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- Title
ORDINAL RANKING AND INTENSITY OF PREFERENCE: A LINEAR PROGRAMMING APPROACH.
- Authors
Ali, Iqbal; Cook, Wade D.; Kress, Moshe
- Abstract
Cook and Kress (1985) 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.
- Subjects
CONSUMER preferences; VOTING; VOTERS; INTEGER programming; LINEAR programming; MATHEMATICAL programming; CONVEX functions; DECISION making; MATRICES (Mathematics); CONSENSUS (Social sciences); MATHEMATICAL models; PROBLEM solving
- Publication
Management Science, 1986, Vol 32, Issue 12, p1642
- ISSN
0025-1909
- Publication type
Article
- DOI
10.1287/mnsc.32.12.1642