Writings

This article describes WhatIf: Software for Evaluating Counterfactuals, an R package that implements the methods for evaluating counterfactuals introduced in King and Zeng (2006a) and King and Zeng (2006b). It offers easy-to-use techniques for assessing a counterfactual’s model dependence without having to conduct sensitivity testing over specified classes of models. These same methods can be used to approximate the common support of the treatment and control groups in causal inference.

Classic (or "cumulative") case-control sampling designs do not admit inferences about quantities of interest other than risk ratios, and then only by making the rare events assumption. Probabilities, risk differences, and other quantities cannot be computed without knowledge of the population incidence fraction. Similarly, density (or "risk set") case-control sampling designs do not allow inferences about quantities other than the rate ratio. Rates, rate differences, cumulative rates, risks, and other quantities cannot be estimated unless auxiliary information about the underlying cohort such as the number of controls in each full risk set is available. Most scholars who have considered the issue recommend reporting more than just the relative risks and rates, but auxiliary population information needed to do this is not usually available. We address this problem by developing methods that allow valid inferences about all relevant quantities of interest from either type of case-control study when completely ignorant of or only partially knowledgeable about relevant auxiliary population information.

Although not widely known until much later, Al Gore received 202 more votes than George W. Bush on election day in Florida. George W. Bush is president because he overcame his election day deficit with overseas absentee ballots that arrived and were counted after election day. In the final official tally, Bush received 537 more votes than Gore. These numbers are taken from the official results released by the Florida Secretary of State's office and so do not reflect overvotes, undervotes, unsuccessful litigation, butterfly ballot problems, recounts that might have been allowed but were not, or any other hypothetical divergence between voter preferences and counted votes. After the election, the New York Times conducted a six month long investigation and found that 680 of the overseas absentee ballots were illegally counted, and no partisan, pundit, or academic has publicly disagreed with their assessment. In this paper, we describe the statistical procedures we developed and implemented for the Times to ascertain whether disqualifying these 680 ballots would have changed the outcome of the election. The methods involve adding formal Bayesian model averaging procedures to King's (1997) ecological inference model. Formal Bayesian model averaging has not been used in political science but is especially useful when substantive conclusions depend heavily on apparently minor but indefensible model choices, when model generalization is not feasible, and when potential critics are more partisan than academic. We show how we derived the results for the Times so that other scholars can use these methods to make ecological inferences for other purposes. We also present a variety of new empirical results that delineate the precise conditions under which Al Gore would have been elected president, and offer new evidence of the striking effectiveness of the Republican effort to convince local election officials to count invalid ballots in Bush counties and not count them in Gore counties.

The 2000 U.S. presidential election rekindled interest in possible electoral reform. While most of the popular and academic accounts focused on balloting irregularities in Florida, such as the now infamous "butterfly" ballot and mishandled absentee ballots, some also noted that this election marked only the fourth time in history that the candidate with a plurality of the popular vote did not also win the Electoral College. This "anti-democratic" outcome has fueled desire for reform or even outright elimination of the electoral college. We show that after appropriate statistical analysis of the available historical electoral data, there is little basis to argue for reforming the Electoral College. We first show that while the Electoral College may once have been biased against the Democrats, the current distribution of voters advantages neither party. Further, the electoral vote will differ from the popular vote only when the average vote shares of the two major candidates are extremely close to 50 percent. As for individual voting power, we show that while there has been much temporal variation in relative voting power over the last several decades, the voting power of individual citizens would not likely increase under a popular vote system of electing the president.

We address two long-standing survey research problems: measuring complicated concepts, such as political freedom or efficacy, that researchers define best with reference to examples and and what to do when respondents interpret identical questions in different ways. Scholars have long addressed these problems with approaches to reduce incomparability, such as writing more concrete questions – with uneven success. Our alternative is to measure directly response category incomparability and to correct for it. We measure incomparability via respondents’ assessments, on the same scale as the self-assessments to be corrected, of hypothetical individuals described in short vignettes. Since actual levels of the vignettes are invariant over respondents, variability in vignette answers reveals incomparability. Our corrections require either simple recodes or a statistical model designed to save survey administration costs. With analysis, simulations, and cross-national surveys, we show how response incomparability can drastically mislead survey researchers and how our approach can fix them.