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To award delegates in their presidential primary elections, the US Democratic Party uses Hamilton’s method of apportionment after eliminating any candidates (and their votes) that receive less than 15% of the total votes cast. We illustrate how a remaining candidate may have his or her delegate total decline as a result of other candidates being eliminated; this leads to a new elimination paradox. We relate that paradox to the new states, no show, and population paradoxes and show that divisor methods are not susceptible to the elimination paradox. We conclude with instances in which the elimination paradox may occur in other contexts, including parliamentary systems.

This paper examines the effect of redistricting on the law of 1/n, which posits that government spending increases with the number of legislative districts. Our analysis suggests that court-ordered redistricting in the 1960s significantly influenced the 1/n effect, because dividing districts (increasing their number) and merging districts (reducing their number) both reduce public spending. After redistricting, the positive relationship between seats and spending holds for lower chambers in bicameral legislatures. The US experience informs those interested in the design of bicameral institutions about the fiscal implications of legislative apportionment.

Different institutions can produce more (or less) preferred outcomes, in terms of citizens’ preferences. Consequently, citizen preferences over institutions may “inherit”—to use William Riker’s term—the features of preferences over outcomes. But the level of information and understanding required for this effect to be observable seems quite high. In this paper, we investigate whether Riker’s intuition about citizens acting on institutional preferences is borne out by an original empirical dataset collected for this purpose. These data, a survey commissioned specifically for this project, were collected as part of a larger nationally representative sample conducted right before the 2004 election. The results show that support for a reform to split a state’s Electoral College votes proportionally is explained by (1) which candidate one supports, (2) which candidate one thinks is likely to win the election under the existing system of apportionment, (3) preferences for abolishing the Electoral College in favor of the popular vote winner, and (4) statistical interactions between these variables. In baldly political terms, Kerry voters tend to support splitting their state’s Electoral College votes if they felt George W. Bush was likely to win in that state. But Kerry voters who expect Kerry to win their state favor winner-take-all Electoral College rules for their state. In both cases, mutatis mutandis, the reverse is true for Bush voters.

Estimating the impact of turnout on House election results is problematic because of endogeneity and omitted variable bias. The following study proposes an instrumental approach to correct for these problems by using a series of fixed effects two-stage least squares panel-data regression models covering three congressional apportionment cycles (1972–1980; 1982–1990; 1992–2000). The analysis tests whether voter participation decreases the House incumbent’s electoral support, regardless of the level of competition in the district. The study also aims to determine if an increase in participation benefits Democratic candidates and whether this effect is constant across apportionment cycles. The results show that the influence of turnout on incumbency vote share is conditional on the level of presidential support in the district. This finding is explained by the surge and decline thesis of Campbell (1960).

Partisan bias occurs when the translation of the popular vote into legislative seats differs between competing parties. This paper contains a theoretical and empirical analysis of the consequences of an efficient gerrymander for the partisan bias of an electoral system. Under partisan apportionment, bias is shown to depend on some structural features of the electoral environment; namely, the size of the voting population and the number of single-member districts within a political jurisdiction. A statistical analysis reveals the predicted relationships in data on Congressional elections across states in the 1950–1984 period. This paper highlights the importance of some measurable features of the electoral environment for determining bias and provides an indirect test of partisan gerrymandering in congressional apportionment processes.

One of the few “laws” of political science is the fairly regular relationship in any given plurality electoral system known as thecube law, transforming vote shares into seat shares. In this paper, we develop an altogether different and more robust paradigm relating seats to votes which generates similar results as the cube law. In our model, political parties bargain with each other for an expected number of seats using the ability to gerrymander in determining their bargaining strength. We find that an arbitrated solution to the seat-vote allocation problem generates solutions remarkably similar to the conventional cube-law-based solutions. Thus our model can in some way replace the cube law paradigm. With our model, we are able to evaluate the impact ofBaker v. Carr (1962) on gerrymandering. We also find that proportional representation results can be achieved within our model by allowing non-zero population deviations between districts.

This paper provides the first empirical study of delegate voting behavior on issues of slavery at the U.S. Constitutional Convention. We analyze two categories of votes: those related to apportionment and those related to the regulation of the slave trade. Although it is widely believed that delegates voted consistent with the interests of their states on issues of slavery, we find that for votes on apportionment, the effect of state interests was enhanced by both the delegate’s personal interest and his religious background. For votes regulating the slave trade, state interests had a significant effect but only within specific regions.