Further perceptions of probability: Accurate, stepwise updating is contingent on prior information about the task and the response mode.

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To adapt to an uncertain world, humans must learn event probabilities. These probabilities may be stationary, such as that of rolling a 6 on a die, or changing over time, like the probability of rainfall over the year. Research on how people estimate and track changing probabilities has recently reopened an old epistemological issue. A small, mostly recent literature finds that people accurately track the probability and change their estimates only occasionally, resulting in staircase-shaped response patterns. This has been taken as evidence that people entertain beliefs about unknown, distal states of the world, which are tested against observations to produce discrete shifts between hypotheses. That idea stands in contrast to the claim that people learn by continuously updating associations between observed events. The purpose of this article is to investigate the generality and robustness of the accurate, staircase-shaped pattern. In two experiments, we find that the response pattern is contingent on the response mode and prior information about the generative process. Participants exist on continua of accuracy and staircase-ness and we only reproduce previous results when changing estimates is effortful and prior information is provided-the specific conditions of previous experiments. We conclude that explaining this solely through either hypotheses or associations is untenable. A complete theory of probability estimation requires the interaction of three components: (i) online tracking of observed data, (ii) beliefs about the unobserved "generative process," and (iii) a response updating process. Participants' overt estimates depend on how the specific task conditions jointly determine all three.