the conjunction fallacy as well as other probability estimation data. PIP provided better fits overall than the signed summation model and the configural weighted average model. The quantum probability model provided good fits for the conjunction fallacy data but not for other probability judgments.

Surprising rationality in probability judgment: Assessing two competing models

We describe 4 experiments testing contrasting predictions of two recent models of probability judgment: the quantum probability model (Busemeyer, Pothos, Franco, & Trueblood, 2011) and the probability theory plus noise model (Costello & Watts, 2014, 2016a). Both models assume that people estimate probability using formal processes that follow or subsume standard probability theory. One set of predictions concerned agreement between people's probability estimates and standard probability theory identities. The quantum probability model predicts people's estimates should agree with one set of identities, while the probability theory plus noise model predicts a specific pattern of violation of those identities. Experimental results show the specific pattern of violation predicted by the probability theory plus noise model. Another set of predictions concerned the conjunction fallacy, which occurs when people judge the probability of a conjunction P(A∧B) to be greater than one or other constituent probabilities P(A) or P(B), contrary to the requirements of probability theory. In cases where A causes B, the quantum probability model predicts that the conjunction fallacy should only occur for constituent B and not for constituent A: the noise model predicts that the fallacy should occur for both A and B. Experimental results show that the fallacy occurs equally for both, contrary to the quantum probability prediction. These results suggest that people's probability estimates do not follow quantum probability theory. These results support the idea that people estimate probabilities using mechanisms that follow standard probability theory but are subject to random noise.

The Conjunction and Disjunction Fallacies: Explanations of the Linda Problem by the Equate-to-Differentiate Model

We propose the use of the equate-to-differentiate model (Li, S. (2004), Equate-to-differentiate approach, Central European Journal of Operations Research, 12) to explain the occurrence of both the conjunction and disjunction fallacies. To test this model, we asked participants to judge the likelihood of two multi-statements and their four constituents in two modified versions of the Linda problem in two experiments. The overall results underpin this pragmatic model's inference and also reveal that (1) single conjunction and disjunction fallacies are most prevalent, (2) the incidence of the conjunction fallacy is proportional to the distance between the constituent probabilities, and (3) some participants misinterpreted A ∧ B either as ¬ A ∧ B or A ∨ B. The findings were generally consistent with the configural weighted average model (Nilsson, H., Winman, A., Juslin, P., & Hansson, G. (2009), Linda is not a bearded lady, Journal of Experimental Psychology: General, 138) and the potential surprise conceptual framework (Fisk, J. E. (2002), Judgments under uncertainty, British Journal of Psychology, 93).

Is experiential-intuitive cognitive style more inclined to err on conjunction fallacy than analytical-rational cognitive style?

In terms of prediction by Epstein’s integrative theory of personality, cognitive-experiential self-theory (CEST), those people with experiential-intuitive cognitive style are more inclined to induce errors than the other people with analytical-rational cognitive style in the conjunction fallacy (two events that can occur together are seen as more likely than at least one of the two events). We tested this prediction in a revised Linda problem. The results revealed that rational and experiential cognitive styles do not statistically influence the propensity for committing the conjunction fallacy, which is contrary to the CEST’s predictions. Based on the assumption that the rational vs. experiential processing is a personality trait with comparatively stabile specialities, these findings preliminarily indicate that those people who are characterized by “rational thinking” are not more inclined to use Bayes’ deduction than the other people who are labeled by “intuitive thinking” or by “poor thinking.”

Corpus-based estimates of word association predict biases in judgment of word co-occurrence likelihood

This paper draws a connection between statistical word association measures used in linguistics and confirmation measures from epistemology. Having theoretically established the connection, we replicate, in the new context of the judgments of word co-occurrence, an intriguing finding from the psychology of reasoning, namely that confirmation values affect intuitions about likelihood. We show that the effect, despite being based in this case on very subtle statistical insights about thousands of words, is stable across three different experimental settings. Our theoretical and empirical results suggest that factors affecting traditional reasoning tasks are also at play when linguistic knowledge is probed, and they provide further evidence for the importance of confirmation in a new domain.

Judgment and decision making: Behavioral approaches

The area of judgment and decision making has given rise to the study of many interesting phenomena, including reasoning fallacies, which are also of interest to behavior analysts. Indeed, techniques and principles of behavior analysis may be applied to study these fallacies. This article reviews research from a behavioral perspective that suggests that humans are not the information-seekers we sometimes suppose ourselves to be. Nor do we utilize information effectively when it is presented. This is shown from the results of research utilizing matching to sample and other behavioral tools (monetary reward, feedback, instructional control) to study phenomena such as the conjunction fallacy, base-rate neglect, and probability matching. Research from a behavioral perspective can complement research from other perspectives in furthering our understanding of judgment and decision making.

The sunk cost effect with pigeons: some determinants of decisions about persistence

The sunk cost effect occurs when an individual persists following an initial investment, even when persisting is costly in the long run. The current study used a laboratory model of the sunk cost effect. Two response alternatives were available: Pigeons could persist by responding on a schedule key with mixed ratio requirements, or escape by responding on a second key. In Experiment 1, mean response requirements for persistence and escape were varied across conditions. Pigeons persisted (committing the sunk cost error) when persisting increased the mean response requirement only slightly but not when persisting was sufficiently nonoptimal. Experiment 2 explored more systematically combinations of ratios and probabilities assigned to the schedule key. Persistence varied with the ratio of the mean global response requirements for persistence and escape. In Experiment 3, transitions between ratios were signaled. This reduced nonoptimal persistence, and produced some instances of a reverse sunk cost error--escaping when persistence was optimal. In Experiment 4, it was optimal to escape after the second-smallest ratio ever presented. Pigeons escaped at approximately the optimal juncture, especially in conditions with added signals. Overall, this series of experiments suggests that the sunk cost error may arise in part because persistence is the default behavioral strategy in situations where the contingencies for escape and persistence are insufficiently disparate and/or it is relatively difficult to discriminate when to escape. The study also demonstrates the utility of animal models of complex decision making situations.

"Falácia da conjunção": definição e variáveis de controle

A falácia da conjunção ocorre quando a conjunção de dois eventos é julgada como mais provável de ocorrer do que seus eventos constituintes. Esse fenômeno tem sido investigado principalmente por psicólogos cognitivistas, mas, recentemente, tem atraído o interesse de alguns analistas do comportamento. O presente trabalho consiste em um resumo da literatura sobre falácia, no qual são enfatizadas as estratégias metodológicas utilizadas e os resultados empíricos obtidos. Dentre as variáveis controladoras analisadas, são destacadas a representatividade, o uso inadequado de regras probabilísticas, as experiências passadas com os eventos constituintes e compostos, o treino estatístico e os aspectos verbais e contextuais.

Testing boundary conditions for the conjunction fallacy: effects of response mode, conceptual focus, and problem type

Two experiments used within-subject designs to examine how conjunction errors depend on the use of (1) choice versus estimation tasks, (2) probability versus frequency language, and (3) conjunctions of two likely events versus conjunctions of likely and unlikely events. All problems included a three-option format verified to minimize misinterpretation of the base event. In both experiments, conjunction errors were reduced when likely events were conjoined. Conjunction errors were also reduced for estimations compared with choices, with this reduction greater for likely conjuncts, an interaction effect. Shifting conceptual focus from probabilities to frequencies did not affect conjunction error rates. Analyses of numerical estimates for a subset of the problems provided support for the use of three general models by participants for generating estimates. Strikingly, the order in which the two tasks were carried out did not affect the pattern of results, supporting the idea that the mode of responding strongly determines the mode of thinking about conjunctions and hence the occurrence of the conjunction fallacy. These findings were evaluated in terms of implications for rationality of human judgment and reasoning.

The rules we choose by

Hutchinson & Gigerenzer's functional approach to decision making has much in common with behavioral approaches. One of their central points is that "rules-of-thumb" often provide efficient decision strategies, use of which is both rational and generally optimal. We agree, but also caution that the misapplication of rules sometimes leads to non-optimal decisions.