Strategy-Proof Aggregation of Approximate and Imprecise Judgments

The present work is devoted to the study of aggregation rules for several types of approximate judgments and their strategy-proofness properties when the relevant judgment space is lattice-ordered and endowed with a natural metric, and the agents/experts have single-peaked preferences consistent with it. In particular, approximate probability estimates as modeled by intervals of probability values, numerical measurements with explicit error bounds, approximate classifications, and conditional judgments that are amenable to composition by means of a set of logical connectives are considered. Relying on (bounded) distributivity of the relevant lattices, we prove the existence of a large class of inclusive and unanimity-respecting strategy-proof aggregation rules for approximate assessments or conditional judgments, consisting of sup-projections and sup-inf polynomials as parameterized by certain families of locally winning coalitions called committees. Amongst them, the majority aggregation rule is characterized as the only one that ensures both anonymity (i.e. an equal treatment of agents) and bi-idempotence (i.e. a definite choice between the only two judgments nominated by a maximally polarized body).