Note---Ordinal Ranking and Intensity of Preference: A Linear Programming Approach

Iqbal Ali, Wade D. Cook and Moshe Kress
Additional contact information
Iqbal Ali: Department of General Business, University of Texas, Austin, Texas 78712
Wade D. Cook: Faculty of Administrative Studies, York University, Toronto, Ontario, Canada M3J 2R6
Moshe Kress: CEMA, P.O. Box 2250, Haifa, Israel

Management Science, 1986, vol. 32, issue 12, 1642-1647

Abstract: Cook and Kress (Cook, Wade D., Moshe Kress. 1985. Ordinal ranking with intensity of preference. Management Sci. 31 (1) 26--32.) present a model for representing ordinal preference rankings, where the voter can express intensity or degree of preference. The consensus of a set of m rankings is that ranking whose distance from this set is minimal. The consensus problem is then shown to be an integer programming problem with a piecewise linear convex objective function. In the present note we prove that the constraint matrix for this integer problem is totally unimodular. In addition, it is shown that the problem can be expressed as an equivalent integer linear programming problem. These two facts allow us to represent the consensus problem as a linear programming model. To further facilitate an efficient solution procedure to the consensus problem, it is shown that the number of columns in the L.P. model can generally be reduced significantly. Computational results on a wide range of problems is presented.

Keywords: group decisions; voting/committees; integer programming (search for similar items in EconPapers)
Date: 1986
References: Add references at CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://dx.doi.org/10.1287/mnsc.32.12.1642 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:32:y:1986:i:12:p:1642-1647

Access Statistics for this article

More articles in Management Science from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().