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Social Choice and Welfare

, Volume 21, Issue 3, pp 433–454 | Cite as

Some startling inconsistencies when electing committees

  • Thomas C. Ratliff
Article

Abstract

We generalize the idea of a Condorcet winner to committee elections to select a Condorcet committee of size m. As in the case of a Condorcet winner, the Condorcet committee need not exist. We adapt two methods to measure how far a set of m candidates is from being the Condorcet committee. In particular, we generalize a procedure proposed by Lewis Carroll for selecting the candidate that is closest to being the Condorcet winner to allow the selection of a committee. We also generalize Kemeny’s method, which gives a complete transitive ranking, to the selection of committees and show that it is closely related to the first method.We show that these methods lead to some surprising inconsistencies. For example, the committee of size k may be disjoint from the committee of size j or they may overlap in any manner, the committee arising from Carroll’s method may appear at any locations in the Kemeny ranking, and except for two highly restrictive cases, the members of the committee arising from Kemeny’s method may appear at any location in the Kemeny ranking.

Keywords

Condorcet Winner Restrictive Case Committee Election Transitive Ranking Kemeny Ranking 
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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Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.Department of MathematicsWheaton CollegeNortonUSA

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