Social Choice and Welfare

, Volume 44, Issue 1, pp 31–50 | Cite as

Axiomatic districting



We study the districting problem from an axiomatic point of view in a framework with two parties, deterministic voter preferences and geographical constraints. The axioms are normatively motivated and reflect a notion of fairness to voters. Our main result is an “impossibility” theorem demonstrating that all anonymous districting rules are necessarily complex in the sense that they either use information beyond the mere number of districts won by the parties, or they violate an appealing consistency requirement according to which an acceptable districting rule should induce an acceptable districting of appropriate subregions.


Districting Gerrymandering Normative political analysis 

JEL Classifications




We are most grateful to John Duggan, an associate editor and two anonymous referees for their thorough remarks and suggestions which helped to improve the first version of this paper.


  1. Balinski M, Young HP (2001) Fair representation. Meeting the ideal of one man, one vote, 2nd edn. Brookings Institution Press, WashingtonGoogle Scholar
  2. Bervoets S, Merlin V (2012) Gerrymander-proof representative democracies. Int J Game Theory 41:473–488CrossRefGoogle Scholar
  3. Besley T, Preston I (2007) Electoral bias and public choice: theory and evidence. Q J Econ 122:1473–1510CrossRefGoogle Scholar
  4. Chambers PC (2008) Consistent representative democracy. Games Econ Behav 62:348–363CrossRefGoogle Scholar
  5. Chambers PC (2009) An axiomatic theory of political representation. J Econ Theory 144:375–389CrossRefGoogle Scholar
  6. Chambers PC, Miller AD (2010) A measure of bizarreness. Q J Polit Sci 5:27–44CrossRefGoogle Scholar
  7. Chambers PC, Miller AD (2013) Measuring legislative boundaries. Math Soc Sci 66:268–275CrossRefGoogle Scholar
  8. Coate S, Knight B (2007) Socially optimal districting: a theoretical and empirical exploration. Q J Econ 122:1409–1471CrossRefGoogle Scholar
  9. Friedman JN, Holden RT (2008) Optimal gerrymandering: sometimes pack, but never crack. Am Econ Rev 98:113–144CrossRefGoogle Scholar
  10. Gul R, Pesendorfer W (2010) Strategic redistricting. Am Econ Rev 100:1616–1641CrossRefGoogle Scholar
  11. Landau Z, Reid O, Yershov I (2009) A fair division solution to the problem of redestricting. Soc Choice Welf 32:479–492CrossRefGoogle Scholar
  12. Puppe C, Tasnádi A (2008) A computational approach to unbiased districting. Math Comput Model 48:1455–1460CrossRefGoogle Scholar
  13. Ricca F, Scozzari A, Simeone B (2011) Political districting: from classical models to recent approaches. 4OR—Q J Oper Res 9:223–254CrossRefGoogle Scholar
  14. Tasnádi A (2011) The political districting problem: a survey. Soc Econ 33:543–554CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Economics and ManagementKarlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.MTA-BCE “Lendület” Strategic Interactions Research Group, Department of MathematicsCorvinus University of BudapestBudapest Hungary

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