Economic Theory Bulletin

, Volume 7, Issue 2, pp 209–220 | Cite as

Monotonicity and qualified majority rules

  • Uuganbaatar NinjbatEmail author
Research Article


This paper reflects on some results characterizing qualified majority rules using monotonicity as a key axiom. In particular, some errors in the existing literature are detected and ways to fix them are proposed. Then, the role of monotonicity axiom in characterizing majority rules is analyzed. There, among other findings, we show that its marginal contribution in characterizing relative qualified majority rules is the difference between two properties called sum-invariance and sum-monotonicity. Finally, a new class of qualified majority rules where voters exercise a veto power is introduced and axiomatically characterized.


Monotonicity Qualified majority rule Anonymity Majority rule with vetoes Qualified Pareto rule 

JEL Classification

D70 D71 



I am thankful to M. Remzi Sanver, to the editor and anonymous referees of this journal and to seminar participants of the department of economics at the National University of Mongolia for helpful comments and discussions.


  1. Aşan, G., Sanver, R.: Maskin monotonic aggregation rules. Econ. Lett. 91, 179–193 (2006)CrossRefGoogle Scholar
  2. Eliaz, K.: Social aggregators. Soc. Choice Welf. 22, 317–330 (2004)CrossRefGoogle Scholar
  3. Fey, M.: An application of asymptotic density to characterizing voting rules. Tatra Mt. Math. Publ. 31, 29–37 (2005)Google Scholar
  4. Houy, N.: Some further characterizations for the forgotten voting rules. Math. Soc. Sci. 53, 111–121 (2007a)CrossRefGoogle Scholar
  5. Houy, N.: A characterization for qualified majority voting rules. Math. Soc. Sci. 54, 17–24 (2007b)CrossRefGoogle Scholar
  6. Llamazares, B.: The forgotten decision rules: majority rules based on difference of votes. Math. Soc. Sci. 51, 311–326 (2006)CrossRefGoogle Scholar
  7. Perry, J., Powers, R.C.: Anonymity, monotonicity, and quota pair systems. Math. Soc. Sci. 60, 57–60 (2010)CrossRefGoogle Scholar
  8. Sandel, M.J.: Justice: What’s The Right Thing To Do?. Penguin Books, London (2009)Google Scholar
  9. Sanver, R.: Characterizations of majoritarianism: a unified approach. Soc. Choice Welf. 33(1), 159–171 (2009)CrossRefGoogle Scholar

Copyright information

© Society for the Advancement of Economic Theory 2018

Authors and Affiliations

  1. 1.Department of MathematicsThe National University of MongoliaUlaanbaatarMongolia

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