Back to Search
Start Over
The best-worst-choice polytope on four alternatives.
- Source :
-
Journal of Mathematical Psychology . Jun2023, Vol. 114, pN.PAG-N.PAG. 1p. - Publication Year :
- 2023
-
Abstract
- Several papers co-authored by A.A.J. Marley helped in popularizing the best-worst-choice paradigm due to Finn and Louviere (1992). Inspired by Block and Marschak (1960), Marley conceived a random utility model for the choice frequencies of the best and worst alternatives in any proposed set of alternatives (Marley and Louviere, 2005). He then asked for a characterization of the prediction range of the model. The range being a convex polytope, an affine description of this polytope would provide a solution to Marley problem. For four alternatives, we show that a minimal such description consists in 26 affine equalities and 144 affine inequalities. The result derives from the Gale transform of the set of polytope vertices: the transform being a family of 24 vectors in a one-dimensional vector space, it plainly reveals the affine structure of the polytope. As far as we know, Marley problem is still open when the number of alternatives exceeds 4. • Investigates the prediction range of the best-worst-choice model, a convex polytope. • Exposes the geometric structure of the above polytope in case of four alternatives. • Applies the Gale transform technique to fully analyze this geometric structure. • Marley characterization problem remains unsolved for more than four alternatives. [ABSTRACT FROM AUTHOR]
- Subjects :
- *VECTOR spaces
*POLYTOPES
*LOGITS
*PREDICTION models
*WINDSTORMS
Subjects
Details
- Language :
- English
- ISSN :
- 00222496
- Volume :
- 114
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Psychology
- Publication Type :
- Periodical
- Accession number :
- 163795216
- Full Text :
- https://doi.org/10.1016/j.jmp.2023.102769