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In this study, we explore how people integrate risks of assets in a simulated financial market into a judgment of the conjunctive risk that all assets decrease in value, both when assets are independent and when there is a systematic risk present affecting all assets. Simulations indicate that while mental calculation according to naïve application of probability theory is best when the assets are independent, additive or exemplar-based algorithms perform better when systematic risk is high. Considering that people tend to intuitively approach compound probability tasks using additive heuristics, we expected the participants to find it easiest to master tasks with high systematic risk – the most complex tasks from the standpoint of probability theory – while they should shift to probability theory or exemplar memory with independence between the assets. The results from 3 experiments confirm that participants shift between strategies depending on the task, starting off with the default of additive integration. In contrast to results in similar multiple cue judgment tasks, there is little evidence for use of exemplar memory. The additive heuristics also appear to be surprisingly context-sensitive, with limited generalization across formally very similar tasks.

A joint probability judgment is an estimation of the probability that a number of uncertain events will occur simultaneously. Many cognitive theories suggest processes by which the probability estimates of individual events are combined to form a joint probability judgment, often supported by behavioral experiments. However, representative selections of algorithms have rarely been compared side by side in order to evaluate their performance in a wide variety of ecological contexts, which could constitute an important insight into why and when people are likely to use different algorithms. To this end, five models informed by current research in joint probability judgment were applied to both computer generated and real-world data. The data were systematically varied regarding the number of events in a judgment, dependence between events, and precision in individual probability estimates. The models represented, respectively, (naïve) application of probability theory via multiplication, the representativeness heuristic, a variation on the take-the-best heuristic, weighted additive integration, and a general exemplar-based process. Application of the models to real-world data confirmed the conclusions from the computer generated data relative to real-world contexts. The results indicate that the weighted addition and exemplar-based models process information in a more efficient manner relative to the other models and perform accurately across a wide variety of contexts. It follows that weighted addition and/or exemplar-based models can represent “general-purpose” cognitive processes for joint probability judgment, in turn lending further credence to exemplar-based models as a mechanism for Bayesian inference.

Do people think of their environments in probabilistic concepts like “dependent” or “independent” events? Research has shown that people can learn from feedback to make accurate joint probability judgments in both cases, but it is unclear whether this implies an understanding of the task structure with respect to dependence. In this article, we report two experiments that investigate if accuracy in joint probability judgment tasks implies understanding the presence or absence of dependencies between the events in the task. Experiment 1 involved a symbolic task with stated numerical risks, whereas Experiment 2 compared this format with judgments from experience where the participants learned the joint probabilities from direct (binary) experience of the events occurring or not. The results demonstrate that participants rapidly learned to make accurate judgments of the joint probability both when events where dependent and independent, and computational modeling suggests that they draw on a variety of strategies ranging from analytic multiplication informed by probability theory, over heuristic weighted additive or weighted minimum models, to sampled proportions or exemplar memory. Despite successfully learning to accurately assess the joint probabilities, there were no indications that the participants successfully discovered whether the events were dependent or not. This suggests that rather than spontaneously thinking of the world in probabilistic terms, participants draw on generic cognitive resources with little or no conceptual overlap with notions of probability theory.