Ranking participants in generalized tournaments

International Journal of Game Theory

Volumn 33, Issue 2, 2005, Pages 255-270

  Slutzki, Giora ^a   Volij, Oscar ^b,c  

^a Iowa State University   (United States)

^b IOWA STATE UNIVERSITY   (United States)

^c BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

Birkhoff's theorem; Perron Frobenius theorem; Ranking and scoring methods; Tournaments

Indexed keywords

EID: 33644526601     PISSN: 00207276     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00182-005-0197-5     Document Type: Article

References (26)

1. Arrow KJ (1963) Social Choice and Individual Values (2nd ed). Yale University Press, New Haven
2. Birkhoff G (1946) Tres observaciones sobre el àlgebra lineal. Univ Nac Tucumán Rev Ser A 5:147-150
3. Bouyssou D (1992) Ranking methods based on valued preference relations: A characterization of the net flow method. European Journal of Operational Research 60:61-67
4. Conner GR, Grant CP (2000) An extension of Zermelo's model for ranking by paired comparisons. European Journal of Applied Mathematics 11:225-247
5. Daniels HE (1969) Round-robin tournament scores. Biometrika 56:295-299
6. David HA (1987) Ranking from unbalanced paired-comparison data. Biometrika 74:432-436
7. David HA (1988) The Method of Paired Comparisons (2 ed). Charles Griffin and Company, London
8. Henriet D (1985) The Copeland choice function: an axiomatic characterization. Social Choice and Welfare 2:49-63
9. Herings J-J, van der Laan G, Talman D (2004) The positional power of nodes in digraphs. Social Choice and Welfare, forthcoming
10. Kano M, Sakamoto A (1985) Ranking the vertices of a paired comparison digraph. SIAM Journal on Algebraic and Discrete Methods 6:79-92
11. Keener JP (1993) The Perron-Frobenius theorem and the ranking of footbal teams. SIAM Review 35:80-93
12. Kendall MG (1955) Further contributions to the theory of paired comparisons. Biometrics 11:43-62
13. Laslier J (1997) Tournament Solutions and Majority Voting. Springer, Berlin
14. Levchenkov VS (1992) Social choice theory: a new insight. Discussion paper, Institute of Systems Analysis, Moscow
15. Levchenkov VS (1995) Self-consistent rule for group choice. I: Axiomatic approach. Discussion Paper 95-3, Conservatoire National des Arts et Métiers
16. Minc H (1988) Nonnegative Matrices. John Wiley & Sons
17. Moon JW (1968) Topics on Tournaments. Holt, Rinehart and Winston, New York
18. Moon JW, Pullman NJ (1970). On generalized tournament matrices. SIAM Review 12:384-399
19. Moulin H (1988) Axioms of Cooperative Decision Making. Cambridge University Press, Cambridge, UK
20. Palados-Huerta I, Volij O (2004) The measurement of intellectual influence. Econometrica 72:963-977
21. Rubinstein A (1980) Ranking the participants in a tournament. SIAM Journal of Applied Mathematics 38:108-111
22. Sen A (1970) Individual Choice and Social Welfare. Holden Day, San Francisco
23. Slutzki G, Volij O (2004) Scoring of web pages and tournaments - axiomatizations. Social Choice and Welfare, forthcoming
24. van den Brink, Gilles R (2000) Measuring domination in directed networks. Social Networks 22:141-157
25. Wei T (1952) The algebraic foundation of ranking theory. Ph. D. Thesis, Cambridge University
26. Zermelo E (1929) Die Berechnung der Turnier-Ergebnisse als ein Maximalproblem der Wahrscheinlichkeitsrechnung. Mathematische Zeitschrift 29:436-460