To bring apportionment closer to quotas or the apportionment quotient closer to the population quotient, instead of using “distance,” we introduce f-divergence for utilitarianism and Bregman divergence for suitable optimization. Even in our relaxed condition, we find that we must use alpha-divergence for optimization and show that the minimization of alpha-divergence induces the same divisor methods that correspond to the Kolm-Atkinson social welfare function, which is bounded by constant relative risk aversion.