How do people respond to a question when they are not certain of the answer? Probabilistic theories of cognition assume that the mind represents probability distributions over possible answers, but in practice people rarely recite these probability distributions out loud: instead they make simple guesses. Consider how you would express your belief about how many people live in the European Union. You would probably not say “a Gaussian with mean 300 million and standard deviation 50 million” — you would make a simple guess, such as “between 200 and 400 million”. Here we present a simple rational analysis of these guesses. We assume that communicating the full probability distribution in one’s head would take too much time, so people offer simple guesses in order to communicate a compressed version of this distribution. Drawing on information theory, we show that it is possible to measure how well a guess encodes a given probability distribution, and suggest that people tend to make guesses that provide the best such encoding. Two experiments provide preliminary evidence for the model. Our theory explains from first principles why guesses seem to strike a balance between accuracy and informativeness.
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