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Estimating Partisan Bias of the Electoral College Under Proposed Changes in Elector Apportionment

A. C. Thomas
  • Corresponding author
  • Visiting Assistant Professor, Department of ­Statistics, Carnegie Mellon University, Pittsburgh, PA, USA
  • Email:
/ Andrew Gelman
  • Professor, Departments of Statistics and Political Science, Columbia University
/ Gary King
  • Albert J. Weatherhead III University Professor, Harvard University, Cambridge, MA, USA
/ Jonathan N. Katz
  • Kay Sugahara Professor of Social Sciences and Statistics and Chair of the Division of the Humanities and Social Sciences, California Institute of Technology, Pasadena, CA, USA
Published Online: 2013-01-11 | DOI: https://doi.org/10.1515/spp-2012-0001


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.


  • Gelman, Andrew and Gary King (1990) “Estimating the Electoral Consequences of Legislative Redistricting,” Journal of the American Statistical Association 85(410):274–82.

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  • Gelman, Andrew, Gary King, and W. John Boscardin (1998) “Estimating the Probability of Events That Have Never Occurred: When Is Your Vote Decisive?” Journal of the American Statistical Association 93(441):1–9.

  • Gelman, Andrew, Gary King, and Andrew C. Thomas (2008) “JudgeIt II: A Program for Evaluating Electoral Systems and Redistricting Plans.” R Package. Available on CRAN.

  • Katz, Jonathan N., Andrew Gelman, and Gary King (2004) “Empirically Evaluating the Electoral College,” Chapter 5, pp. 75–88, in Rethinking the Vote: The Politics and Prospects of American Electoral Reform. Ann N. Crigler, Marion R. Just, and Edward J. McCaffery, eds. New York: Oxford University Press.

  • King, Gary and Robert X. Browning (1987) “Democratic Representation and Partisan Bias in Congressional Elections,” American Political Science Research 81(4):1251–73.

  • Lane, Randall (2008) “A Ballot Buddy System,” New York Times, December 15, p. A35.

  • Petition to the Office of the Attorney General. July 17, 2007. (http://ag.ca.gov/cms_pdfs/initiatives/2007-07-17_07-0032_Initiative.pdf).

  • Thomas, Andrew C. (2008) Reply to “A Ballot Buddy System,” New York Times, December 22.

About the article

Corresponding author: A. C. Thomas, Visiting Assistant Professor, Department of Statistics, Carnegie Mellon University, Pittsburgh, PA, USA

Published Online: 2013-01-11

Although there are total of 535 members of Congress, the District of Columbia gets three electoral votes under the 23rd Amendment of the U.S. Constitution even though it has no members of Congress.

Petitioner Thomas W. Hiltachk, the signed author of the proposal and representative of Californians for Equal Representation, is a partner of law firm Bell, McAndrews and Hiltachk, LLP, which has represented the California Republican Party.

See http://www.post-gazette.com/stories/local/state/change-proposed-for-states-electoral-vote-process-314523/ and http://fivethirtyeight.blogs.nytimes.com/2011/09/15/pennsylvania-electoral-college-plan-could-backfire-on-g-o-p/ for more background.

Another way to define the influence of states in the Electoral College is by comparing the empirical voting power, or the probability that an individual vote is decisive, in different states. Voting power varies greatly from state to state – for example, Utah is so far from the national median that voters there have almost zero chance of determining the national electoral vote winner – but, overall, voters in small states have slightly higher voting power; see (Gelman, King and Boscardin 1998).

Michigan enacted this system for the 1892 election, but removed it for the subsequent election in 1896.

Proportional representation, a system in which S equals V by design, is a special case of partisan symmetry, but one that has no role in American elections.

The year 1968 is the only recent presidential contest where a major third-party candidate appears after the fact to have made a major impact on the properties of the election. We ought to consider the impact of shifting votes to and from George Wallace, who won five southern states and 46 electoral votes, but we do not have the model framework to do so; as a result, votes are only shifted between Hubert Humphrey and Richard Nixon. Results for this year are therefore more speculative than in all others. We also note that for Florida’s electoral votes in 2000, third-party candidates Nader and Buchanan each had vote counts that were far more than the ultimate vote difference between candidates Bush and Gore, but far less than the effective uncertainty of this difference, so that their presence can be safely ignored for our purposes.

Citation Information: Statistics, Politics and Policy, ISSN (Online) 2151-7509, ISSN (Print) 2194-6299, DOI: https://doi.org/10.1515/spp-2012-0001. Export Citation

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