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.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
The author wishes to express his thanks to Don Saari for his conversations and suggestions for the paper and to the Institute for Mathematical Behavioral Sciences at the University of California at Irvine where the initial work for this paper took place. He also wishes to thank the anonymous reviewer whose careful reading and suggestions greatly improved the paper.
Rights and permissions
About this article
Cite this article
Ratliff, T. Some startling inconsistencies when electing committees. Soc Choice Welfare 21, 433–454 (2003). https://doi.org/10.1007/s00355-003-0209-y
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s00355-003-0209-y