A Winner--Loser Labeled Tournament Has at Most Twice as Many Outdegree Misrankings as Pair Misrankings

In any tournament, with the players partitioned any way into two groups called Winners and Losers, we define two measures: is the number of vertex pairs consisting of a labeled “loser” and a “winner” where the loser beats the winner, and similarly is the number of such pairs where the loser has at least as many total wins as the winner. We prove that and this bound is tight. The result has a natural interpretation and easy generalization in the domain of majorization.

By: Nikhil Bansal; Don Coppersmith; Gregory B. Sorkin

Published in: RC24107 in 2006


This Research Report is available. This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). I have read and understand this notice and am a member of the scientific community outside or inside of IBM seeking a single copy only.


Questions about this service can be mailed to reports@us.ibm.com .