Public Choice

, Volume 36, Issue 1, pp 89–114 | Cite as

Approval voting, Condorcet's principle, and runoff elections

  • Peter C. Fishburn
  • Steven J. Brams
Articles

Abstract

Approval voting allows each voter to vote for as many candidates as he wishes in an election but not cast more than one vote for each candidate of whom he approves. If there is a strict Condorcet candidate — a candidate who defeats all others in pairwise contests — approval voting is shown to be the only nonranked voting system that is always able to elect the strict Condorcet candidate when voters use sincere admissible strategies. Moreover, if a strict Condorcet candidate must be elected under ordinary plurality voting when voters use admissible strategies, then he must also be elected under approval voting when voters use admissible strategies, but the converse does not hold.

The widely used plurality runoff method can also elect a strict Condorcet candidate when voters use admissible strategies on the first ballot, but some of these may have to be insincere to get the strict Condorcet candidate onto the runoff ballot. Furthermore, there is no case in which the strict Condorcet candidate is invariably elected under the plurality runoff method when voters use admissible first-ballot strategies. Thus, approval voting is superior to the plurality runoff method with respect to the Condorcet principle in its ability to elect the strict Condorcet candidate by sincere voting and in its ability to guarantee the election of the strict Condorcet candidate when voters use admissible strategies. In addition, approval voting is more efficient since it requires only one election and is probably less subject to strategic manipulation.

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References

  1. [1]
    Brams, S.J., and Fishburn, P.C. (1978). ‘Approval Voting.’ American Political Science Review, 72: 831–847.Google Scholar
  2. [2]
    Brams, S.J., and Fishburn, P.C. (1978). ‘Reconstructing Voting Processes: The 1976 House Majority Leader Election under Present and Alternative Rules.’ Mimeo.Google Scholar
  3. [3]
    Fishburn, P.C. (1978). ‘A Strategic Analysis of Nonranked Voting Systems.’ SIAM Journal on Applied Mathematics, 35: 488–495.Google Scholar
  4. [4]
    Gehrlein, W.V., and Fishburn, P.C. ‘The Effects of Abstentions on Election Outcomes.’ Public Choice (forthcoming).Google Scholar
  5. [5]
    Kellett, J., and Mott, K. (1977). ‘Presidential Primaries: Measuring Popular Choice.’ Polity, 9: 528–537.Google Scholar
  6. [6]
    Kiewiet, D.R. (1979). ‘Approval Voting: The Case of the 1978 Presidential Election.’ Polity, 12:170–181.Google Scholar
  7. [7]
    Merrill, S., III. (1980). ‘Strategic Decisions under One-stage Multi-candidate Voting Systems.’ Public Choice, 36:115–134.Google Scholar

Copyright information

© Martinus Nijhoff Publishers bv 1981

Authors and Affiliations

  • Peter C. Fishburn
    • 1
  • Steven J. Brams
    • 2
  1. 1.College of Business AdministrationThe Pennsylvania State UniversityUSA
  2. 2.Department of PoliticsNew York UniversityNew YorkUSA

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