Agreement and Diversity in Interpretation

2026-07-06

AI Summary

This work addresses how interpretive disagreements may arise in joint decision-making among agents who share identical environments and signal likelihoods but hold divergent subjective models. The authors propose a decision-theoretic measure of disagreement by comparing the extent to which different subjective models support signal-contingent plans. They construct a prior-independent consistency ordering and show that its unique rotation-invariant scalar completion is the cosine similarity. This ordering is independent of Blackwell dominance and favors quadratic over KL-type Bregman divergences. Greater interpretive consistency narrows speculative trading wedges, expands the ex ante Pareto frontier, and enlarges the set of strategies rationalizable under a single model.

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.

Problem

• interpretive disagreement
• signal likelihoods
• decision-making
• subjective models
• agreement

Innovation

• interpretive disagreement
• agreeability
• cosine similarity
• subjective models
• Bregman divergences