  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 a 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 their
hierarchical structure, and analyze clone structures in single-peaked and
single-crossing elections. We give 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.
