A minimum violations ranking method
- 275 Downloads
We present a rating method that, given information on the pairwise comparisons of n items, minimizes the number of inconsistencies in the ranking of those items. Our Minimum Violations Ranking (MVR) Method uses a binary linear integer program (BILP) to do this. We prove conditions when the relaxed LP will give an optimal solution to the original BILP. In addition, the LP solution gives information about ties and sensitivities in the ranking. Lastly, our MVR method makes use of bounding and constraint relaxation techniques to produce a fast algorithm for the linear ordering problem, solving an instance with about one thousand items in less than 10 minutes.
KeywordsMinimum violations rating Linear ordering Integer programming Linear programming Optimization Ties Sensitivity
Unable to display preview. Download preview PDF.
- Colley WN (2002) Colley’s bias free college football ranking method: the colley matrix explained Google Scholar
- Kemeny JG (1959) Mathematics without numbers. Daedalus 88(4):577–591 Google Scholar
- Kolen AWJ, Lenstra JK (1995) Combinatorics in operations research. In: Handbook of combinatorics, pp 1875–1910 Google Scholar
- Massey K (1997) Statistical models applied to the rating of sports teams. Bachelor’s thesis, Bluefield College Google Scholar
- Park J (2005) On minimum violations ranking in paired comparisons. arXiv:physics/0510242
- Reinelt G, Grötschel M, Jünger M (1983) Optimal triangulation of large real world input-output matrices. Stat Pap 25(1):261–295 Google Scholar