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Rank
disequilibrium in multiple-criteria evaluation schemes
Jonathan K. Hodge, Faye Sprague-Williams and Jamie Woelk
Vol. 10 (2017), No. 1, 165–180
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 91B08, 91B14
Secondary: 06A07
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Milestones
Received: 16 October 2015
Revised: 17 December 2015
Accepted: 25 December 2015
Published: 11 October 2016
Communicated by Kenneth S. Berenhaut
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Authors |
| Jonathan K. Hodge | |
| Department of Mathematics Grand Valley State University Allendale, MI 49401 United States |
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| Faye Sprague-Williams | |
| Mount Holyoke College South Hadley, MA 01075 United States |
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| Jamie Woelk | |
| Western State Colorado
University Gunnison, CO 81231 United States |
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