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Agreement and Diversity in Interpretation

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  • Francesco Bilotta
  • Luca Braghieri
  • Collin Raymond
  • Mark Whitmeyer

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.

Suggested Citation

  • Francesco Bilotta & Luca Braghieri & Collin Raymond & Mark Whitmeyer, 2026. "Agreement and Diversity in Interpretation," Papers 2607.05558, arXiv.org.
    • Handle: RePEc:arx:papers:2607.05558
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    File URL: https://arxiv.org/pdf/2607.05558
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