Agreement and Diversity in Interpretation

Francesco Bilotta, Luca Braghieri, Collin Raymond and Mark Whitmeyer

Papers from arXiv.org

Abstract: We study joint decision-making when agents agree on all primitives other than signal likelihoods. We propose a decision-theoretic measure of interpretive disagreement: a pair of subjective models is more agreeable than another if, uniformly across decision problems, it supports a larger set of signal-contingent plans that both agents weakly prefer ex-ante to the common reservation payoff. We show that this measure is prior independent and can be represented as an inclusion preorder over pairs of subjective models: each model in the more agreeable pair is a convex combination of the two models in the less agreeable pair. We then show that the measure's unique rotation-invariant scalar completion is cosine similarity. Applications show that greater agreement reduces speculative-trade wedges, expands a normalized version of the ex-ante Pareto frontier, and enlarges the set of single-model rationalizations. Our order is independent of Blackwell dominance and selects quadratic over KL-type Bregman divergences.

Date: 2026-07
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