Upper set rules with binary ranges

  • Makoto HagiwaraEmail author
  • Hirofumi Yamamura
Original Paper


We investigate the social choice problem in which the range of a rule consists of only two alternatives. While Barberà et al. (Int J Game Theory 41:791–808, 2012a) capture the feature of “strategy-proof” rules based on the monotonicity condition of winning coalitions, we newly consider the “monotonicity condition with respect to the direction of preference changes.” We show that a rule is strategy-proof if and only if it satisfies the monotonicity condition of preference changes. In addition, we define the class of “upper set rules,” and show that these rules are characterized by strategy-proofness.



  1. Alcalde-Unzu J, Vorsatz M (2018) Strategy-proof location of public facilities. Games Econ Behav 112:21–48CrossRefGoogle Scholar
  2. Barberà S, Jackson M (1994) A characterization of strategy-proof social choice functions for economies with pure public goods. Soc Choice Welf 11:241–252CrossRefGoogle Scholar
  3. Barberà S, Jackson M (1995) Strategy-proof exchange. Econometrica 63:51–87CrossRefGoogle Scholar
  4. Barberà S, Sonnenschein H, Zhou L (1991) Voting by committees. Econometrica 59:595–609CrossRefGoogle Scholar
  5. Barberà S, Berga D, Moreno B (2010) Individual versus group strategy-proofness: when do they coincide? J Econ Theory 145:1648–1674CrossRefGoogle Scholar
  6. Barberà S, Berga D, Moreno B (2012a) Group strategy-proof social choice functions with binary ranges and arbitrary sets: characterization results. Int J Game Theory 41:791–808CrossRefGoogle Scholar
  7. Barberà S, Berga D, Moreno B (2012b) Domains, ranges and strategy-proofness: the case of single-dipped preferences. Soc Choice Welf 39:335–352CrossRefGoogle Scholar
  8. Hagiwara M, Ochiai G, Yamamura H (2019) Strategy-proofness and single peakedness: a full characterization. mimeoGoogle Scholar
  9. Harless P (2015) Reaching consensus: solidarity and strategic properties in binary social choice. Soc Choice Welf 45:97–121CrossRefGoogle Scholar
  10. Lahiri A, Pramanik A (2019) On strategy-proof social choice between two alternatives. Soc Choice Welf.
  11. Larsson B, Svensson L-G (2006) Group strategy-proof voting on the full preference domain. Math Soc Sci 52:272–287CrossRefGoogle Scholar
  12. Manjunath V (2012) Group strategy-proofness and voting between two alternatives. Math Soc Sci 63:239–242CrossRefGoogle Scholar
  13. Manjunath V (2014) Efficient and strategy-proof social choice when preferences are single-dipped. Int J Game Theory 43:579–597CrossRefGoogle Scholar
  14. Marchant T, Mishra D (2015) Efficient and mechanism design with two alternatives in quasi-linear environments. Soc Choice Welf 44:433–455CrossRefGoogle Scholar
  15. Massó J, Moreno de Barreda I (2011) On strategy-proofness and symmetric single-peakedness. Games Econ Behav 72:467–484CrossRefGoogle Scholar
  16. Rao S, Basile A, Bhaskara Rao KPS (2018) On the ultrafilter representation of coalitionally strategy-proof social choice functions. Econ Theory Bull 6:1–13CrossRefGoogle Scholar
  17. Vannucci S (2013) On two-valued nonsovereign strategy-proof voting rules. Department of Economics University of Siena 672. University of Siena, Department of EconomicsGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Industrial Engineering and Economics, School of EngineeringTokyo Institute of TechnologyTokyoJapan
  2. 2.Faculty of Business AdministrationKomazawa UniversityTokyoJapan

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