{"id":"palomar/PALOMAR-2026-10-03-000007","url":"https://github.com/Arthur742Ramos/milgrom-shannon-monotonicity-lean/tree/50a69ed78003a84ea849ed72dd24e0146829c4a6","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-03-000007-v1.json","repo":"https://github.com/Arthur742Ramos/milgrom-shannon-monotonicity-lean","tags":["econ.TH","math.OC","msc:91B02","msc:06B05","msc:03B35","monotone-comparative-statics","decision-theory","lattice-theory","economic-theory"],"score":0,"title":"Milgrom–Shannon's Monotonicity Theorem: the Full 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":"Milgrom and Shannon (1994), Theorem 4, in both directions: for an arbitrary lattice X, partially ordered parameter space T, and real-valued objective, strong-set monotonicity of constrained maximizers over every pair of strongly ordered feasible subsets is equivalent to quasisupermodularity of every section and both weak and strict preference-preservation clauses of single crossing. The theorem imposes no finiteness, completeness, topology, continuity, compactness, nonemptiness, or optimizer existence assumptions. Supporting results and counterexamples distinguish crossing clauses and…","category":"research","comments":0,"disputed":false,"division":"econ","mentions":0,"verified":true,"discussed":0,"published":"2026-10-03","reactions":{},"formalized":true,"formalizes":[{"title":"Monotone Comparative Statics","identifier":"","relationship":"formalizes"}]}