Hostname: page-component-7c8c6479df-5xszh Total loading time: 0 Render date: 2024-03-28T15:16:53.733Z Has data issue: false hasContentIssue false

Theoretical Foundations and Empirical Evaluations of Partisan Fairness in District-Based Democracies

Published online by Cambridge University Press:  23 October 2019

JONATHAN N. KATZ*
Affiliation:
California Institute of Technology
GARY KING*
Affiliation:
Harvard University
ELIZABETH ROSENBLATT*
Affiliation:
Harvard University
*
*Jonathan N. Katz, Kay Sugahara Professor of Social Sciences and Statistics, California Institute of Technology, jkatz@caltech.edu.
Gary King, Albert J. Weatherhead III University Professor, Institute for Quantitative Social Science, Harvard University, King@Harvard.edu.
Elizabeth Rosenblatt, Post-BA Affiliate, Institute for Quantitative Social Science, Harvard University, ERosenblatt@alumni.harvard.edu.

Abstract

We clarify the theoretical foundations of partisan fairness standards for district-based democratic electoral systems, including essential assumptions and definitions not previously recognized, formalized, or in some cases even discussed. We also offer extensive empirical evidence for assumptions with observable implications. We cover partisan symmetry, the most commonly accepted fairness standard, and other perspectives. Throughout, we follow a fundamental principle of statistical inference too often ignored in this literature—defining the quantity of interest separately so its measures can be proven wrong, evaluated, and improved. This enables us to prove which of the many newly proposed fairness measures are statistically appropriate and which are biased, limited, or not measures of the theoretical quantity they seek to estimate at all. Because real-world redistricting and gerrymandering involve complicated politics with numerous participants and conflicting goals, measures biased for partisan fairness sometimes still provide useful descriptions of other aspects of electoral systems.

Type
Research Article
Copyright
Copyright © American Political Science Association 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

All appendices are available at GaryKing.org/symmetry; all data and information necessary to replicate our results are available in Katz, King, and Rosenblatt (2019). Our thanks to Steve Ansolabehere, Peter Aronow, Robin Best, Jowei Chen, Shawn Donahue, Moon Duchin, Jon Eguia, Andrew Gelman, Kosuke Imai, Jonathan Krasno, Eric Lander, Daniel Magleby, Michael D. McDonald, Eric McGhee, John Nagle, Nate Persily, Jameson Quinn, Nick Stephanopoulos, Tyler VanderWeele, Sam Wang, Greg Warrington, and Xiang Zhou for their helpful comments.

References

REFERENCES

Best, Robin E., Donahue, Shawn J., Krasno, Jonathan, Magleby, Daniel B., and McDonald, Michael D.. 2018. “Considering the Prospects for Establishing a Packing Gerrymandering Standard.” Election Law Journal 17 (1): 1–20.CrossRefGoogle Scholar
Blackburn, Simon. 2003. Ethics: A Very Short Introduction. Vol. 80. New York: Oxford University Press.CrossRefGoogle Scholar
Brady, David W., and Grofman, Bernard. 1991. “Sectional Differences in Partisan Bias and Electoral Responsiveness in US House Elections, 1850–1980.” British Journal of Political Science 21 (2): 247–56.CrossRefGoogle Scholar
Brunell, Thomas. 1999. “Partisan Bias in US Congressional Elections, 1952–1996: Why the Senate Is Usually More Republican Than the House of Representatives.” American Politics Quarterly 27 (3): 316–37.CrossRefGoogle Scholar
Brunell, Thomas. 2010. Redistricting and Representation: Why Competitive Elections Are Bad for America. New York: Routledge.CrossRefGoogle Scholar
Butler, David E. 1951. “Appendix.” In The British General Election of 1950, ed. Nicholas, H.G.. London: Macmillan, 306–33.Google Scholar
Cain, Bruce E., Tam Cho, Wendy K., Liu, Yan Y., and Zhang, Emily R.. 2017. “A Reasonable Bias Approach to Gerrymandering: Using Automated Plan Generation to Evaluate Redistricting Proposals.” William & Mary Law Review 59: 1521.Google Scholar
Campbell, James E. 1996. Cheap Seats: The Democratic Party’s Advantage in US House Elections. Columbus, OH: The Ohio State University Press.Google Scholar
Chambers, Christopher P., Miller, Alan D., and Sobel, Joel. 2017. “Flaws in the Efficiency gap.” Journal of Law & Politics 33: 1.Google Scholar
Chen, Jowei, and Rodden, Jonathan. 2013. “Unintentional Gerrymandering: Political Geography and Electoral Bias in Legislatures.” Quarterly Journal of Political Science 8 (3): 239–69.CrossRefGoogle Scholar
Chikina, Maria, Frieze, Alan, and Pegden, Wesley. 2017. “Assessing Significance in a Markov Chain without Mixing.” Proceedings of the National Academy of Sciences 114 (11): 2860–4.CrossRefGoogle Scholar
Cho, Wendy K. Tam. 2017. “Measuring Partisan Fairness: How Well Does the Efficiency gap Guard against Sophisticated as Well as Simple-Minded Modes of Partisan Discrimination.” University of Pennsylvania Law Review Online 166: 17.Google Scholar
Cox, Adam B. 2006. “Designing Redistricting Institutions.” Election Law Journal 5 (4): 412–24.CrossRefGoogle Scholar
Cox, Gary W. 1997. Making Votes Count: Strategic Coordination in the World’s Electoral Systems: Cambridge University Press.CrossRefGoogle Scholar
Cox, Gary W., and Katz, Jonathan N.. 1999. “The Reapportionment Revolution and Bias in US Congressional Elections.” American Journal of Political Science 43 (3): 812–41.CrossRefGoogle Scholar
Cox, Gary W., and Katz, Jonathan N.. 2002. Elbridge Gerry’s Salamander: The Electoral Consequences of the Reapportionment Revolution. New York: Cambridge University Press.CrossRefGoogle Scholar
Duchin, Moon. 2018. “Gerrymandering Metrics: How to Measure? What’s the Baseline?” arXiv:1801.02064.Google Scholar
Duchin, Moon, Gladkova, Taissa, Henninger-Voss, Eugene, Klingensmith, Ben, Newman, Heather, and Wheelen, Hannah. n.d. Obstructions to Proportional Representation: Republicans in Massachusetts. Tufts University.Google Scholar
Erikson, Robert S. 1972. “Malapportionment, Gerrymandering, and Party Fortunes in Congressional Elections.” American Political Science Review 66 (4): 1234–45.CrossRefGoogle Scholar
Fifield, Benjamin, Higgins, Michael, Imai, Kosuke, and Tarr, Alexander. 2018. “A New Automated Redistricting Simulator Using Markov Chain Monte Carlo.” Working Paper, Princeton, NJ: Princeton University.Google Scholar
Friedman, John N., and Holden, Richard T.. 2008. “Optimal Gerrymandering: Sometimes Pack, but Never Crack.” The American Economic Review 98 (1): 113–44.CrossRefGoogle Scholar
Garand, James C., and Parent, T. Wayne. 1991. “Representation, Swing, and Bias in US Presidential Elections, 1872–1988.” American Journal of Political Science 35 (4): 1011–31.CrossRefGoogle Scholar
Gelman, Andrew, and King, Gary. May 1994a. “A Unified Method of Evaluating Electoral Systems and Redistricting Plans.” American Journal of Political Science 38 (2): 514–54. URL: http://j.mp/unifiedEc.CrossRefGoogle Scholar
Gelman, Andrew, and King, Gary. September 1994b. “Enhancing Democracy through Legislative Redistricting.” American Political Science Review 88 (3): 541–59. URL: http://j.mp/redenh.CrossRefGoogle Scholar
Gerber, Elisabeth R., and Lewis, Jeffrey B.. 2004. “Beyond the Median: Voter Preferences, District Heterogeneity, and Political Representation.” Journal of Political Economy 112 (6): 1364–83.CrossRefGoogle Scholar
Gilligan, Thomas W., and Matsusaka, John G.. 1999. “Structural Constraints on Partisan Bias under the Efficient Gerrymander.” Public Choice 100 (1–2): 65–84.CrossRefGoogle Scholar
Greene, Joshua D. 2009. “The Cognitive Neuroscience of Moral Judgment.” The cognitive neurosciences 4: 1–48.Google Scholar
Grofman, Bernard, and Brunell, Thomas L.. 2005. “The Art of the Dummymander: The Impact of Recent Redistrictings on the Partisan Makeup of Southern House Seats.” In Redistricting in the New Millennium, ed. Peter F. Galderisi. New York: Lexington Books, 183–99.Google Scholar
Grofman, Bernard, and King, Gary. January 2007. “The Future of Partisan Symmetry as a Judicial Test for Partisan Gerrymandering after LULAC V. Perry.” Election Law Journal 6 (1): 2–35. http://gking.harvard.edu/files/abs/jp-abs.shtml.CrossRefGoogle Scholar
Herron, Michael C., and Wiseman, Alan E.. 2008. “Gerrymanders and Theories of Law Making: A Study of Legislative Redistricting in Illinois.” The Journal of Politics 70 (1): 151–67.CrossRefGoogle Scholar
Iacus, Stefano M., King, Gary, and Porro, Giuseppe. 2018. “A Theory of Statistical Inference for Matching Methods in Causal Research.” Political Analysis: 1–23. URL: http://j.mp/Nt9TkZ.Google Scholar
Jackman, Simon. 1994. “Measuring Electoral Bias: Australia, 1949–93.” British Journal of Political Science 24 (3): 319–57.CrossRefGoogle Scholar
Katz, Jonathan N., and King, Gary. March 1999. “A Statistical Model for Multiparty Electoral Data.” American Political Science Review 93 (1): 15–32. URL: http://bit.ly/mtypty.CrossRefGoogle Scholar
Katz, Jonathan N., King, Gary, and Rosenblatt, Elizabeth. 2019. Replication Data for: Theoretical Foundations and Empirical Evaluations of Partisan Fairness in District-Based Democracies. doi: 10.7910/DVN/FTYHPJ.Google Scholar
Kaufman, Aaron, King, Gary, and Komisarchik, Mayya. Forthcoming. “How to Measure Legislative District Compactness if You Only Know it when You See it.” American Journal of Political Science. URL: http://j.mp/2u9OWrG.Google Scholar
King, Gary. November 1989. “Representation through Legislative Redistricting: A Stochastic Model.” American Journal of Political Science 33 (4): 787–824. URL: http://j.mp/2o46Gkk.CrossRefGoogle Scholar
King, Gary. May 1990. “Electoral Responsiveness and Partisan Bias in Multiparty Democracies.” Legislative Studies Quarterly XV (2): 159–81. URL: http://bit.ly/ErespMP.CrossRefGoogle Scholar
King, Gary, and Browning, Robert X.. December 1987. “Democratic Representation and Partisan Bias in Congressional Elections.” American Political Science Review 81 (4): 1252–73. URL: http://j.mp/parSym.CrossRefGoogle Scholar
King, Gary, and Gelman, Andrew. February 1991. “Systemic Consequences of Incumbency Advantage in the US House.” American Journal of Political Science 35 (1): 110–38. URL: http://bit.ly/SystCs.CrossRefGoogle Scholar
King, Gary, Rosen, Ori, Tanner, Martin, and Wagner, Alexander F.. 2008. “Ordinary Economic Voting Behavior in the Extraordinary Election of Adolf Hitler.” The Journal of Economic History 68 (4): 951–96. URL: http://bit.ly/nazivote.CrossRefGoogle Scholar
Klarner, Carl. 2018. State Legislative Election Returns, 1967–2016: Restructured for Use. doi: 10.7910/DVN/DRSACA.Google Scholar
Krasno, Jonathan, Magleby, Daniel B., McDonald, Michael D., Donahue, Shawn J., and Best, Robin E.. 2018. “Can Gerrymanders Be Detected? An Examination of Wisconsin’s State Assembly.” American Politics Research: 1–40. Published Online May 14, 2018.Google Scholar
Lander, Eric S. 2018. “Brief for Amicus Curiae Eric S. Lander in Support of Appellees.” Gill v. Whitford 585 U.S. (2018).Google Scholar
Magleby, Daniel B., and Mosesson, Daniel B.. 2018. “A New Approach for Developing Neutral Redistricting Plans.” Political Analysis 26 (2): 147–67.CrossRefGoogle Scholar
Mann, Thomas E. 1978. Unsafe at Any Margin: Interpreting Congressional Elections. Vol. 220. Washington DC: American Enterprise Institute for Public Policy Research.Google Scholar
May, Kenneth O. 1952. “A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decision.” Econometrica 20 (4): 680–4.CrossRefGoogle Scholar
McCarty, Nolan, Poole, Keith T., and Rosenthal, Howard. 2009. “Does Gerrymandering Cause Polarization?American Journal of Political Science 53 (3): 666–80.CrossRefGoogle Scholar
McDonald, Michael D., and Best, Robin E.. 2015. “Unfair Partisan Gerrymanders in Politics and Law: A Diagnostic Applied to Six Cases.” Election Law Journal 14 (4): 312–30.CrossRefGoogle Scholar
McDonald, Michael P. 2007. “Regulating Redistricting.” PS: Political Science & Politics 40 (4): 675–9.Google Scholar
McGann, Anthony J., Smith, Charles Anthony, Latner, Michael, and Keena, J. Alex. 2015. “A Discernable and Manageable Standard for Partisan Gerrymandering.” Election Law Journal 14 (4): 295–311.CrossRefGoogle Scholar
McGhee, Eric M. 2017. “Measuring Efficiency in Redistricting.” Election Law Journal: Rules, Politics, and Policy 16 (4): 417–42.CrossRefGoogle Scholar
Nagle, John F. 2015. “Measures of Partisan Bias for Legislating Fair Elections.” Election Law Journal 14 (4): 346–60.CrossRefGoogle Scholar
Niemi, Richard G., and Jackman, Simon. 1991. “Bias and Responsiveness in State Legislative Districting.” Legislative Studies Quarterly 16 (2): 183–202.CrossRefGoogle Scholar
Owen, Guillermo, and Grofman, Bernard. 1988. “Optimal Partisan Gerrymandering.” Political Geography Quarterly 7 (1): 5–22.CrossRefGoogle Scholar
Petracca, Mark P. 1996. “A History of Rotation in Office.” In Legislative Term Limits: Public Choice Perspectives, ed. Bernard Groffman. Boston: Kluwer Academic Publishers, 247–77.CrossRefGoogle Scholar
Puppe, Clemens, and Tasnadi, Attila. 2009. “Optimal Redistricting under Geographical Constraints: Why ‘pack and Crack’ Does Not Work.” Economics Letters 105 (1): 93–6.CrossRefGoogle Scholar
Rave, D. Theodore. 2012. “Politicians as Fiduciaries.” Harvard Law Review 126: 671.Google Scholar
Rubin, Donald B. 1991. “Practical Implications of Modes of Statistical Inference for Causal Effects and the Critical Role of the Assignment Mechanism.” Biometrics 47: 1213–34.CrossRefGoogle ScholarPubMed
Sen, Amartya. 1976. “Liberty, Unanimity and Rights.” Economica 43 (171): 217–45.CrossRefGoogle Scholar
Stephanopoulos, Nicholas O., and McGhee, Eric M.. 2015. Partisan Gerrymandering and the Efficiency Gap. The University of Chicago Law Review 82: 831–900.Google Scholar
Stephanopoulos, Nicholas O., and McGhee, Eric M.. 2018. “The Measure of a Metric: The Debate over Quantifying Partisan Gerrymandering.” Stanford Law Review 70: 1503.Google Scholar
Tam Cho, Wendy K., and Rubinstein-Salzedo, Simon. 2019. “Understanding Significance Tests from a Non-mixing Markov Chain for Partisan Gerrymandering Claims.” Statistics and Public Policy 6 (1): 1–10.CrossRefGoogle Scholar
Tapp, Kristopher. 2018. “Measuring Political Gerrymandering.” arXiv:1801.02541.Google Scholar
Tufte, Edward R. 1973. “The Relationship between Seats and Votes in Two-Party Systems.” American Political Science Review 67 (2): 540–54.CrossRefGoogle Scholar
VanderWeele, Tyler J., and Hernan, Miguel A.. 2012. “Causal Inference under Multiple Versions of Treatment.” Journal of Causal Inference 1: 1–20.CrossRefGoogle Scholar
Veomett, Ellen. 2018. “Efficiency Gap, Voter Turnout, and the Efficiency Principle.” Election Law Journal: Rules, Politics, and Policy 17 (4): 249–63.CrossRefGoogle Scholar
Wang, Samuel. 2016a. “Three Practical Tests for Gerrymandering: Application to Maryland and Wisconsin.” Election Law Journal 15 (4): 367–84.CrossRefGoogle Scholar
Wang, Samuel. 2016b. “Three Tests for Practical Evaluation of Partisan Gerrymandering.” Stanford Law Review 68: 1263.Google Scholar
Warrington, Gregory S. 2018a. “Introduction to the Declination Function for Gerrymanders.” arXiv preprint arXiv:1803.04799.Google Scholar
Warrington, Gregory S. 2018b. “Quantifying Gerrymandering Using the Vote Distribution.” Election Law Journal 17 (1): 39–57.CrossRefGoogle Scholar
Wimmer, Karl. 2010. “Agnostically Learning under Permutation Invariant Distributions.” In 51st Annual IEEE Symposium on Foundations of Computer Science: IEEE, 113–22.CrossRefGoogle Scholar
Yoshinaka, Antoine, and Murphy, Chad. 2009. “Partisan Gerrymandering and Population Instability: Completing the Redistricting Puzzle.” Political Geography 28 (8): 451–62.CrossRefGoogle Scholar
Supplementary material: Link

Katz et al. Dataset

Link
Supplementary material: PDF

Katz et al. supplementary material

Online Appendix

Download Katz et al. supplementary material(PDF)
PDF 225.9 KB