Geometric and combinatorial properties of the polytope of binary choice probabilities

Random Utility Representations of Finitem-ary Relations

“…Koppen (1995) gives the most recent discussion of the characterization problem for binary choices to be induced by rankings. He also provides a detailed reference list of the vast literature (e.g., Fishburn, 1992;Marley, 1990;Suck, 1992). The difficulty of the characterization problems for binary choice and the traditional preoccupation with binary choice data may be largely responsible for the lack of popularity of nonparametric random utility models.…”

“…The standard empirical paradigms include binary choice (e.g., Fishburn, 1992;Koppen, 1995;Marley, 1990;Suck, 1992) and choosing one among several alternatives (Barbera 6 Pattanaik, 1986;Falmagne, 1978). For a given empirical choice paradigm such as binary choice, these two assumptions together give rise to three problems.…”

Random Relations, Random Utilities, and Random Functions

“…These and many related (much more) complex results can be derived using various general techniques. Excellent entrees into this literature are Fishburn (1992), Koppen (1995), Niedere e and Heyer (1997), and Suck (1992Suck ( , 1995Suck ( , 1996.We will illustrate one of these powerful general techniques in a later example. This concludes our motivating example.…”

A general concept of majority rule

“…2. The research on nonparametric random utility models is quite extensive and has focused mainly on the characterization problems of probabilistic binary choice (Fishburn, 1992;Koppen, 1995;Marley, 1991;Marschak, 1960;Suck, 1992Suck, , 1995á nd of probabilistic multiple choice (Barbera, 1979;Barbera and Pattanaik, 1986;Falmagne, 1978). The interpretation of our family U of jointly distributed utility random variables is simply that utilities of objects vary and co-vary.…”