On the combinatorial structure of the approval-voting polytope

Journal of Mathematical Psychology

Volumn 46, Issue 5, 2002, Pages 554-563

  Doignon, Jean Paul ^a   Regenwetter, Michel ^b  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

Adjacency; Approval voting polytope; Combinatorial automorphism; Facet; Probabilistic choice model

Indexed keywords

EID: 0036800382     PISSN: 00222496     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmps.2001.1411     Document Type: Article

References (18)

1. Borndörfer, R., & Weismantel, R. (2000). Set packing relaxations of some integer programs. Mathematical Programming, 88, 425-450.
2. Bosma, W., Cannon, J., & Playoust, C. (1997). The Magma algebra system. I. The user language. Journal of Symbolic Computation, 24, 235-265.
3. Christof, T. (1996). PORTA-A polyhedron representation transformation algorithm [Computer ware]. Retrieved from ftp://ftp.zib-berlin.de/pub/mathprog/polyth/porta/index.html.
4. Doignon, J.-P., & Falmagne, J.-C. (1994). A polynomial time algorithm for unidimensional unfolding representations. Journal of Algorithms, 16, 218-233.
5. Doignon, J.-P., & Fiorini, S. (submitted). The facets and the symmetries of the approval-voting polytope.
6. Doignon, J.-P., & Regenwetter, M. (1997). An approval-voting polytope for linear orders. Journal of Mathematical Psychology, 41, 171-188.
7. Falmagne, J.-C., & Regenwetter, M. (1996). A random utility model for approval voting. Journal of Mathematical Psychology, 40, 152-159.
8. Fiorini, S. (2001). Determining the automorphism group of the linear ordering polytope. Discrete Applied Mathematics, 112, 121-128.
9. Fiorini, S., & Fishburn, P. (2001). Weak order polytopes. Manuscript under review.
10. Grünbaum, B. (1967). Convex Polytopes. New York: Wiley.
11. Koppen, M. (1995). Random utility representations of binary choice probabilities: Critical graphs yielding critical necessary conditions. Journal of Mathematical Psychology, 39, 21-39.
12. Marley, A. A. J. (1993). Aggregation theorems and the combination of probabilistic rank orders. In D. E. Critchlow, M. A. Fligner, and J. S. Verducci (Eds.), Probability models and statistical analyses for ranking data (pp. 216-240). New York: Springer.
13. Matsui, T., & Tamura, S. (1995). Adjacency on combinatorial polyhedra. Discrete Applied Mathematics, 56, 311-321.
14. Naddef, D., & Pulleyblank, W. R. (1981). Hamiltonicity and combinatorial polyhedra. Journal of Combinatorial Theory, Series B, 31, 297-312.
15. Regenwetter, M., & Doignon, J.-P. (1998). The choice probabilities of the latent-scale model satisfy the size-independent model when n is small. Journal of Mathematical Psychology, 42, 102-106.
16. Regenwetter, M., Marley, A., & Joe, H. (1998). Random utility threshold models of subset choice. [Special issue on mathematical psychology]. Australian Journal of Psychology, 50, 175-185.
17. Reinelt, G. (1985). The linear ordering problem: algorithms and applications. Berlin: Heldermann.
18. Ziegler, G. M. (1995). Lectures on polytopes. Berlin: Springer-Verlag.