Speaker:     Adam Clearwater
Affiliation: The University of Auckland
Title:       The single-crossing property on a tree
Date:        Tuesday, 11 Mar 2014
Time:        5:00 pm
Location:    Room 412, Science Centre (303)

We generalize the classical single-crossing property to single-crossing property on trees and obtain new ways to construct the so-called Condorcet domains which are sets of linear orders which possess the property that every profile composed from those orders have transitive majority relation. We prove that for any tree there exist profiles that are single-crossing on that tree; moreover, that tree is minimal in this respect for at least one such profile. Finally, we provide a polynomial-time algorithm to recognize whether or not a given profile is single-crossing with respect to some tree. We also show that finding winners for Chamberlin-Courant rule is polynomial  for profiles that are single-crossing on trees.

This paper is a product of Adam’s Summer Scholarship project. The research was conducted jointly with Clemens Puppe (KIT, Germany) and Arkadii Slinko.