School of Mathematical Sciences

Record breaking Condorcet domains menu

Record breaking Condorcet domains

Soren Riis (EECS, QMUL)
Fri, 24/02/2017 - 16:00
Queen's building W316
Seminar series: 

The theory of rankings and voting is riddled with curious “paradoxes” related to non-transitivity. I will introduce a few new results on non-transitive dice games (joint work with Mike Paterson) and relate this to the area of Condorcet domains.
A Condorcet domain (CD) consists of a collection of linear orderings of a fixed finite set that satisfies a particular type of constraint for each 3-element subset.
One fundamental problem is to construct large CDs for a given finite set of size n. Already in the 1950s some constructions of CD domains were known, and these were then improved in the mid-1980s. Until recently only optimal values (9 and 20) for n=4 and n=5 were known. Recently, we showed (by heavy use of computer calculations) that the optimal values for n=6 and n=7 are 45 and 100 respectively (joint work with Akello-Egwel, Leedham-green, Litterrick, Markstrom). This result was already conjectured in the early 1990s. In the talk, I will present a new class of schemes for constructing large Condorcet domains that beat the 20+-year-old records. I will conclude with a list of open questions for further research.