A New Perspective on Impartial and Unbiased Apportionment

TL;DR

This paper introduces a novel perspective on apportionment by focusing on 'families' of states and develops impartial and unbiased methods that improve fairness in seat allocation based on population distributions.

Contribution

It proposes a new family-based framework for apportionment and develops methods ensuring impartiality and unbiasedness in seat distribution.

Findings

Impartial methods allocate seats consistently across state families.

Unbiased methods ensure expected seat counts match divisor-method quotas.

The approach offers a fairer alternative to traditional apportionment techniques.

Abstract

How to fairly apportion congressional seats to states has been debated for centuries. We present an alternative perspective on apportionment, centered not on states but "families" of state, sets of states with "divisor-method" quotas with the same integer part. We develop ``impartial" and ``unbiased" apportionment methods. Impartial methods apportion the same number of seats to families of states containing the same total population, whether a family consists of many small-population states or a few large-population states. Unbiased methods apportion seats so that if states are drawn repeatedly from the same distribution, the expected number of seats apportioned to each family equals the expected divisor-method quota for that family.