Social Choice and Welfare

, Volume 34, Issue 3, pp 487–496 | Cite as

Characterizing best–worst voting systems in the scoring context

  • José Luis García-LaprestaEmail author
  • A. A. J. Marley
  • Miguel Martínez-Panero
Original Paper


An increasing body of theoretical and empirical work on discrete choice considers a choice design in which a person is asked to select both the best and the worst alternative in an available set of alternatives, in contrast to more traditional tasks, such as where the person is asked to: select the best alternative; select the worst alternative; rank the alternatives. Here we consider voting systems motivated by such “best–worst” choice; characterize a class of “best–worst” voting systems in terms of a set of axioms in the context of scoring rules; and discuss briefly possible extensions to approval–disapproval systems.


Econ Theory Vote System Discrete Choice Experiment Social Choice Function Approval Vote 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Arrow KJ (1963) Social choice and individual values, 2nd edn [1st edition: 1951] Wiley, New YorkGoogle Scholar
  2. Baharad E, Nitzan S (2005) The inverse plurality rule—an axiomatization. Soc Choice Welf 25: 173–178CrossRefGoogle Scholar
  3. Barberà S, Dutta B (1982) Implementability via protective equilibria. J Math Econ 10: 49–65CrossRefGoogle Scholar
  4. Chebotarev PY, Shamis E (1998) Characterizations of scoring methods for preference aggregation. Ann Oper Res 80: 299–332CrossRefGoogle Scholar
  5. Ching S (1996) A simple characterization of plurality rule. J Econ Theory 71: 298–302CrossRefGoogle Scholar
  6. Cohen S (2003) Maximum difference scaling: improved measures of importance and preference for segmentation. Sawtooth Software Conference Proceedings, Sawtooth Software, Inc. 530 W. Fir St. Sequim, WA (, pp 61–74
  7. Cohen S, Neira L (2004) Measuring preference for product benefits across countries: overcoming scale usage bias with maximum difference scaling. Paper presented at the Latin American Conference of the European Society for opinion and marketing research, Punta del Este, Uruguay (2003). Reprinted in Excellence in International Research: ESOMAR, Amsterdam, The Netherlands, pp 1–22Google Scholar
  8. Dummett M (1984) Voting procedures. Clarendon Press, OxfordGoogle Scholar
  9. Finn A, Louviere JJ (1992) Determining the appropriate response to evidence of public concern: the case of food safety. J Public Policy Mark 11: 12–25Google Scholar
  10. Fishburn PC (1978) Axioms for approval voting: direct proof. J Econ Theory 19: 180–185CrossRefGoogle Scholar
  11. Gärdenfors P (1973) Positionalist voting functions. Theory Decis 4: 1–24CrossRefGoogle Scholar
  12. Lepelley D (1992) Une caracterérisation du vote à la majorité simple. RAIRO Oper Res 26: 361–365Google Scholar
  13. Marchant T (2007) An axiomatic characterization of different majority concepts. Eur J Oper Res 179: 160–173CrossRefGoogle Scholar
  14. Marley AAJ (2009) The best–worst method for the study of preferences: theory and applications. Proceedings of XXIX international congress of psychology. Psychology Press (in press)Google Scholar
  15. Marley AAJ, Louviere JJ (2005) Some probabilistic models of best, worst, and best–worst choices. J Math Psychol 49: 464–480CrossRefGoogle Scholar
  16. May KO (1952) A set of independent necessary and sufficient conditions for simple majority decision. Econometrica 20: 680–684CrossRefGoogle Scholar
  17. Merlin V (2003) The axiomatic characterizations of majority voting and scoring rules. Mathématiques et Sciences Humaines. Math Soc Sci 161: 87–109Google Scholar
  18. Merlin V, Naeve J (2000) Implementation of social choice functions via demanding equilibria. Diskussionspapiere aus dem Institut für Volkswirtschaftslehre der Universität Hohenheim from Department of Economics, University of Hohenheim, No 191/2000Google Scholar
  19. Richelson JT (1978) A characterization result for the plurality rule. J Econ Theory 19: 548–550CrossRefGoogle Scholar
  20. Smith JH (1973) Aggregation of preferences with variable electorate. Econometrica 41: 1027–1041CrossRefGoogle Scholar
  21. Woeginger GH (2003) A note on scoring rules that respect majority in choice and elimination. Math Soc Sci 46: 347–354CrossRefGoogle Scholar
  22. Young HP (1974) An axiomatization of Borda’s rule. J Econ Theory 9: 43–52CrossRefGoogle Scholar
  23. Young HP (1975) Social choice scoring functions. SIAM J Appl Math 28: 824–838CrossRefGoogle Scholar
  24. Young HP, Levenglick A (1978) A consistent extension of Condorcet’s election principle. SIAM J Appl Math 35: 285–300CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • José Luis García-Lapresta
    • 1
    Email author
  • A. A. J. Marley
    • 2
    • 3
  • Miguel Martínez-Panero
    • 1
  1. 1.PRESAD Research Group, Department of Applied EconomicsUniversity of ValladolidValladolidSpain
  2. 2.Department of PsychologyUniversity of VictoriaVictoriaCanada
  3. 3.Centre for the Study of ChoiceUniversity of TechnologySydneyAustralia

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