Distinguishing between the effects of swing ratio and bias on outcomes in the US Electoral College, 1900–1992

We review a number of different statistical techniques for creating seats-votes curves and apply the most reliable of these to estimate seats-votes relationships in the US electoral college 1900–1992. We consider the now rejected claim, once firmly established as part of the common journalistic and even academic wisdom, that the US Electoral College has recently been strongly biased in favor of Republicans, and show that this claim was based largely on a confusion between bias (asymmetry in the electoral college gains earned by the votes received by different parties or candidates) and swing ratio (responsiveness of change in electoral college seat share to change in popular vote). Although there has been substantial bias during this century in the way the electoral college translates Democratic and Republican votes into electoral college seats, and for the earlier party of this century (from 1900 to 1940) that bias has been in favor of Republicans, to explain why many recent electoral college majorities have been so lopsided we must look not at bias but at swing ratio.We show that the swing ratio in the electoral college has generally been increasing since 1900, rising from an average value (1900–1924) around three to an average value (1976–1992) ranging from about five to about eight, depending upon which of the various statistical estimation techniques we use. Thus, for every one point vote share gain above 50 per cent, a winning presidential candidate in a two-candidate competition can now expect to pick up somewhere between a 5 percentage point and an 8 percentage point increase in electoral college seats—giving the illusion of mandate even for relatively close contests and frequently creating apparent landslides. We show that this historical rise in swing ratio in presidential elections is due almost entirely to changes in the responsiveness of outcomes in the US South as the influence of the Civil War slowly (very slowly) erodes. Drawing on the analysis of the determinants of bias and of swing ratio in the House of Representatives in Brady and Grofman (1991b), we show that the increases in electoral college swing can be accounted for by the nationalization of presidential competition as signaled by the decrease over time in the standard deviation of Democratic share of the two-party vote across states, and that changes in bias can be linked to changes in the magnitude of differences between the mean and the median of that distribution.     

Conceptualizing voter choice for directional and discounting models of two-candidate spatial competition in terms of shadow candidates

In contrast to the traditional modeling of voter choice based on proximity, under directional models, selection of candidates is based on the direction and/or intensity of change from a status quo or neutral point. Voter choice can also be modeled as representing both approaches, e.g., as a directional model with proximity restraint, or alternatively, in terms of proximity to discounted positions. We provide a unified perspective for these seemingly disparate models in terms of what we call “shadow” positions. We demonstrate that voter choice in a variety of spatial models including directional components can be viewed as proximity-based choices. Voters choose the candidate whose shadow is nearer, where shadow locations are defined by a simple transformation. We apply this approach to equilibrium analysis, showing that results for a discounted proximity model can be carried over – via shadows – to a variety of directional models.     

Optimizing group judgmental accuracy in the presence of interdependencies

Consider a group of people confronted with a dichotomous choice (for example, a yes or no decision). Assume that we can characterize each person by a probability, p _i, of making the ‘better’ of the two choices open to the group, such that we define ‘better’ in terms of some linear ordering of the alternatives. If individual choices are independent, and if the a priori likelihood that either of the two choices is correct is one half, we show that the group decision procedure that maximizes the likelihood that the group will make the better of the two choices open to it is a weighted voting rule that assigns weights, w _i, such that $$w_i \propto \log \frac{{p_i }} {{1 - p_i }}.$$ We then examine the implications for optimal group choice of interdependencies among individual choices.     

If you like the alternative vote (a.k.a. the instant runoff), then you ought to know about the Coombs rule

We consider four factors relevant to picking a voting rule to be used to select a single candidate from among a set of choices: (1) avoidance of Condorcet losers, (2) choice of Condorcet winners, (3) resistance to manipulability via strategic voting, (4) simplicity. However, we do not try to evaluate all voting rules that might be used to select a single alternative. Rather, our focus is restricted to a comparison between a rule which, under the name ‘instant runoff,’ has recently been pushed by electoral reformers in the US to replace plurality-based elections, and which has been advocated for use in plural societies as a means of mitigating ethnic conflict; and another similar rule, the ‘Coombs rule.’ In both rules, voters are required to rank order candidates. Using the instant runoff, the candidate with the fewest first place votes is eliminated; while under the Coombs rule, the candidate with the most last place votes is eliminated. The instant runoff is familiar to electoral system specialists under the name ‘alternative vote’ (i.e., the single transferable vote restricted to choice of a single candidate). The Coombs rule has gone virtually unmentioned in the electoral systems literature (see, however, Chamberlin et al., 1984). Rather than considering the properties of these two rules in the abstract, we evaluate them in the politically realistic situations where voters are posited to have (at least on balance) single-peaked preferences over alternatives. Evaluating the two rules under this assumption, we argue that the Coombs rule is directly comparable in that Coombs is always as good as AV with respect to two of our four criteria and it is clearly superior to AV with respect to one of the four criteria, namely criterion (2), and is potentially inferior only with respect to criterion (3). Key to this argument are two new propositions. The first new result shows that, under the posited assumption, for four alternatives or fewer, AV is always as likely or more likely to select the Condorcet winner than plurality. The second new result shows that, under the same assumptions, the Coombs rule will always select the Condorcet winner regardless of the number of alternatives.     

Nash equilibrium strategies in directional models of two- candidate spatial competition

The standard approach to two-party political competition in a multi-dimensional issue space models voters as voting for the alternative that is located closest to their own most preferred location. Another approach to understanding voter choice is based on preferred direction of change with respect to some specified neutral point (e.g., an origin or status quo point). For the two-dimensional Matthews directional model (Matthews, 1979), we provide geometric conditions in terms of the number of medians through the neutral point for there to be a Condorcet (undominated) direction. In this two-dimensional setting, the set of residual locations for which no Condorcet directions exist is identical to the null dual set (Schofield, 1978) and to the heart (Schofield, 1993). In two dimensions, for most locations of the origin/status quo point, a Condorcet direction exists and points toward the yolk, a geometric construct first identified by McKelvey (1986). We also provide some simulation results on the size of the null dual set in two dimensions when the underlying distribution of points is non-symmetric.     

Rethinking the partisan effects of higher turnout: So what's the question?

Controversy persists over the link between turnout and the likelihood of success of Democratic candidates (e.g., DeNardo, 1980, 1986; Zimmer, 1985; Tucker and Vedlitz, 1986; Piven and Cloward, 1988; Texeira, 1992; Radcliff, 1994, 1995; Erikson, 1995a, b). We argue that the authors in this debate have largely been talking past one another because of a failure to distinguish three quite different questions. The first question is: “Are low turnout voters more likely to vote Democratic than high turnout voters?” The second question is: “Should we expect that elections in which turnout is higher are ones in which we can expect Democrats to have done better?” The third question is the counterfactual: “If turnout were to have increased in some given election, would Democrats have done better?” We show the logical independence of the first two questions from one another and from the third, and argue that previous researchers have failed to recognize this logical independence – sometimes thinking they were answering question three when in fact they were answering either question one or question two. Reviewing previous research, we find that the answer to the first question once was YES but, for more recent elections at the presidential level, now appears to be NO, while, for congressional and legislative elections, the answer to the second question appears generally to be NO. However, the third question is essentially unanswerable absent an explicit model of why and how turnout can be expected to increase, and/or analyses of individual level panel data. Thus, the cross-sectional and pooled data analyses of previous research are of almost no value in addressing this third question.