Open Research Index

Milgrom–Shannon's Monotonicity Theorem: the Full Characterization

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

Palomar Registrypalomar/PALOMAR-2026-10-03-000007Oct 3, 2026econ.THscore 0

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…

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