Ranking by pairwise comparisons for Swiss-system tournaments
- 518 Downloads
Pairwise comparison matrices are widely used in multicriteria decision making. This article applies incomplete pairwise comparison matrices in the area of sport tournaments, namely proposing alternative rankings for the 2010 Chess Olympiad Open tournament. It is shown that results are robust regarding scaling technique. In order to compare different rankings, a distance function is introduced with the aim of taking into account the subjective nature of human perception. Analysis of the weight vectors implies that methods based on pairwise comparisons have common roots. Visualization of the results is provided by multidimensional scaling on the basis of the defined distance. The proposed rankings give in some cases intuitively better outcome than currently used lexicographical orders.
KeywordsMulticriteria decision making Incomplete pairwise comparison matrix Ranking for Swiss-system tournaments Multidimensional scaling
Unable to display preview. Download preview PDF.
- Crawford G, Williams C (1980) Analysis of subjective judgment matrices. The Rand Corporation, Office of the Secretary of Defense USA, R-2572-AFGoogle Scholar
- De Graan JG (July 22–25 1980) Extensions of the multiple criteria analysis method of T.L. Saaty. Presented at EURO IV Conference, CambridgeGoogle Scholar
- Gass SI (1998) Tournaments, transitivity and pairwise comparison matrices. J Oper Res Soc 49: 616–624Google Scholar
- Handbook of FIDE. D.II.02 (2010) Regulations for specific competitions, Chess Olympiad, Olympiad pairing rules. Approved by the 1994 and 1998 Executive Councils, amended by the 2006 Presidential Board and the 2007 and 2009 Executive Council. http://www.fide.com/fide/handbook.html?id=95&view=article
- Kruskal JB, Wish M (1978) Multidimensional scaling. Sage, Beverly HillsGoogle Scholar
- Norris AN (2005) The isotropic material closest to a given anisotropic material. J Mech Mater Struct 1(2): 231–246Google Scholar
- Results of the 39th Olympiad Khanty-Mansiysk 2010 Open tournament (2010) http://chess-results.com/tnr36795.aspx?lan=1
- Saaty TL (1980) The analytic hierarchy process. McGraw-Hill, New YorkGoogle Scholar
- Tarsitano A (2008) Nonlinear rank correlations. Working Paper. Agostino Tarsitano, Italy (in press). http://eprints.bice.rm.cnr.it/586/