Objectives. We offer a typology of possible reforms to the Electoral College (EC) in terms of changes to its two most important structural features: seat allocations that are not directly proportional to population and winner-take-all outcomes at the state level. This typology allows us to classify four major variants of "reform" to the present EC in a parsimonious fashion. Many of the proposals we consider have been suggested by well-known figures, some debated in Congress, and they include what we view as most likely to be taken seriously. We evaluate these proposals solely in terms of one simple criterion: "Would they be expected to reduce the likelihood of inversions between EC and popular vote outcomes?" Methods. We answer this question by looking at the data on actual presidential election outcomes at the state level over the entire period 1868-2016, and at the congressional-district level over the period 1956-2016. We consider the implications for presidential outcomes of these different alternative mechanisms, in comparison to the actual electoral outcome and the popular vote outcome. In addition, we consider the implications of a proposal to increase the size of the U.S. House (Ladewig and Jasinski, 2008). Results. Our results show that inversions from the popular vote happen under all proposed alternatives at nearly the same rate as under the current EC rules, with some proposals actually making inversions more frequent. Conclusions. The major difference between the present EC rule and alternative rules is not in frequency of inversions, but is in which particular years the inversions occur. As for the proposal to increase the size of the House, we show that any realistic increase in House size would have made no difference for the 2016 outcome."The Electoral College is a disaster for democracy."

Democracy often fails to meet its ideals, and these failures may be made worse by electoral institutions. Unwanted outcomes include elite polarization, unresponsive representatives, and the ability of a faction of voters to gain power at the expense of the majority. Various reforms have been proposed to address these problems, but their effectiveness is difficult to predict against a backdrop of complex interactions. Here we outline a path for systems-level modeling to help understand and optimize repairs to US democracy. Following the tradition of engineering and biology, models of systems include mechanisms with dynamical properties that include nonlinearities and amplification (voting rules), positive feedback mechanisms (single-party control, gerrymandering), negative feedback (checks and balances), integration over time (lifetime judicial appointments), and low dimensionality (polarization). To illustrate a systems-level approach, we analyze three emergent phenomena: low dimensionality, elite polarization, and antimajoritarianism in legislatures. In each case, long-standing rules now contribute to undesirable outcomes as a consequence of changes in the political environment. Theoretical understanding at a general level will also help evaluate whether a proposed reform’s benefits will materialize and be lasting, especially as conditions change again. In this way, rigorous modeling may not only shape new lines of research but aid in the design of effective and lasting reform.

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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