Preference fusion when the number of alternatives exceeds two: Indirect scoring procedures

Journal of the Franklin Institute

Volumn 336, Issue 2, 1999, Pages 205-226

  Chebotarev, Pavel Yu ^a   Shamis, Elena ^a  

^a TRAPEZNIKOV INSTITUTE OF CONTROL SCIENCES   (Russian Federation)

Author keywords

Aggregation of incomplete preferences; Axiomatic approach; Paired comparisons

Indexed keywords

EID: 0039170109     PISSN: 00160032     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0016-0032(98)00017-9     Document Type: Article

References (66)

1. M.J.A. Marquis de Condorcet, Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix, Paris, 1785.
2. B. Grofman, G. Owen (Eds.), Review essay: Condorcet models, avenues for further research, in: Information Pooling and Group Decision Making, Jai Press, Greenwich, CT, 1986, pp. 93-102.
3. S. Berg, Evaluation of some weighted majority decision rules under dependent voting, Math. Social Sci. 28 (1994) 71-83.
4. K. May, A set of independent necessary and sufficient condition for simple majority decision. Econometrica 20 (1952) 680-684.
5. H.A. David, The Method of Paired Comparisons, 2nd ed., Griffin, London, 1988.
6. M.A. Fligner, J.S. Verducci (Eds.), Probability Models and Statistical Analyses for Ranking Data, Springer, New York, 1993.
7. P.Yu. Chebotarev, E. Shamis, Constructing an objective function for aggregating incomplete preferences, in: A. Tangian, J. Gruber (Eds.), Econometric Decision Models. Lecture Notes in Economics and Mathematical Systems, Springer, Berlin, 1997, pp. 100-124.
8. J.W. Moon, Topics on Tournaments, Holt, Rinehart and Winston, New York, 1968.
9. A.R. Belkin, M.S. Levin, Decision Making: Combinatorial Models of Information Approximation, Nauka, Moscow, 1990 (in Russian).
10. R. Van Blokland-Vogelesang, Unfolding and Group Consensus Ranking for Individual Preferences, DSWO Press, Leiden, 1991.
11. W.D. Cook, M. Kress, Ordinal Information and Preference Structures: Decision Models and Applications, Prentice-Hall, Englewood Cliffs, NJ. 1992.
12. H.E. Daniels, Round-robin tournament scores, Biometrika 56 (1969) 295-299.
13. J.W. Moon, N.J. Pullman, On generalized tournament matrices, SIAM Rev. 12 (1970) 384-399.
14. H.A. David, Ranking the players in a round robin tournament. Rev. Int. Stat. Inst. 39 (1971) 137-147.
15. D.S. Shmerling, S.A. Dubrovskii, D. Arzhanova, A.A. Frenkel, Expert judgments: Methods and applications, in: Statistical Methods of Analysis of Expert Judgments, Uchen. Zap. Stat., vol. 29, Nauka, Moscow, 1977 (in Russian), pp. 290-382.
16. H.A. David, D.M. Andrews, Nonparametric methods of ranking from paired comparisons, in: M.A. Fligner, J.S. Verducci (Eds.), Probability Models and Statistical Analyses for Ranking Data, Springer, New York, 1993, pp. 20-36.
17. J.P. Keener, The Perron Frobenius theorem and the ranking of football teams, SIAM Rev. 35 (1993) 80-93.
18. J. Levin, B. Nalebuff, An introduction to vote-counting schemes, J. Economic Perspectives 9 (1995) 3-26.
19. G. Laffond, J.-F. Laslier, M. Lebreton, Condorcet choice correspondences: A set-theoretical comparisons, Math. Social Sci. 30 (1995) 23-35.
20. G. Laffond. J. Lainé, J.-F. Laslier, Composition-consistent tournament solutions and social choice functions, Social Choice Welfare 13 (1996) 75-93.
21. R.B. Myerson, Axiomatic derivation of scoring rules without the ordering assumption, Social Choice Welfare 12 (1995) 59-74.
22. T. Wei, The algebraic foundations of ranking theory, Ph.D. Thesis, Cambridge University, 1952.
23. M.G. Kendall, Further contributions to the theory of paired comparisons, Biometrika 11 (1955) 43-62.
24. M. Hasse, Über die Behanglung graphentheoretischer Probleme unter Verwendung der Matrizenrechnung, Wiss. Z. Tech. Univ. Dresden 10 (1961) 1313-1316.
25. C. Ramanujacharyulu, Analysis of preferential experiments, Psychometrika 29 (1964) 257-261.
26. L. Katz, A new status index derived from sociometric analysis, Psychometrika 18 (1953) 39-43.
27. G.L. Thompson, Lectures on game theory, Markov chains and related topics, Sandia Corporation Monograph SCR-11, 1958.
28. M. Taylor, Graph-theoretic approaches to the theory of social choice, Public Choice 4 (1968) 35-47.
29. G. Laffond, J.-F. Laslier, M. Lebreton, The bipartisan set of a tournament game, Games Econ. Behav. 15 (1993) 182-201.
30. I.A. Ushakov, The problem of choosing the preferable object, Izv. Akad. Nauk SSSR. Tekhn. Kibernet. (1971) 3-7 (in Russian).
31. S.T. Goddard, Ranking in tournaments and group decisionmaking, Manage. Sci. 29 (1983) 1384-1392.
32. V.S. Levchenkov, Entropy analysis of the majority rule, Automat. Remote Control 51 (1990) 517-524.
33. V.S. Levchenkov, Choice without Arrow's axiom on the independence of irrelevant alternatives, Dok. Akad. Nauk SSSR, 322 (1992) 651-655 (in Russian).
34. K. Lehrer, W. Wagner, Rational Consensus in Science and Society. Reidel, Dordrecht, 1981.
35. I.A. Ushakov, The problem of choosing the preferred element: An application to sport games, in: R.E. Machol, S.P. Ladany, D.G. Morrison (Eds.), Management Science in Sports, North-Holland, Amsterdam, 1976, pp. 153-161.
36. K.A. Berman, A graph theoretical approach to handicap ranking of tournaments and paired comparisons, SIAM J. Algebraic Discrete Methods 1 (1980) 359-361.
37. D.J. Daley, Markov chains and a pecking order problem, in: D. McNeil (Ed.), Interactive Statistics, North-Holland, Amsterdam, 1979, pp. 247-254.
38. V.S. Levchenkov, Choosing by tournament relations, Dokl. Akad. Nauk 336 (1994) 324-327 (in Russian).
39. V.S. Levchenkov, I.L. Grivko. Some properties of self-consistent choice, Dokl. Akad. Nauk 327 (1992) 42-47 (in Russian).
40. V.S. Levchenkov, Axiomatic approach to the self-consistent choice, Dokl. Akad. Nauk 330 (1993) 173-176 (in Russian).
41. I.L. Grivko, V.S. Levchenkov, Intrinsic properties of the self-consistent choice rule, Automat. Remote Control 55 (1994) 689-697.
42. V.S. Levchenkov, Self-consistent description of the manipulation by alternatives, Dokl. Akad. Nauk 331 (1993) 567-570 (in Russian).
43. V.S. Levchenkov, Strategic scheme for group choice, Dokl. Akad. Nauk 341 (1995) 320-323 (in Russian).
44. H.A. David, Ranking from unbalanced paired-comparison data, Biometrika 74 (1987) 432-436.
45. D.J. Cowden, A method of evaluating contestants. Am. Stat. 29 (2) (1975) 82-84.
46. V.D. Ginovker, On one approach to evaluating objects from paired comparison results, VINITI manuscript no. 3431-81DEP, 1981 (in Russian).
47. J.H. Morrissey, New method for the assignment of psychometric scale values from incomplete paired comparisons, J. Optical Soc. Amer. 45 (1955) 373-378.
48. J.H. Smith, Adjusting baseball standings for strength of teams played, Am. Stat. 10 (3) (1956) 23-24.
49. H. Gulliksen, A least squares solution for paired comparisons with incomplete data, Psychometrika 21 (1956) 125-134.
50. G.E. Noether, Remarks about a paired comparison model, Psychometrika 25 (1960) 357-367.
51. P.S.H. Leeflang, B.M.S. Van Praag, A procedure to estimate relative powers in binary contacts and an application to Dutch football league results, Stat. Neerlandica 25 (1971) 63-80.
52. T. Indow, M. Ida, On scaling from incomplete paired comparison matrix, Japan Psychol. Res. 17 (1975) 98-105.
53. R.J. Leake, A method for ranking teams: With an application to college football, in: R.E. Machol, S.P. Ladany, D.G. Morrison (Eds.), Management Science in Sports, North-Holland, Amsterdam, 1976, pp. 27-46.
54. H.F. Kaiser, R.C. Serlin, Contributing to the method of paired comparisons, Appl. Psychol. Meas. 2 (1978) 421-430.
55. A.I. Vereskov, Extended methods of regression analysis in the problems of identification of nonlinear models, Ph.D. Thesis, VNIISI, Moscow, 1986 (in Russian).
56. V.M. Pliner, On one approach to incomplete paired comparisons, in Abstracts of the 4th All-Union Conf. on Applications of Multivariate Statistical Analysis in Economics and Quality Evaluation, Tartu, 1989 (in Russian), pp. 29-30.
57. P.Yu. Chebotarev, Generalization of the row sum method for incomplete paired comparisons, Automat. Remote Control 50 (1989) 1103-1113.
58. P.Yu. Chebotarev, Aggregation of preferences by the generalized row sum method. Math. Social Sci. 27 (1994) 293-320.
59. E. Shamis, Graph-theoretic interpretation of the generalized row sum method, Math. Social Sci. 27 (1994) 321-333.
60. P.Yu. Chebotarev, E. Shamis, On the proximity measure for graph vertices provided by the inverse Laplacian characteristic matrix, in Abstracts of the 5th Conf. of the International Linear Algebra Society, Atlanta, Georgia State University, 1995, pp. 30-31.
61. P.Yu. Chebotarev, E. Shamis, Characterizations of scoring methods for preference aggregation, Ann. Oper. Res. 80 (1998) 299-332.
62. E. Zermelo, Die Berechnung der Turnier-Ergebnisse als ein Maximumproblem der Wahrscheinlichkeitsrechnung, Math. Zeit. 29 (1928) 436-460.
63. R.A. Bradley, M.E. Terry, The rank analysis of incomplete block designs. 1. The method of paired comparisons, Biometrika 39 (1952) 324-345.
64. M. Taylor, Influence structures, Sociometry 32 (1969) 490-502.
65. N.E. Friedkin, Theoretical foundations for centrality measures, Am. J. Sociol. 96 (1991) 1478-1504.
66. I. Bomze, W. Gutjahr, Estimating qualifications in a self-evaluating group, Quality & Quantity 29 (1995) 241-250.