Agreement and Diversity in Interpretation

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.