  Is it possible to understand or imitate a policy maker's rationale by looking
at past decisions they made? We formalize this question as the problem of
learning social welfare functions belonging to the well-studied family of power
mean functions. We focus on two learning tasks; in the first, the input is
vectors of utilities of an action (decision or policy) for individuals in a
group and their associated social welfare as judged by a policy maker, whereas
in the second, the input is pairwise comparisons between the welfares
associated with a given pair of utility vectors. We show that power mean
functions are learnable with polynomial sample complexity in both cases, even
if the comparisons are social welfare information is noisy. Finally, we design
practical algorithms for these tasks and evaluate their performance.
