The Colley Method is an Extension of the Borda Count

Summary

The Colley and Massey methods are two well-known methods to rate sports teams. We prove that when the Colley method is applied to election data, then it returns the same outcome as the Borda count, a well-known election procedure. Hence, the Colley method is an extension of the Borda count to partial orderings of candidates. A similar relationship holds between the Massey method and range voting. Real data from Major League Baseball is used.

MSC:

• Primary 91B14

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Michael A. Jones

MICHAEL A. JONES (MR Author ID: 640157) is the Managing Editor and an Associate Editor at Mathematical Reviews. The idea for this paper came about while teaching the Colley matrix and the Borda count to high school students in his “The Mathematics of Decisions, Elections and Games” class as part of the Michigan Math and Science Scholars summer program at the University of Michigan.

Jennifer Wilson

JENNIFER WILSON (MR Author ID: 848485) is Associate Professor of Mathematics at Eugene Lang College at The New School. She is interested in problems that use mathematics to analyze fairness, and works in a number of areas including social choice theory, resource allocation and game theory.