  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.
