Truthful germs are contagious: A local-to-global characterization of truthfulness

We study the question of which social choice functions from an abstract type space to a set of outcomes are truthful, i.e., implementable by truthful mechanisms, when utilities are quasi-linear. For convex domains, our main theorem characterizes truthful social choice functions as those satisfying two properties: local weak monotonicity and vortex-freeness. The first of these constrains the function values at any two sufficiently proximal points, while the second asserts that its line integrals around sufficiently small triangular loops must vanish.