Ample empirical evidence shows that, when faced with the same set of alternatives, people may make different choices.
[citation needed] Falmagne[10] solved this problem for the case in which the set of alternatives is finite: he proved that a probability distribution exists iff a set of polynomials derived from the choice-probabilities, denoted Block-Marschak polynomials, are nonnegative.
[15] The Plackett-Luce model was applied in econometrics,[16] for example, to analyze automobile prices in market equilibrium.
[18] It was also applied in social choice, to analyze an opinion poll conducted during the Irish presidential election.
[23] One approach to social choice, first formalized by Condorcet's jury theorem, is that there is a "ground truth" - a true ranking of the alternatives.
Moreover, for some common probability distributions (particularly, the Plackett-Luce model), the maximum likelihood estimators can be computed efficiently.
[citation needed] Walker and Ben-Akiva[25] generalize the classic RUM in several ways, aiming to improve the accuracy of forecasts: Blavatzkyy[26] studies stochastic utility theory based on choices between lotteries.