TY - JOUR
T1 - The Choice Probabilities of the Latent-Scale Model Satisfy the Size-Independent Model WhennIs Small
AU - Regenwetter, Michel
AU - Doignon, Jean Paul
N1 - Funding Information:
* This work is supported by a postdoctoral fellowship to M. R. at McGill University, partially funded by NSERC Collaborative Research Grant CGP0164211 to A. A. J. Marley (P.I.) and others. We thank U.L.B. for having financially supported a visit of M.R. to its campus. Jean-Pierre Barthelemy, Bernard Monjardet, Tony Marley, and Reinhard Suck gave very helpful comments on an earlier draft.
PY - 1998/3
Y1 - 1998/3
N2 - Two probabilistic models for subset choices are compared. The first one, due to Marley (1993), was dubbed the latent-scale model by Regenwetter, Marley, and Joe (1996). The second one is Falmagne and Regenwetter's (1996) size-independent model of approval voting. We show that for up to five choice alternatives, the choice probabilities generated by the latent-scale model can be explained also by the size-independent model. The proof uses the König-Hall theorem of graph theory and the characterization of the size-independent model by the approval-voting polytope of Doignon and Regenwetter (1997). The problem remains open for the case with more than five choice alternatives.
AB - Two probabilistic models for subset choices are compared. The first one, due to Marley (1993), was dubbed the latent-scale model by Regenwetter, Marley, and Joe (1996). The second one is Falmagne and Regenwetter's (1996) size-independent model of approval voting. We show that for up to five choice alternatives, the choice probabilities generated by the latent-scale model can be explained also by the size-independent model. The proof uses the König-Hall theorem of graph theory and the characterization of the size-independent model by the approval-voting polytope of Doignon and Regenwetter (1997). The problem remains open for the case with more than five choice alternatives.
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U2 - 10.1006/jmps.1998.1207
DO - 10.1006/jmps.1998.1207
M3 - Article
C2 - 9606163
AN - SCOPUS:0010977774
SN - 0022-2496
VL - 42
SP - 102
EP - 106
JO - Journal of Mathematical Psychology
JF - Journal of Mathematical Psychology
IS - 1
ER -