Generalizing the concept of binary choice systems induced by rankings: one way of probabilizing deterministic measurement structures

Individual differences in the algebraic structure of preferences

“…Heyer & Niederée, 1992;Loomes & Sugden, 1995). This perspective allows for a general test of the mathematical structures of interest.…”

Analysis of multinomial models under inequality constraints: Applications to measurement theory

“…The problem of determining whether binary choices are induced by linear orders over the set K is often referred to as the binary choice problem (Bolotashvili, Kovalev, & Girlich, 1999;Cohen & Falmagne, 1978Fiorini, 2001a;Fishburn, 1990Fishburn, , 1992Fishburn & Falmagne, 1989;Gilboa, 1990;Grotschel, Junger, & Reinelt, 1985;Heyer & Niederee, 1992;Koppen, 1991Koppen, , 1995Suck, 1992). See Marley (1990) for a detailed review of earlier work on this topic.…”

Random Utility Representations of Finitem-ary Relations

“…The two most obvious ways, then, to view AV as a probabilistic relation are (a) to call it a probabilistic relation of type ( 1) on 2 C , if we replace C in Definition 3 by 2 C and m by 1; or (b) to call it a probabilistic relation of type ( |C|) on [0, 1] if we replace C in Definition 3 by [0, 1] and m by |C|. Correspondingly, the characterization problem as in Heyer and Niedere e (1992) in terms of probabilistic relations would be to find conditions on AV for it to be a probabilistic mixture of deterministic structures (a) of type ( 1) on 2 C , or (b) of type ( |C| ) on [0, 1]. However, semiorders are relations of type ( 2) on C, and their topsets are relations of type ( 1) on C. Thus, it is not straightforward to apply Heyer and Niedere e's approach to this model.…”