Tractable Agreement Protocols
Natalie Collina, Surbhi Goel, Varun Gupta, Aaron Roth
TL;DR
This paper introduces a tractable framework to convert any predictive model into an interactive agreement protocol with a human or another agent, relying on calibration relaxations of Bayesian rationality rather than full Bayesian optimality. It defines conversation calibration, distance-to-calibration, and decision-calibration to guarantee fast agreement and utility improvements across canonical (1D) and multidimensional settings, including action-feedback and multi-party extensions. The authors provide efficient reductions to implement these protocols from arbitrary models, establish convergence rates that are independent of dimension in the action-feedback setting, and show that Bayesian agents satisfy the calibration conditions, yielding one-shot equivalents to classical Aumann-type results. This work advances practical human–AI collaboration by delivering provable guarantees of rapid agreement and accuracy gains under computationally feasible assumptions, with potential applications to medical decision support and large-language-model debates. The framework unifies calibration theory with interactive prediction, enabling scalable, provably beneficial exchanges between AI systems and humans.
Abstract
We present an efficient reduction that converts any machine learning algorithm into an interactive protocol, enabling collaboration with another party (e.g., a human) to achieve consensus on predictions and improve accuracy. This approach imposes calibration conditions on each party, which are computationally and statistically tractable relaxations of Bayesian rationality. These conditions are sensible even in prior-free settings, representing a significant generalization of Aumann's classic "agreement theorem." In our protocol, the model first provides a prediction. The human then responds by either agreeing or offering feedback. The model updates its state and revises its prediction, while the human may adjust their beliefs. This iterative process continues until the two parties reach agreement. Initially, we study a setting that extends Aumann's Agreement Theorem, where parties aim to agree on a one-dimensional expectation by iteratively sharing their current estimates. Here, we recover the convergence theorem of Aaronson'05 under weaker assumptions. We then address the case where parties hold beliefs over distributions with d outcomes, exploring two feedback mechanisms. The first involves vector-valued estimates of predictions, while the second adopts a decision-theoretic approach: the human, needing to take an action from a finite set based on utility, communicates their utility-maximizing action at each round. In this setup, the number of rounds until agreement remains independent of d. Finally, we generalize to scenarios with more than two parties, where computational complexity scales linearly with the number of participants. Our protocols rely on simple, efficient conditions and produce predictions that surpass the accuracy of any individual party's alone.