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9x d Z/X alternatives binary choice probabilities binary random utility binary relation Block and Marschak Campello de Souza choice behavior choice set choose component random utility constant utility model convex combinations convex set Cornell University decision maker define descriptive aspects E-model E(ii E(iv EMST point extended moderate stochastic extreme point fluctuations in choice Hence hypercube introspection noise l-pik l-pjk least n-1 lexicographic ordering Marschak 9 matrix mixed model moderate stochastic transitivity Pernambuco preference patterns probabilistic choice model probability measure probability vectors Proof random utility model random utility set random variables representation is straightforward s*d Z/X satisfy the triangle second option Set of orderings stochastic transitivity condition strong constant utility tp^j triangle inequality condition triple of binary Universidade Federal vector yield this ordering