Legal, Political Science, and Economics Approaches to Measuring Malapportionment: The U.S. House, Senate, and Electoral College 1790–2010

Abstract

Objective. We compare and contrast methods for measuring malapportionment from different disciplines: law, political science, and economics. Methods. With data from the U.S. House, Senate, and Electoral College (EC) over the period 1790-2010, we compare disproportionality measures and compare both across time and between institutions. Results. We demonstrate that which approach to measurement we take can dramatically affect some of the conclusions we reach. However, we also demonstrate that the House and the EC are hardly malapportioned, regardless of which measure we use, while the level of malapportionment we observe in the Senate can depend on which measure we use. Conclusion. Since there are many axiomatic properties we might wish to satisfy, no one measure is uniformly best with respect to all feasible desiderata. However, one measure, the minimum population needed to win a majority, offers a readily comparable measure across legislatures and jurisdictions, and is easy for nonspecialists to understand. A view supported by some distinguished political scientists (see, e.g., Lee and Oppenheimer, 1999; Dahl, 2003) and repeated by journalists (see, e.g., Badger, 2016) is that the U.S. Senate is inherently undemocratic because of the equal weight given to each state in the Senate despite the vast discrepancy in population across the states. Similarly, it is part of the common wisdom that the Electoral College (EC) is currently highly malapportioned because its two-seat bonus based on Senate seats overweights small states (see, e.g., Toles, 2018). In addition to structural malapportionment introduced by the three-fifth's clause of the U.S. Constitution in the antebellum period, though there are some features of House apportionment that keep it from perfect proportionality, in the post-Baker v.

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