A New Perspective on Impartial and Unbiased Apportionment

AbstractHow 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 states, 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. ACKNOWLEDGMENTThe authors thank the editor, editorial board, and reviewers for suggestions that improved the paper, and Carlos Reyes Zgarrick for his illustration of the apportionment slide rule.Additional informationNotes on contributorsRoss HymanROSS HYMAN received his Ph.D. in physics from Indiana University. He has been a physicist, a community organizer, a corporate researcher, a science teacher, a patent analyst, and a data scientist. He is currently a Grant Solutions Architect at the Research Computing Center of the University of Chicago. He has published academic papers in condensed matter theory, materials science, and voting theory. rhyman@uchicago.eduNicolaus TidemanNICOLAUS TIDEMAN received his Ph.D. in economics from the University of Chicago. He was an Assistant Professor at Harvard University and a Senior Staff Economist at the President’s Council of Economic Advisors before moving to Virginia Tech, where he is now a Professor. He publishes primarily in voting theory, public finance, and economic justice. ntideman@vt.edu