As Duncan Luce and other prominent scholars have pointed out on several occasions, testing algebraic models against empirical data raises difficult conceptual, mathematical, and statistical challenges. Empirical data often result from statistical sampling processes, whereas algebraic theories are nonprobabilistic. Many probabilistic specifications lead to statistical boundary problems and are s...

In the literature on social choice with fuzzy preferences, a central question is how to represent the transitivity of a fuzzy binary relation. Arguably the most general way of doing this is to assume a form of transitivity called max-star transitivity. The star operator in this formulation is commonly taken to be a triangular norm. The familiar max-min transitivity condition is a member of this...

This paper presents some generalizations of the Gibbard -Satterthwaite result (1973, 1975) for fuzzy preference relations. It explores the implication of weakening the transitivity condition of the Ben Abdealziz et al.’s (2008) fuzzy manipulability concept. For this purpose, the max-min transitivity is replaced by weaker transitivity: the max-?-transitivity, where ? is a t-norm. In addition, th...

Let P be the transition matrix of a finite, irreducible and reversible Markov chain. We say the continuous time Markov chain X has transition matrix P and speed λ if it jumps at rate λ according to the matrix P . Fix λX , λY , λZ ≥ 0, then let X,Y and Z be independent Markov chains with transition matrix P and speeds λX , λY and λZ respectively, all started from the stationary distribution. Wha...