Volume 4, Issue 1

This paper demonstrates that conventional single regression estimators of voting preferences for groups within the electorate are unreliable when group-specific turnout rates are unknown. In this context, the relationship between voting choices and the composition of the electorate is defined by two applications of Goodman’s Identity. Several methods appear in the scholarly and litigation literature which attempt to estimate characteristics of this relationship with variants of “Goodman’s regression”, including “correlation analysis” and “homogeneous precinct analysis”. Most of these methods are inconsistent with the Identities. For all methods, the expected values and variances of the dependent variables and of all regression statistics are unknown. None of these methods are capable of identifying any of the underlying parameters, much less the statistical significance of any estimators. Consequently, none has any scientific validity.

Public policy relies strongly upon expert opinion, especially in risk assessment for rare events. But expert opinion is often inconsistent, both within and between experts. We therefore develop a statistical model for the elicited opinions, and use that to borrow strength across the responses through an exchangeable prior. Several versions of that prior are considered; the most advanced uses covariate information on the experts to characterize their areas of agreement and disagreement, which ultimately allows the estimation of the opinion of a synthetic expert whose covariates are selected by the analyst.This result depends upon a novel technique that incorporates the background information of the expert using hierarchical Dirichlet regression and a latent space model. As an illustration, in October 2008 we elicited opinions on the percentage of the popular vote that presidential candidate Barack Obama would win in North Carolina. Among the respondents, those who were conservative or who had lived in North Carolina for a longer period of time gave systematically lower percentages. Our method enables the analyst to infer the opinion of a respondent with a specified political inclination or number of years of residency.

In the election for President of the United States, the Electoral College is the body whose members vote to elect the President directly. Each state sends a number of delegates equal to its total number of representatives and senators in Congress; all but two states (Nebraska and Maine) assign electors pledged to the candidate that wins the state’s plurality vote. We investigate the effect on presidential elections if states were to assign their electoral votes according to results in each congressional district, and conclude that the direct popular vote and the current electoral college are both substantially fairer compared to those alternatives where states would have divided their electoral votes by congressional district.

Recent years have seen a wave of laws making it more difficult to vote in the United States. Their ostensible purpose is to prevent voting by persons not legally qualified, and thus to improve public confidence in electoral integrity. Are such laws in fact needed to address serious fraud problems? On the other hand, how many and what kinds of legitimate voters will be, or have been, disenfranchised by them? Is voter confidence positively, or negatively, affected by voter ID laws? This article surveys what is known about these issues and offers suggestions for how statisticians can contribute.

Post-election audits are an important method for verifying the outcome of an election. Recent work on risk-limiting, post-election audits has focused almost exclusively on plurality elections. Several organization and municipalities use nonplurality methods such as range voting, the Borda count, and instant-runoff voting (IRV). We believe that it is crucial to develop effective methods of performing risk-limiting, post-election audits for these methods. We define a general notion of the margin of victory and develop risk-limiting auditing procedures for these nonplurality methods. For scored systems, we show how to adapt methods from plurality auditing. For IRV, the situation is markedly different. We provide a risk-limiting method for auditing the candidate elimination order. We provide a more efficient audit for the elections in which the margin of the IRV election can be efficiently calculated or bounded. We provide efficiently computable upper and lower bounds on the margin and, where possible, compare them to the exact margins for a large number of real elections.

This article examines some claims made in a recent popular book of political sociology, with the intent not being to debunk any claims but rather to connect some important social and policy positions to statistical data on income, social class, and political attitudes. The thesis of Charles Murray’s book is that America’s upper and lower classes have become increasingly separate, with elites living more disciplined, orderly lives (characterized by marriage, work, and stable families) while being largely unaware of the lifestyles of the majority of Americans. I argue that some of Murray’s conclusions are sensitive to particular choices of whom to label as elite or upper-class. From my analysis of survey data, I see the big culture war occurring within the upper class, whereas Murray focuses on differences in attitudes and lifestyles comparing rich to poor. Coming Apart is a lively contribution to current debates and complements more statistical analyses of political and social polarization.