Clone structures in voters' preferences

Authors:
Edith Elkind;Piotr Faliszewski;Arkadii Slinko
Affiliations:
Nanyang Technological University, Singapore, Singapore;AGH University of Science and Technology, Krakow, Poland;University of Auckland, Auckland, New Zealand
Venue:
Proceedings of the 13th ACM Conference on Electronic Commerce
Year:
2012

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Abstract

In elections, a set of candidates ranked consecutively (though possibly in different order) by all voters is called a clone set, and its members are called clones. A clone structure is the family of all clone sets of a given election. In this paper we study properties of clone structures. In particular, we give an axiomatic characterization of clone structures, show that they are organized hierarchically, and analyze clone structures in single-peaked and single-crossing elections. We describe a polynomial-time algorithm that finds a minimal collection of clones that need to be collapsed for an election to become single-peaked, and we show that this problem is NP-hard for single-crossing elections.