Public Choice

, Volume 172, Issue 1–2, pp 233–263 | Cite as

The relationship between the normalized gradient addition mechanism and quadratic voting

  • Daniel Benjamin
  • Ori Heffetz
  • Miles Kimball
  • Derek Lougee


Quadratic voting and the normalized gradient addition mechanism are both social choice mechanisms that confront individuals with quadratic budget constraints, but they are applicable in different contexts. Adapting one or both to apply to the same context, this paper explores the relationship between these two mechanisms in three contexts: marginal adjustments of continuous policies, simultaneous voting on many public choices, and voting on a single public choice accompanied by private monetary consequences. In the process, we provide some formal analysis of quadratic voting when (instead of money) votes are paid for with abstract tokens that are equally distributed by the mechanism designer.


Public goods Normalized gradient addition mechanism Quadratic voting 

JEL Classification




The authors would like to thank Glen Weyl for multiple rounds of detailed editorial feedback that significantly improved the paper; Itai Sher, Gabriel Carroll, and participants in the Becker-Friedman Institute’s “Quadratic Voting and the Public Good” conference for helpful comments and suggestions; and Assaf Kott and especially Rebecca Royer for excellent research assistance.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Daniel Benjamin
    • 1
    • 8
  • Ori Heffetz
    • 2
    • 3
    • 8
  • Miles Kimball
    • 4
    • 5
    • 6
    • 8
  • Derek Lougee
    • 7
  1. 1.Center for Economic and Social Research and Economics DepartmentUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Samuel Curtis Johnson Graduate School of ManagementCornell UniversityIthacaUSA
  3. 3.Department of EconomicsHebrew University of JerusalemJerusalemIsrael
  4. 4.Department of EconomicsUniversity of ColoradoBoulderUSA
  5. 5.Survey Research CenterUniversity of MichiganAnn ArborUSA
  6. 6.Center for Economic and Social ResearchUniversity of Southern CaliforniaLos AngelesUSA
  7. 7.Department of EconomicsCornell UniversityIthacaUSA
  8. 8.National Bureau of Economic ResearchCambridgeUSA

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