On Generalized Tournament Matrices

Previous article Next article On Generalized Tournament MatricesJ. W. Moon and N. J. PullmanJ. W. Moon and N. J. Pullmanhttps://doi.org/10.1137/1012081PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 G. G. Alway, Matrices and sequences, Math. Gaz., 46 (1962), 208–213 0106.24005 CrossrefGoogle Scholar2 Ralph Allan Bradley and , Milton E. Terry, Rank analysis of incomplete block designs. I. The method of paired comparisons, Biometrika, 39 (1952), 324–345 MR0070925 0047.12903 ISIGoogle Scholar3 Alfred Brauer and , Ivey C. Gentry, On the characteristic roots of tournament matrices, Bull. Amer. Math. Soc., 74 (1968), 1133–1135 MR0232784 0167.03002 CrossrefISIGoogle Scholar4 H. E. Daniels, Round-robin tournament scores, Biometrika, 56 (1969), 295–299 CrossrefISIGoogle Scholar5 H. A. David, The method of paired comparisons, Hafner Publishing Co., New York, 1963, 124– MR0174105 Google Scholar6 L. R. Ford, Jr., Solution of a ranking problem from binary comparisons, Amer. Math. Monthly, 64 (1957), 28–33 MR0097876 0089.15304 CrossrefGoogle Scholar7 L. R. Ford, Jr. and , D. R. Fulkerson, Flows in networks, Princeton University Press, Princeton, N.J., 1962xii+194 MR0159700 0106.34802 Google Scholar8 D. R. Fulkerson, Upsets in round robin tournaments, Canad. J. Math., 17 (1965), 957–969 MR0188092 0135.01304 CrossrefISIGoogle Scholar9 David Gale, A theorem on flows in networks, Pacific J. Math., 7 (1957), 1073–1082 MR0091855 0087.16303 CrossrefGoogle Scholar10 F. R. Gantmacher, The theory of matrices. Vol. 2, Translated by K. A. Hirsch, Chelsea Publishing Co., New York, 1959ix+276 MR0107649 Google Scholar11 M. G. Kendall, Further contributions to the theory of paired comparisons, Biometrics, 11 (1955), 43–62 MR0075506 CrossrefISIGoogle Scholar12 H. G. Landau, On dominance relations and the structure of animal societies. III. The condition for a score structure, Bull. Math. Biophys., 15 (1953), 143–148 MR0054933 CrossrefGoogle Scholar13 Marvin Marcus and , Henryk Minc, A survey of matrix theory and matrix inequalities, Allyn and Bacon Inc., Boston, Mass., 1964xvi+180 MR0162808 0126.02404 Google Scholar14 J. W. Moon, An extension of Landau's theorem on tournaments, Pacific J. Math., 13 (1963), 1343–1345 MR0155763 0133.13303 CrossrefISIGoogle Scholar15 J. W. Moon and , N. J. Pullman, On the powers of tournament matrices, J. Combinatorial Theory, 3 (1967), 1–9 MR0213264 0166.00901 CrossrefGoogle Scholar16 N. J. Pullman and , J. W. Moon, Tournaments and handicapsInformation Processing 68 (Proc. IFIP Congress, Edinburgh, 1968), Vol. 1: Mathematics, Software, North-Holland, Amsterdam, 1969, 219–223 MR0272643 0191.49901 Google Scholar17 R. Rado, Theorems on linear combinatorial topology and general measure, Ann. of Math. (2), 44 (1943), 228–270 MR0009445 0061.09702 CrossrefGoogle Scholar18 C. Ramanujacharyulu, Analysis of preferential experiments, Psychometrika, 29 (1964), 257–261 10.1007/BF02289722 0126.36603 CrossrefISIGoogle Scholar19 Bernard Roy, Sur quelques propriétés des graphes fortement connexes, C. R. Acad. Sci. Paris, 247 (1958), 399–401 MR0096237 0086.16302 Google Scholar20 H. J. Ryser, Matrices of zeros and ones in combinatorial mathematicsRecent Advances in Matrix Theory (Proc. Advanced Seminar, Math. Res. Center, U.S. Army, Univ. Wisconsin, Madison, Wis., 1963), Univ. Wisconsin Press, Madison, Wis., 1964, 103–124 MR0164905 0129.00802 Google Scholar21 G. L. Thompson, Lectures on game theory, Markov chains, and related topics, Monograph SCR-11, Sandia Corporation, Albuquerque, N.M, 1958 0089.16103 CrossrefGoogle Scholar22 T. H. Wei, Masters Thesis, The algebraic foundations of ranking theory, Doctoral thesis, Cambridge University, Cambridge, 1952 Google Scholar23 E. Zermelo, Die Berechnung der Turnier-Ergebnisse als ein Maximumproblem der Wahrscheinlichkeitsrechnung, Math. Z., 29 (1929), 436–460 10.1007/BF01180541 MR1545015 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails A stochastic method for exploiting outranking relations in multicriteria choice problems22 August 2022 | Annals of Operations Research, Vol. 200 Cross Ref To stay discovered: On tournament mean score sequences and the Bradley–Terry modelStochastic Processes and their Applications, Vol. 150 Cross Ref Pooling Rankings to Obtain a Set of Scores for a Composite Indicator of Erasmus + Mobility Effects15 October 2020 | Social Indicators Research, Vol. 156, No. 2-3 Cross Ref Group decisions from individual rankings: The Borda–Condorcet ruleEuropean Journal of Operational Research, Vol. 291, No. 2 Cross Ref Dealing with categorical data in a multidimensional context: The multidimensional balanced worthSocial Science Research, Vol. 96 Cross Ref Generalized tournament matrices with the same principal minors26 April 2021 | Linear and Multilinear Algebra, Vol. 485 Cross Ref Preference Graph of Potential Method as a Fuzzy GraphAdvances in Fuzzy Systems, Vol. 2020 Cross Ref Random walks and diffusion on networksPhysics Reports, Vol. 716-717 Cross Ref The Herrero-Villar approach to citation impactJournal of Informetrics, Vol. 11, No. 2 Cross Ref The Landau Legacy: From Chess to PagerankSSRN Electronic Journal Cross Ref Some properties complementary to Brualdi-Li matrices15 April 2015 | Czechoslovak Mathematical Journal, Vol. 65, No. 1 Cross Ref A graph interpretation of the least squares ranking method11 May 2014 | Social Choice and Welfare, Vol. 44, No. 1 Cross Ref Pseudo-Tournament Matrices and Their Eigenvalues28 May 2015 | East Asian Journal on Applied Mathematics, Vol. 4, No. 3 Cross Ref Paired comparisons analysis: an axiomatic approach to ranking methods20 February 2013 | Social Choice and Welfare, Vol. 42, No. 1 Cross Ref Tournaments26 November 2013 Cross Ref Matrices of Forests, Analysis of Networks, and Ranking ProblemsProcedia Computer Science, Vol. 17 Cross Ref Uniform sampling of k -hypertournamentsLinear and Multilinear Algebra, Vol. 61, No. 1 Cross Ref A network-based dynamical ranking system for competitive sports5 December 2012 | Scientific Reports, Vol. 2, No. 1 Cross Ref Internal slackening scoring methods13 October 2011 | Theory and Decision, Vol. 72, No. 4 Cross Ref Bimodal invitation-navigation fair bets model for authority identification in a social network Cross Ref Fair Seeding in Knockout TournamentsACM Transactions on Intelligent Systems and Technology, Vol. 3, No. 1 Cross Ref Directed Graphs22 February 2011 Cross Ref Paired Comparisons Analysis: An Axiomatic Approach to Rankings in TournamentsSSRN Electronic Journal Cross Ref Dynamics-based centrality for directed networks8 November 2010 | Physical Review E, Vol. 82, No. 5 Cross Ref Visualisation and ordering of many-objective populations Cross Ref Tournaments of Weakly Heterogeneous PlayersJournal of Public Economic Theory, Vol. 11, No. 5 Cross Ref The Predictive Power of Three Prominent Tournament FormatsManagement Science, Vol. 54, No. 3 Cross Ref Scoring of web pages and tournaments—axiomatizations30 March 2006 | Social Choice and Welfare, Vol. 26, No. 1 Cross Ref Three Prominent Tournament Formats: Predictive Power and CostsSSRN Electronic Journal Cross Ref On two new social choice correspondencesMathematical Social Sciences, Vol. 47, No. 1 Cross Ref On the location of the spectrum of hypertournament matricesLinear Algebra and its Applications, Vol. 323, No. 1-3 Cross Ref Some results on h-hypertournament matricesComputers & Mathematics with Applications, Vol. 35, No. 4 Cross Ref Generalized bicyclesDiscrete Applied Mathematics, Vol. 78, No. 1-3 Cross Ref Multivariate Description of Comparison MatricesJournal of Multi-Criteria Decision Analysis, Vol. 5, No. 2 Cross Ref Eigenvalues of oriented-graph matricesLinear Algebra and its Applications, Vol. 221 Cross Ref Spectral radii of tournament matrices whose graphs are related by an arc reversalLinear Algebra and its Applications, Vol. 217 Cross Ref Aggregation of preferences by the generalized row sum methodMathematical Social Sciences, Vol. 27, No. 3 Cross Ref Pick's inequality and tournamentsLinear Algebra and its Applications, Vol. 186 Cross Ref A reversal index for tournament matrices *Linear and Multilinear Algebra, Vol. 34, No. 3-4 Cross Ref Nonparametric Methods of Ranking from Paired Comparisons Cross Ref Algebraic multiplicity of the eigenvalues of a tournament matrixLinear Algebra and its Applications, Vol. 169 Cross Ref Hypertournament matrices, score vectors and eigenvaluesLinear and Multilinear Algebra, Vol. 30, No. 4 Cross Ref Tournament matrices and their generalizations, I.Linear and Multilinear Algebra, Vol. 28, No. 1-2 Cross Ref Comparaisons par paires : une interprétation et une généralisation de la méthode des scores29 March 2011 | RAIRO - Operations Research, Vol. 20, No. 3 Cross Ref Ranking the Vertices of a Paired Comparison DigraphMikio Kano and Akio Sakamoto17 July 2006 | SIAM Journal on Algebraic Discrete Methods, Vol. 6, No. 1AbstractPDF (1341 KB)The median procedure in cluster analysis and social choice theoryMathematical Social Sciences, Vol. 1, No. 3 Cross Ref A Graph Theoretical Approach to Handicap Ranking of Tournaments and Paired ComparisonsKenneth A. Berman17 July 2006 | SIAM Journal on Algebraic Discrete Methods, Vol. 1, No. 3AbstractPDF (364 KB)Transitivity and United States Migration Streams: A Comment1 April 1980 | Environment and Planning A: Economy and Space, Vol. 12, No. 4 Cross Ref Recent progress and unsolved problems in dominance theory24 August 2006 Cross Ref Mixtures of order matrices and generalized order matricesDiscrete Mathematics, Vol. 19, No. 2 Cross Ref Directed Graphs Cross Ref Preference aggregation and statistical estimationTheory and Decision, Vol. 4, No. 1 Cross Ref PageRank as a Weak Tournament Solution Cross Ref Volume 12, Issue 3| 1970SIAM Review History Submitted:11 June 1968Published online:18 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1012081Article page range:pp. 384-399ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics