Signed Orders, Choice Probabilities, and Linear Polytopes

Journal of Mathematical Psychology

Volumn 45, Issue 1, 2001, Pages 53-80

  Fishburn, Peter C ^a  

^a AT AND T LABS RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0141977545     PISSN: 00222496     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmps.1999.1288     Document Type: Article

References (46)

1. Bauer, P. (1997). The circuit of polytope: Facets. Mathematics of Operations Research, 22, 110-145.
2. Block, H. D., & Marschak, J. (1960). Random orderings and stochastic theories of responses. In I. Olkin, S. G. Ghurye, W. Hoeffding, W. G. Madow, & H. B. Mann (Eds.), Contributions to probability and statistics: essays in honor of Harold Hotelling (pp. 97-132). Stanford, CA: Stanford Univ. Press.
3. Bossert, W. (1995). Preference extension rules for ranking sets of alternatives with a fixed cardinality. Theory and Decision, 39, 301-317.
4. Bossert, W., Pattanaik, P. K., & Xu, Y. (1994). Ranking opportunity sets: An axiomatic approach. Journal of Economic Theory, 63, 326-345.
5. Chopra, S., & Rao, M. R. (1995). Facets of the k-partition polytope. Discrete Applied Mathematics, 61, 27-48.
6. Christof, T., & Reinelt, G. (1997). Low-dimensional linear ordering polytopes. Preprint, Univ. of Heidelberg.
7. Cohen, M., & Falmagne, J.-C. (1990). Random utility representation of binary choice probabilities: a new class of necessary conditions. Journal of Mathematical Psychology, 34, 88-94.
8. Daniels, H. E. (1950). Rank correlation and population models. Biometrika, 33, 129-135.
9. Doignon, J. P., & Regenwetter, M. (1997). An approval-voting polytope for linear orders. Journal of Mathematical Psychology, 41, 171-188.
10. Dridi, T. (1980). Sur les distributions binaires associees à des distributions ordinales. Mathematiques et Sciences Humaines, 69, 15-31.
11. Dutta, B., & Sen, A. (1996). Ranking opportunity sets and Arrow impossibility theorems: correspondence results. Journal of Economic Theory, 71, 90-101.
12. Falmagne, J.-C., & Regenwetter, M. (1996). Random utility models for approval voting. Journal of Mathematical Psychology, 40, 152-159.
13. Fischetti, M. (1991). Facets of the asymmetric traveling salesman polytope. Mathematics of Operations Research, 16, 42-56.
14. Fishburn, P. C. (1992a). Signed orders and power set extensions. Journal of Economic Theory, 56, 1-19.
15. Fishburn, P. C. (1992b). Induced binary probabilities and the linear ordering polytope: A status report. Mathematical Social Sciences, 23, 67-80.
16. Fishburn, P. C. (1992c). Multiattribute signed orders. Journal of Multicriteria Decision Analysis, 1, 3-16.
17. Fishburn, P. C., & LaValle, I. H. (1993). Subset preferences in linear and nonlinear utility theory. Journal of Mathematical Psychology, 37, 611-623.
18. Fishburn, P. C., & LaValle, I. H. (1996). Binary interactions and subset choice. European Journal of Operational Research, 92, 182-192.
19. Gilboa, I. (1990). A necessary but insufficient condition for the stochastic binary choice problem. Journal of Mathematical Psychology, 34, 371-392.
20. Grötschel, M., Jünger, M., & Reinelt, G. (1985a). On the acyclic subgraph polytope. Mathematical Programming, 33, 28-42.
21. Grötschel, M., Jünger, M., & Reinelt, G. (1985b). Facets of the linear ordering polytope. Mathematical Programming, 33, 43-60.
22. Grünbaum, B. (1970). Polytopes, graphs, and complexes. Bulletin of the American Mathematical Society, 76, 1131-1201.
23. Henk, M., Richter-Gebert, J., & Ziegler, G. M. (1997). Basic properties of convex polytopes. In J. E. Goodman & J. O'Rourke (Eds.), Handbook of discrete and computational geometry (pp. 243-270). New York: CRC Press.
24. Koppen, M. (1995). Random utility representation of binary choice probabilities: Critical graphs yielding critical necessary conditions. Journal of Mathematical Psychology, 39, 21-39.
25. Lee, J. (1990). Characterizations of the dimension for classes of concordant polytopes. Mathematics of Operations Research, 15, 139-154.
26. Leung, J., & Lee, J. (1994). More facets from fences for linear ordering and acyclic subgraph polytopes. Discrete Applied Mathematics, 50, 185-200.
27. Luce, R. D., & Suppes, P. (1965). Preference, utility and subjective probability. In R. D. Luce, R. R. Bush, & E. Galanter (Eds.), Handbook of mathematical psychology, III (pp. 249-410). New York: Wiley.
28. Marley, A. A. J. (1993). Aggregation theorems and the combination of probabilistic rank orders. In D. E. Critchlow, M. A. Fligner, & J. S. Verducci (Eds.), Probabilistic models and statistical analysis for ranking data (pp. 216-240). New York: Springer.
29. Marschak, J. (1960). Binary-choice constraints and random utility indicators. In K. J. Arrow, S. Karlin, & P. Suppes (Eds.), Mathematical methods in the social sciences 1959 (pp. 312-329). Stanford, CA: Stanford Univ. Press.
30. McFadden, D., & Richter, M. K. (1990). Stochastic rationality and revealed stochastic preference. In J. S. Chipman, D. McFadden, & M. K. Richter (Eds.), Preferences, uncertainty, and optimality (pp. 161-186). Boulder, CO: Westview Press.
31. McLennan, A. (1990). Binary stochastic choice. In J. S. Chipman, D. McFadden, & M. K. Richter (Eds.), Preferences, uncertainty, and optimality (pp. 187-202). Boulder, CO: Westview Press.
32. Megiddo, N. (1977). Mixtures of order matrices and generalized order matrices. Discrete Mathematics, 19, 177-181.
33. Nehring, K., & Puppe, C. (1996). Continuous extensions of an order on a set to the power set. Journal of Economic Theory, 68, 456-479.
34. Niederée, R., & Heyer, D. (1997). Generalized random utility models and the representational theory of measurement: A conceptual link. In A. A. J. Marley (Ed.), Choice, decision and measurement: Essays in honor of R. Duncan Luce (pp. 155-189). Mahwah, NJ: Erlbaum.
35. Regenwetter, M. (1997). Probabilistic preferences and topset voting. Mathematical Social Sciences, 34, 91-105.
36. Regenwetter, M., & Grofman, B. (1998a). Approval voting, Borda winners and Condorcet winners: Evidence from seven elections. Management Science, 44, 520-533.
37. Regenwetter, M., & Grofman, B. (1998b). Choosing subsets: A size-independent random utility model and the quest for a social welfare ordering. Social Choice and Welfare, 15, 423-443.
38. Reinelt, G. (1985). The linear ordering problem: Algorithms and applications. Berlin: Heldermann.
39. Reinelt, G. (1993). A note on small linear ordering polytopes. Discrete & Computational Geometry, 10, 67-78.
40. Rockafellar, R. T. (1970). Convex analysis. Princeton, NJ: Princeton Univ. Press.
41. Sierksma, G. (1993). The skeleton of the symmetric traveling salesman polytope. Discrete Applied Mathematics, 43, 63-74.
42. Suck, R. (1984). Factorization and additive decomposition of a weak order. In E. Degreef & J. Van Buggenhaut (Eds.), Trends in mathematical psychology (pp. 347-362). Amsterdam: North Holland.
43. Suck, R. (1990). Conjointness as a derived property. Journal of Mathematical Psychology, 34, 57-80.
44. Suppes, P., Krantz, D. H., Luce, R. D., & Tverksy, A. (1989). Foundations of measurements (Vol. II). San Diego: Academic Press.
45. Thurstone, L. L. (1927). A law of comparative judgment. Psychological Review, 34, 273-286.
46. Yunfeng, L., Chaoyuan, Y., & Ting, C. (1996). A completeness result for extending signed orders. Journal of Economic Theory, 69, 205-210.