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Falmagne–Block–Marschak Random-Utility Characterization

Arthur Freitas Ramos, David Barros Hulak, Ruy Jose Guerra Barretto de Queiroz

Palomar Registrypalomar/PALOMAR-2026-10-03-000008Oct 3, 2026econ.THscore 0

A full constructive formalization of the Falmagne–Block–Marschak theorem for any finite nonempty alternative set, without a cardinality bound. A normalized stochastic choice rule on all nonempty menus is generated by a single probability distribution over complete strict rankings if and only if all Block–Marschak alternating-sum coefficients are nonnegative. The proof derives Boolean-lattice flow conservation, constructs a finite ranking mixture by positive-path subtraction, and proves exact lower-contour probability identities by Möbius inversion. Compiled adversarial examples show that…

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