Apportionment Behind the Veil of Uncertainty

Apportionment of representatives is a basic rule of everyday politics. By definition, this basic rule is a constitutional stage problem and should be decided behind the veil of uncertainty. To bring apportionment closer to quotas, we introduce f-divergence for utilitarianism and Bregman divergence for consistent optimization. Even in our less restricted condition, we find that we must use α-divergence for optimization and show that the minimization of α-divergence induces the same divisor methods that correspond to the maximization of the Kolm–Atkinson social welfare function (or the expected utility function), which is bounded by constant relative risk aversion.