Advertisement

Group Decision and Negotiation

, Volume 28, Issue 1, pp 63–78 | Cite as

Compromise Rules Revisited

  • Vincent Merlin
  • İpek Özkal Sanver
  • M. Remzi SanverEmail author
Article
  • 33 Downloads

Abstract

Decision makers often face a dilemma when they have to arbitrate between the quantity of support for a decision (i.e., the number of people who back it) and the quality of support (i.e., at which level to go down in voters’ preferences to obtain sufficient level of support). The trade-off between the quality and quantity of support behind alternatives led to numerous suggestions in social choice theory: without being exhaustive we can mention Majoritarian Compromise, Fallback Bargaining, Set of Efficient Compromises, Condorcet Practical Method, Median Voting Rule, Majority Judgement. Our point is that all these concepts share a common feature which enables us to gather them in the same class, the class of compromise rules, which are all based upon elementary scoring rules described extensively by Saari. One can exploit his results to analyze the compromise rules with relative ease, which is a major point of our paper.

Keywords

Compromise Voting Scoring rules Borda Condorcet Saari 

JEL Classification

D71 

References

  1. Balinski M, Laraki R (2007) A theory of measuring, electing and ranking. Proc Natl Acad Sci USA 104(21):8720–8725CrossRefGoogle Scholar
  2. Balinski M, Laraki R (2011) Majority judgment: measuring ranking and electing. MIT Press, CambridgeCrossRefGoogle Scholar
  3. Bassett GW, Persky J (1999) Robust voting. Public Choice 99:299–310CrossRefGoogle Scholar
  4. Börgers T, Postl P (2009) Efficient compromising. J Econ Theory 144:2057–2076CrossRefGoogle Scholar
  5. Brams S, Kilgour DM (2001) Fallback bargaining. Group Decis Negot 10:287–316CrossRefGoogle Scholar
  6. Congar R, Merlin V (2012) A characterization of the maximin rule in the context of voting. Theory Decis 72–1:131–147CrossRefGoogle Scholar
  7. de Borda J-C (1781) Mémoire sur les Élections au Scrutin. Histoire de l’Académie Royale des Sciences, ParisGoogle Scholar
  8. de Caritat MJAN (1785) Marquis de Condorcet, Éssai sur l’Application de l’Analyse à la Probabilité des Décisions Rendues à la Pluralité des Voix, L’Imprimerie Royale, ParisGoogle Scholar
  9. Gehrlein WV, Lepelley D (2003) On some limitations of the median voting rule. Public Choice 117–2:177–190CrossRefGoogle Scholar
  10. Goldsmith J, Lang J, Mattei N, Perny P (2016) Voting with rank dependant scoring rules. AAAI, Menlo ParkGoogle Scholar
  11. Nurmi H (1999) Voting paradoxes and how to deal with them. Springer, BerlinCrossRefGoogle Scholar
  12. Özkal-Sanver İ, Sanver MR (2004) Efficiency in the degree of compromise: a new axiom for social choice theory. Group Decis Negot 13:375–380CrossRefGoogle Scholar
  13. Saari DG (1989) A dictionary for voting paradoxes. J Econ Theory 48:443–475CrossRefGoogle Scholar
  14. Saari DG (1992) Millions of election outcomes from a single profile. Social Choice Welf 9:227–306Google Scholar
  15. Saari DG (1994) Geometry of voting. Springer, BerlinCrossRefGoogle Scholar
  16. Saari DG (1999) Explaining all three-alternative voting outcomes. J Econ Theory 87:313–355CrossRefGoogle Scholar
  17. Sertel MR (1986) Lectures notes in microeconomics. Bogazici University, unpublishedGoogle Scholar
  18. Sertel MR, Yilmaz B (1999) The majoritarian compromise is majoritarian optimal and subgame perfect implementable. Social Choice Welf 16:615–627CrossRefGoogle Scholar
  19. Smith JH (1973) Aggregation of preferences with variable electorate. Econometrica 41:1027–1041CrossRefGoogle Scholar
  20. Young HP (1974) A note on preference aggregation. Econometrica 42:1129–1131CrossRefGoogle Scholar
  21. Young HP (1975) Social choice scoring functions. SIAM J Appl Math 28:824–838CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Vincent Merlin
    • 1
  • İpek Özkal Sanver
    • 2
    • 3
  • M. Remzi Sanver
    • 4
    Email author
  1. 1.Normandy University, UNICAEN, CNRS, UMR [6211], CREM, MRSH bureau 131Université de Caen NormandieCaen CedexFrance
  2. 2.Department of Economicsİstanbul Bilgi UniversityEyüp, IstanbulTurkey
  3. 3.Murat Sertel Center for Advanced Economic Studiesİstanbul Bilgi UniversityEyüp, IstanbulTurkey
  4. 4.Université Paris-DauphineUniversité PSL, CNRS, LAMSADEParisFrance

Personalised recommendations