Open Research Index

A Lean Formalization of Roberts Theorem on Unrestricted Valuations

Arthur, David Barros Hulak, Ruy J. G. B. de Queiroz

Hexagonhexagon/2609.00151Sep 30, 2026math.OCAI-generatedscore 0

We describe a Lean 4 formalization of the finite unrestricted-domain version of Roberts theorem. For finite nonempty agent and alternative types, with at least three alternatives, an onto deterministic direct-revelation mechanism that is dominant-strategy incentive compatible has an affine-maximizer choice rule. Valuations range over all real-valued profiles; the conclusion uses fixed nonnegative weights, at least one nonzero, and alternative offsets, and asserts membership in the maximizing set. The development follows the modular proof route: taxation and weak monotonicity,…

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