Many policies allocate harms or benefits that are uncertain in nature: they produce distributions over the population in which individuals have different probabilities of incurring harm or benefit. Comparing different policies thus involves a comparison of their corresponding probability distributions, and we observe that in many instances the policies selected in practice are hard to explain by preferences based only on the expected value of the total harm or benefit they produce. In cases where the expected value analysis is not a sufficient explanatory framework, what would be a reasonable model for societal preferences over these distributions? Here we investigate explanations based on the framework of probability weighting from the behavioral sciences, which over several decades has identified systematic biases in how people perceive probabilities. We show that probability weighting can be used to make predictions about preferences over probabilistic distributions of harm and benefit that function quite differently from expected-value analysis, and in a number of cases provide potential explanations for policy preferences that appear hard to motivate by other means. In particular, we identify optimal policies for minimizing perceived total harm and maximizing perceived total benefit that take the distorting effects of probability weighting into account, and we discuss a number of real-world policies that resemble such allocational strategies. Our analysis does not provide specific recommendations for policy choices, but is instead fundamentally interpretive in nature, seeking to describe observed phenomena in policy choices.
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