Vol. 10, No. 1, 2017

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Rank disequilibrium in multiple-criteria evaluation schemes

Jonathan K. Hodge, Faye Sprague-Williams and Jamie Woelk

Vol. 10 (2017), No. 1, 165–180
Abstract

In multiple-criteria evaluation schemes, rank disequilibrium occurs when an evaluee is rated higher than other evaluees on some criteria and lower than other evaluees on other criteria. In this article, we investigate rank disequilibrium as it relates to the problem of aggregating scores on individual criteria into an overall evaluation. We adopt an axiomatic approach, defining the notion of a rank aggregation function and proposing a set of desirable properties — namely, independence, monotonicity, inclusivity, consistency, and equity — that rank aggregation functions may or may not satisfy. We prove that when there are more than three possible scores on each criterion, it is impossible to define a rank aggregation function that satisfies all of these properties. We then investigate potential resolutions to the problems posed by rank disequilibrium.

Keywords
rank disequilibrium, status inconsistency, inequity, multiple-criteria evaluation, rank aggregation function
Mathematical Subject Classification 2010
Primary: 91B08, 91B14
Secondary: 06A07
Milestones
Received: 16 October 2015
Revised: 17 December 2015
Accepted: 25 December 2015
Published: 11 October 2016

Communicated by Kenneth S. Berenhaut
Authors
Jonathan K. Hodge
Department of Mathematics
Grand Valley State University
Allendale, MI 49401
United States
Faye Sprague-Williams
Mount Holyoke College
South Hadley, MA 01075
United States
Jamie Woelk
Western State Colorado University
Gunnison, CO 81231
United States