Abstract
Padding is the practice of adding nonvoters (e.g., noncitizens or disenfranchised prisoners) to an electoral district in order to ensure that the district meets the size quota prescribed by the one man, one vote doctrine without affecting the voting outcome in the district. We show how padding— and its mirror image, pruning—, can lead to arbitrarily large deviations from the socially optimal composition of elected legislatures. We solve the partisan districter’s optimal padding problem.
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References
Ainsworth R, Munoz EG, Gomez AM (2023) District competitiveness increases voter turnout: evidence from repeated redistricting in North Carolina
Bernstein M, Duchin M (2017) A formula goes to court: partisan gerrymandering and the efficiency gap. Not AMS 64(9):1020–1024
Black D (1958) The theory of committees and elections. Cambridge University Press, Cambridge
Bouton L, Genicot G, Castanheira M, Stashko A (2024) Pack-crack-pack: gerrymandering with differential turnout
Bracco E (2013) Optimal districting with endogenous party platforms. J Public Econ 104(13):1–13
Chambers CP, Miller AD, Sobel J (2010) A measure of bizarreness. Q J Polit Sci 5(1):27–44
Chambers CP, Miller AD, Sobel J (2017) Flaws in the efficiency gap. J Law Polit 33(1):1–33
Chen J, Rodden J (2013) Unintentional gerrymandering: political geography and electoral bias in legislatures. Q J Polit Sci 8:239–269
Coate S, Knight B (2007) Socially optimal districting: a theoretical and empirical exploration. Q J Econ 122(4):1409–1471
Duggan J (2017) A survey of equilibrium analysis in spatial models of elections
Friedman JN, Holden RT (2008) Optimal gerrymandering: sometimes pack, but never crack. Am Econ Rev 98(1):113–144
Gilligan TW, Matsusaka JG (2006) Public choice principles of redistricting. Public Choice 129:381–398
Gomberg A, Pancs R, Sharma T (2023) Electoral maldistricting. Int Econ Rev (forthcoming)
Grofman B, King G, Koetzle W, Brunell T (1997) An integrated perspective on the three potential sources of partisan bias: malapportionment, turnout differences, and the geographic distribution of party vote shares. Elect Stud 16(4):457–470
Grofman B, King G (2007) The future of partisan symmetry as a judicial test for partisan gerrymandering after LULAC v. Perry. Elect Law J
Grofman B, King G, Cervas JR (2020) The terminology of districting: a user guide to understanding gerrymandering
Gul F, Pesendorfer W (2010) Strategic redistricting. Am Econ Rev 100(4):1616–1641
Hinich MJ (1977) Equilibrium in spacial voting: the median voter result is an artifact. J Econ Theory 16(2):208–219
Khan MA, Rath KP, Sun Y (2006) The Dvoretzky–Wald–Wolfowitz theorem and purification in atomless finite-action games. Int J Game Theory 34:91–104
Konishi H, Pan C-Y (2020) Partisan and bipartisan gerrymandering. J Public Econ Theory 22(5):1183–212
Moskowitz DJ, Schneer B (2019) Reevaluating competition and turnout in U.S. house elections. Q J Polit Sci 14(2):191–223
Owen G, Grofman B (1988) Optimal partisan gerrymandering. Polit Geogr Q 7:5–22
Persson T, Tabellini G, Economics P (2000) Explaining economic policy. The MIT Press, Cambridge
Puppe C, Tasnadi A (2009) Optimal redistricting under geographical constraints: why ‘pack and crack’ does not work. Econ Lett 105(1):93–96
Sherstyuk K (1998) How to gerrymander: a formal analysis. Public Choice 95:27–49
Stephanopoulos NO, McGhee EM (2015) Partisan gerrymandering and the efficiency gap. Univ Chic Law Rev 82(2):831–900
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Appendix
Appendix
Lemma A.1
For every nonempty block of locations \(\mathcal{B}\subset \mathcal{L}\) and for every integer \(K'\in \left\{ 2,3,\ldots ,K\right\} \), one can construct \(K'\) equipopulous districts that jointly partition the block \(\mathcal{B}\) so that each district has the same mean voter ideology as \(\mathcal{B}\).
The conclusion of Lemma A.1 would be immediate if we could split a location among multiple districts. The proof shows the conclusion holds even when a location cannot be split, which is a maintained assumption in the paper.
Proof of Lemma A.1
For every location \(\left( \rho ,\tau \right) \) in \(\mathcal{B}\) and for every index k in \(\left\{ 1,2,\ldots ,K'\right\} \), define an auxiliary function \(f_{k}\left( \rho ,\tau \right) \equiv 1/K'\). By the definition of \(f_{k}\), for every k, we have
The Dvoretzky–Wald–Wolfowitz purification theorem reported by Khan et al. (2006, Theorem DWW, p.93) implies the existence of functions \(\left( f_{k}^{*}\right) \) with \(f_{k}^{*}:\mathcal{B}\rightarrow \left\{ 0,1\right\} \) such that, for every k, we have
We interpret each function \(f_{k}^{*}\) as an indicator that places a location \(\left( \rho ,\tau \right) \) in its entirely into district k if and only if \(f_{k}^{*}\left( \rho ,\tau \right) =1\). The district map associated with \(\left( f_{k}^{*}\right) \) is \(\textbf{D}\equiv \left( D_{1},D_{2},\dots ,D_{K'}\right) \), where \(D_{k}\equiv \left\{ \left( \rho ,\tau \right) \in \mathcal{B}\mid f_{k}^{*}\left( \rho ,\tau \right) =1\right\} \). Combining the two displays above with the definition of \(\textbf{D}\) we conclude that all districts in \(\textbf{D}\) are equipopulous,
We also conclude that all districts share with the block \(\mathcal{B}\) the same mean voter ideology:
\(\square \)
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Gomberg, A., Pancs, R. & Sharma, T. Padding and pruning: gerrymandering under turnout heterogeneity. Soc Choice Welf 63, 401–415 (2024). https://doi.org/10.1007/s00355-024-01536-z
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DOI: https://doi.org/10.1007/s00355-024-01536-z