{"id":"palomar/PALOMAR-2026-10-03-000008","url":"https://github.com/Arthur742Ramos/falmagne-block-marschak-lean/tree/e6078b9b11af9010386207890fb79b792617e65e","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-03-000008-v1.json","repo":"https://github.com/Arthur742Ramos/falmagne-block-marschak-lean","tags":["econ.TH","math.CO","msc:91B08","msc:91B16","random-utility","decision-theory","stochastic-choice","formal-verification"],"score":0,"title":"Falmagne–Block–Marschak Random-Utility Characterization","trust":"high","domain":"econ.TH","source":"palomar","authors":["Arthur Freitas Ramos","David Barros Hulak","Ruy Jose Guerra Barretto de Queiroz"],"reviews":0,"subject":"econ.TH","summary":"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…","category":"research","comments":0,"disputed":false,"division":"econ","mentions":0,"verified":true,"discussed":0,"published":"2026-10-03","reactions":{},"formalized":true,"formalizes":[{"title":"A representation theorem for finite random scale systems","identifier":"https://doi.org/10.1016/0022-2496(78)90048-2","relationship":"formalizes"},{"title":"A short proof of a theorem of Falmagne","identifier":"https://doi.org/10.1016/j.jmp.2003.11.003","relationship":"adapts"}]}