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Elections with partially ordered preferences

Author

Listed:
  • Michael Ackerman
  • Sul-Young Choi
  • Peter Coughlin
  • Eric Gottlieb
  • Japheth Wood

Abstract

Suppose an organization has a committee with multiple seats, and the committee members are to be elected by a group of voters. For the organization, the possible alternatives are the possible sets of individuals who could serve together. A common approach is to choose from among these alternatives by having each voter cast separate votes on the candidates for each seat. When this type of ballot is used, important characteristics of the set of individuals on the committee (such as what percentage of the members will be female) might not be explicitly considered by the voters. Another approach that has been used is to have each voter cast a ballot which ranks all possible sets of members. However, this approach can require the voters to weigh a relatively large number of alternatives. This paper considers group decisions where it is desirable to: (1) explicitly consider characteristics of alternatives and (2) have a relatively small number of options upon which a voter has to express his preferences. The approach that we propose has two steps: First voters vote directly on pertinent characteristics of alternatives; Then these votes are used to indirectly specify preferences on alternatives. The indirectly specified preferences are ones that are naturally modeled using partially ordered sets. We identify some specific methods that could be applied in the second step. In addition, by replacing the indirectly specified preferences in a suitable way, we suggest a technique that can use any positional, pairwise, or other voting method that accepts totally (or “completely”) ordered inputs to tally ballots. We also describe another way to potentially compute pairwise rankings from partially ordered alternatives and discuss some practical and theoretical difficulties associated with our approach. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Michael Ackerman & Sul-Young Choi & Peter Coughlin & Eric Gottlieb & Japheth Wood, 2013. "Elections with partially ordered preferences," Public Choice, Springer, vol. 157(1), pages 145-168, October.
    • Handle: RePEc:kap:pubcho:v:157:y:2013:i:1:p:145-168
    DOI: 10.1007/s11127-012-9930-3
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    References listed on IDEAS

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    1. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521808163, October.
    2. Merlin, Vincent R. & Saari, Donald G., 1997. "Copeland Method II: Manipulation, Monotonicity, and Paradoxes," Journal of Economic Theory, Elsevier, vol. 72(1), pages 148-172, January.
    3. Bassett, Gilbert W, Jr & Persky, Joseph, 1999. "Robust Voting," Public Choice, Springer, vol. 99(3-4), pages 299-310, June.
    4. Fuad Aleskerov & Denis Bouyssou & Bernard Monjardet, 2007. "Utility Maximization, Choice and Preference," Springer Books, Springer, edition 0, number 978-3-540-34183-3, January.
    5. Joseph Kadane, 1972. "On division of the question," Public Choice, Springer, vol. 13(1), pages 47-54, September.
    6. Steven J. Brams, 1990. "Constrained Approval Voting: A Voting System to Elect a Governing Board," Interfaces, INFORMS, vol. 20(5), pages 67-80, October.
    7. Duncan Black, 1976. "Partial justification of the Borda count," Public Choice, Springer, vol. 28(1), pages 1-15, December.
    8. Merlin, Vincent & Valognes, Fabrice, 2004. "The impact of indifferent voters on the likelihood of some voting paradoxes," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 343-361, November.
    9. Peter Fishburn, 1973. "On the construction of weak orders from fragmentary information," Psychometrika, Springer;The Psychometric Society, vol. 38(4), pages 459-472, December.
    10. Vincent R. Merlin & Donald G. Saari, "undated". "The Copeland Method I; Relationships and the Dictionary," Discussion Papers 1111, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    11. Michael Taylor, 1968. "Graph-theoretic approaches to the theory of social choice," Public Choice, Springer, vol. 4(1), pages 35-47, March.
    12. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521004046, October.
    13. Donald G. Saari & Vincent R. Merlin, 1996. "The Copeland method (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 51-76.
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    Cited by:

    1. Terzopoulou, Zoi & Endriss, Ulle, 2021. "The Borda class," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 31-40.

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    More about this item

    Keywords

    Committee election; Linear extension; Partial order; Voting theory; D71; D72;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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