Publications by Author: Andrew Gelman

2012
Estimating Partisan Bias of the Electoral College Under Proposed Changes in Elector Apportionment
AC Thomas, Andrew Gelman, Gary King, and Jonathan N Katz. 2012. “Estimating Partisan Bias of the Electoral College Under Proposed Changes in Elector Apportionment.” Statistics, Politics, and Policy, Pp. 1-13. Statistics, Politics and Policy (publisher version)Abstract

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.

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2010
JudgeIt II: A Program for Evaluating Electoral Systems and Redistricting Plans
Andrew Gelman, Gary King, and Andrew Thomas. 2010. “JudgeIt II: A Program for Evaluating Electoral Systems and Redistricting Plans”.Abstract

A program for analyzing most any feature of district-level legislative elections data, including prediction, evaluating redistricting plans, estimating counterfactual hypotheses (such as what would happen if a term-limitation amendment were imposed). This implements statistical procedures described in a series of journal articles and has been used during redistricting in many states by judges, partisans, governments, private citizens, and many others. The earlier version was winner of the APSA Research Software Award.

Track JudgeIt Changes

2005
Gary King, Bernard Grofman, Andrew Gelman, and Jonathan Katz. 2005. “Brief of Amici Curiae Professors Gary King, Bernard Grofman, Andrew Gelman, and Jonathan Katz in Support of Neither Party.” U.S. Supreme Court in Jackson v. Perry.Abstract
For context, see Bernard Grofman and Gary King. 2008. “The Future of Partisan Symmetry as a Judicial Test for Partisan Gerrymandering after LULAC v. Perry.” Election Law Journal, 6, 1, Pp. 2-35.
Amici Brief
2004
Empirically Evaluating the Electoral College
Andrew Gelman, Jonathan Katz, and Gary King. 2004. “Empirically Evaluating the Electoral College.” In Rethinking the Vote: The Politics and Prospects of American Electoral Reform, edited by Ann N Crigler, Marion R Just, and Edward J McCaffery, Pp. 75-88. New York: Oxford University Press.Abstract

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.

Chapter PDF
1999
Not Asked and Not Answered: Multiple Imputation for Multiple Surveys
Andrew Gelman, Gary King, and Chuanhai Liu. 1999. “Not Asked and Not Answered: Multiple Imputation for Multiple Surveys.” Journal of the American Statistical Association, 93, Pp. 846–857.Abstract
We present a method of analyzing a series of independent cross-sectional surveys in which some questions are not answered in some surveys and some respondents do not answer some of the questions posed. The method is also applicable to a single survey in which different questions are asked or different sampling methods are used in different strata or clusters. Our method involves multiply imputing the missing items and questions by adding to existing methods of imputation designed for single surveys a hierarchical regression model that allows covariates at the individual and survey levels. Information from survey weights is exploited by including in the analysis the variables on which the weights are based, and then reweighting individual responses (observed and imputed) to estimate population quantities. We also develop diagnostics for checking the fit of the imputation model based on comparing imputed data to nonimputed data. We illustrate with the example that motivated this project: a study of pre-election public opinion polls in which not all the questions of interest are asked in all the surveys, so that it is infeasible to impute within each survey separately.
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1998
Estimating the Probability of Events that Have Never Occurred: When Is Your Vote Decisive?
Andrew Gelman, Gary King, and John Boscardin. 1998. “Estimating the Probability of Events that Have Never Occurred: When Is Your Vote Decisive?” Journal of the American Statistical Association, 93, Pp. 1–9.Abstract
Researchers sometimes argue that statisticians have little to contribute when few realizations of the process being estimated are observed. We show that this argument is incorrect even in the extreme situation of estimating the probabilities of events so rare that they have never occurred. We show how statistical forecasting models allow us to use empirical data to improve inferences about the probabilities of these events. Our application is estimating the probability that your vote will be decisive in a U.S. presidential election, a problem that has been studied by political scientists for more than two decades. The exact value of this probability is of only minor interest, but the number has important implications for understanding the optimal allocation of campaign resources, whether states and voter groups receive their fair share of attention from prospective presidents, and how formal "rational choice" models of voter behavior might be able to explain why people vote at all. We show how the probability of a decisive vote can be estimated empirically from state-level forecasts of the presidential election and illustrate with the example of 1992. Based on generalizations of standard political science forecasting models, we estimate the (prospective) probability of a single vote being decisive as about 1 in 10 million for close national elections such as 1992, varying by about a factor of 10 among states. Our results support the argument that subjective probabilities of many types are best obtained through empirically based statistical prediction models rather than solely through mathematical reasoning. We discuss the implications of our findings for the types of decision analyses used in public choice studies.
Article
1996
Advantages of Conflictual Redistricting
Andrew Gelman and Gary King. 1996. “Advantages of Conflictual Redistricting.” In Fixing the Boundary: Defining and Redefining Single-Member Electoral Districts, edited by Iain McLean and David Butler, Pp. 207–218. Aldershot, England: Dartmouth Publishing Company.Abstract
This article describes the results of an analysis we did of state legislative elections in the United States, where each state is required to redraw the boundaries of its state legislative districts every ten years. In the United States, redistrictings are sometimes controlled by the Democrats, sometimes by the Republicans, and sometimes by bipartisan committees, but never by neutral boundary commissions. Our goal was to study the consequences of redistricting and at the conclusion of this article, we discuss how our findings might be relevant to British elections.
Chapter PDF
Racial Fairness in Legislative Redistricting
Gary King, John Bruce, and Andrew Gelman. 1996. “Racial Fairness in Legislative Redistricting.” In Classifying by Race, edited by Paul E Peterson, Pp. 85-110. Princeton: Princeton University Press.Abstract
In this chapter, we study standards of racial fairness in legislative redistricting- a field that has been the subject of considerable legislation, jurisprudence, and advocacy, but very little serious academic scholarship. We attempt to elucidate how basic concepts about "color-blind" societies, and similar normative preferences, can generate specific practical standards for racial fairness in representation and redistricting. We also provide the normative and theoretical foundations on which concepts such as proportional representation rest, in order to give existing preferences of many in the literature a firmer analytical foundation.
Chapter PDF
1995
Pre-Election Survey Methodology: Details From Nine Polling Organizations, 1988 and 1992
D. Steven Voss, Andrew Gelman, and Gary King. 1995. “Pre-Election Survey Methodology: Details From Nine Polling Organizations, 1988 and 1992.” Public Opinion Quarterly, 59, Pp. 98–132.Abstract

Before every presidential election, journalists, pollsters, and politicians commission dozens of public opinion polls. Although the primary function of these surveys is to forecast the election winners, they also generate a wealth of political data valuable even after the election. These preelection polls are useful because they are conducted with such frequency that they allow researchers to study change in estimates of voter opinion within very narrow time increments (Gelman and King 1993). Additionally, so many are conducted that the cumulative sample size of these polls is large enough to construct aggregate measures of public opinion within small demographic or geographical groupings (Wright, Erikson, and McIver 1985).

These advantages, however, are mitigated by the decentralized origin of the many preelection polls. The surveys are conducted by diverse private enterprises with procedures that differ significantly. Moreover, important methodological detail does not appear in the public record. Codebooks provided by the survey organizations are all incomplete; many are outdated and most are at least partly inaccurate. The most recent treatment in the academic literature, by Brady and Orren (1992), discusses the approach used by three companies but conceals their identities and omits most of the detail. ...

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1994
Enhancing Democracy Through Legislative Redistricting
Andrew Gelman and Gary King. 1994. “Enhancing Democracy Through Legislative Redistricting.” American Political Science Review, 88, Pp. 541–559.Abstract
We demonstrate the surprising benefits of legislative redistricting (including partisan gerrymandering) for American representative democracy. In so doing, our analysis resolves two long-standing controversies in American politics. First, whereas some scholars believe that redistricting reduces electoral responsiveness by protecting incumbents, others, that the relationship is spurious, we demonstrate that both sides are wrong: redistricting increases responsiveness. Second, while some researchers believe that gerrymandering dramatically increases partisan bias and others deny this effect, we show both sides are in a sense correct. Gerrymandering biases electoral systems in favor of the party that controls the redistricting as compared to what would have happened if the other party controlled it, but any type of redistricting reduces partisan bias as compared to an electoral system without redistricting. Incorrect conclusions in both literatures resulted from misjudging the enormous uncertainties present during redistricting periods, making simplified assumptions about the redistricters’ goals, and using inferior statistical methods.
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Party Competition and Media Messages in U.S. Presidential Election Campaigns
Andrew Gelman, Gary King, and Sandy L Maisel. 1994. “Party Competition and Media Messages in U.S. Presidential Election Campaigns.” In The Parties Respond: Changes in the American Party System, Pp. 255-295. Boulder, Colorado: Westview Press.Abstract

At one point during the 1988 campaign, Michael Dukakis was ahead in the public opinion polls by 17 percentage points, but he eventually lost the election by 8 percent. Walter Mondale was ahead in the polls by 4 percent during the 1984 campaign but lost the election in a landslide. During June and July of 1992, Clinton, Bush, and Perot each had turns in the public opinion poll lead. What explains all this poll variation? Why do so many citizens change their minds so quickly about presidential choices?

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A Unified Method of Evaluating Electoral Systems and Redistricting Plans
Andrew Gelman and Gary King. 1994. “A Unified Method of Evaluating Electoral Systems and Redistricting Plans.” American Journal of Political Science, 38, Pp. 514–554.Abstract
We derive a unified statistical method with which one can produce substantially improved definitions and estimates of almost any feature of two-party electoral systems that can be defined based on district vote shares. Our single method enables one to calculate more efficient estimates, with more trustworthy assessments of their uncertainty, than each of the separate multifarious existing measures of partisan bias, electoral responsiveness, seats-votes curves, expected or predicted vote in each district in a legislature, the probability that a given party will win the seat in each district, the proportion of incumbents or others who will lose their seats, the proportion of women or minority candidates to be elected, the incumbency advantage and other causal effects, the likely effects on the electoral system and district votes of proposed electoral reforms, such as term limitations, campaign spending limits, and drawing majority-minority districts, and numerous others. To illustrate, we estimate the partisan bias and electoral responsiveness of the U.S. House of Representatives since 1900 and evaluate the fairness of competing redistricting plans for the 1992 Ohio state legislature.
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1993
Why are American Presidential Election Campaign Polls so Variable when Votes are so Predictable?
Andrew Gelman and Gary King. 1993. “Why are American Presidential Election Campaign Polls so Variable when Votes are so Predictable?” British Journal of Political Science, 23, Pp. 409–451.Abstract

As most political scientists know, the outcome of the U.S. Presidential election can be predicted within a few percentage points (in the popular vote), based on information available months before the election. Thus, the general election campaign for president seems irrelevant to the outcome (except in very close elections), despite all the media coverage of campaign strategy. However, it is also well known that the pre-election opinion polls can vary wildly over the campaign, and this variation is generally attributed to events in the campaign. How can campaign events affect people’s opinions on whom they plan to vote for, and yet not affect the outcome of the election? For that matter, why do voters consistently increase their support for a candidate during his nominating convention, even though the conventions are almost entirely predictable events whose effects can be rationally forecast? In this exploratory study, we consider several intuitively appealing, but ultimately wrong, resolutions to this puzzle, and discuss our current understanding of what causes opinion polls to fluctuate and yet reach a predictable outcome. Our evidence is based on graphical presentation and analysis of over 67,000 individual-level responses from forty-nine commercial polls during the 1988 campaign and many other aggregate poll results from the 1952–1992 campaigns. We show that responses to pollsters during the campaign are not generally informed or even, in a sense we describe, "rational." In contrast, voters decide which candidate to eventually support based on their enlightened preferences, as formed by the information they have learned during the campaign, as well as basic political cues such as ideology and party identification. We cannot prove this conclusion, but we do show that it is consistent with the aggregate forecasts and individual-level opinion poll responses. Based on the enlightened preferences hypothesis, we conclude that the news media have an important effect on the outcome of Presidential elections–-not due to misleading advertisements, sound bites, or spin doctors, but rather by conveying candidates’ positions on important issues.

Article
1992
JudgeIt I: A Program for Evaluating Electoral Systems and Redistricting Plans
Andrew Gelman and Gary King. 1992. “JudgeIt I: A Program for Evaluating Electoral Systems and Redistricting Plans”.Abstract
A program for analyzing almost any feature of district-level legislative elections data, including prediction, evaluating redistricting plans, estimating counterfactual hypotheses (such as what would happen if a term-limitation amendment were imposed), and others. This implements statistical procedures described in a series of journal articles and has been used during redistricting in many states by judges, partisans, governments, private citizens, and many others. Winner of the APSA Research Software Award.
1991
Systemic Consequences of Incumbency Advantage in the U.S. House
Gary King and Andrew Gelman. 1991. “Systemic Consequences of Incumbency Advantage in the U.S. House.” American Journal of Political Science, 35, Pp. 110–138.Abstract
The dramatic increase in the electoral advantage of incumbency has sparked widespread interest among congressional researchers over the last 15 years. Although many scholars have studied the advantages of incumbency for incumbents, few have analyzed its effects on the underlying electoral system. We examine the influence of the incumbency advantage on two features of the electoral system in the U.S. House elections: electoral responsiveness and partisan bias. Using a district-level seats-votes model of House elections, we are able to distinguish systematic changes from unique, election-specific variations. Our results confirm the significant drop in responsiveness, and even steeper decline outside the South, over the past 40 years. Contrary to expectations, we find that increased incumbency advantage explains less than a third of this trend, indicating that some other unknown factor is responsible. Moreover, our analysis also reveals another dramatic pattern, largely overlooked in the congressional literature: in the 1940’s and 1950’s the electoral system was severely biased in favor of the Republican party. The system shifted incrementally from this severe Republican bias over the next several decades to a moderate Democratic bias by the mid-1980’s. Interestingly, changes in incumbency advantage explain virtually all of this trend in partisan bias since the 1940’s. By removing incumbency advantage and the existing configuration of incumbents and challengers analytically, our analysis reveals an underlying electoral system that remains consistently biased in favor of the Republican party. Thus, our results indicate that incumbency advantage affects the underlying electoral system, but contrary to conventional wisdom, this changes the trend in partisan bias more than electoral responsiveness.
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1990
Estimating Incumbency Advantage Without Bias
Andrew Gelman and Gary King. 1990. “Estimating Incumbency Advantage Without Bias.” American Journal of Political Science, 34, Pp. 1142–1164.Abstract
In this paper we prove theoretically and demonstrate empirically that all existing measures of incumbency advantage in the congressional elections literature are biased or inconsistent. We then provide an unbiased estimator based on a very simple linear regression model. We apply this new method to congressional elections since 1900, providing the first evidence of a positive incumbency advantage in the first half of the century.
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Estimating the Electoral Consequences of Legislative Redistricting
Andrew Gelman and Gary King. 1990. “Estimating the Electoral Consequences of Legislative Redistricting.” Journal of the American Statistical Association, 85, Pp. 274–282.Abstract
We analyze the effects of redistricting as revealed in the votes received by the Democratic and Republican candidates for state legislature. We develop measures of partisan bias and the responsiveness of the composition of the legislature to changes in statewide votes. Our statistical model incorporates a mixed hierarchical Bayesian and non-Bayesian estimation, requiring simulation along the lines of Tanner and Wong (1987). This model provides reliable estimates of partisan bias and responsiveness along with measures of their variabilities from only a single year of electoral data. This allows one to distinguish systematic changes in the underlying electoral system from typical election-to-election variability.
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1989
Andrew Gelman and Gary King. 1989. “Electoral Responsiveness in U.S. Congressional Elections, 1946-1986.” Proceedings of the Social Statistics Section, American Statistical Association, Pp. 208.