Learning Unanimously Acceptable Lotteries via Queries

2026-04-19

AI Summary

This work addresses the challenge of identifying a universally acceptable randomized allocation—termed a “lottery”—among stakeholders in high-stakes AI deployments. The authors propose an adaptive query framework that efficiently determines the existence of such a feasible lottery by iteratively presenting candidate allocations to stakeholders and collecting binary feedback. Their key contributions include deterministic and randomized algorithms that substantially reduce the number of required queries, as well as a learning-augmented mechanism that, when predictions are accurate, dramatically lowers query complexity while preserving worst-case theoretical guarantees. They also establish an information-theoretic lower bound showing that query complexity must scale linearly with the number of stakeholders and logarithmically with the desired accuracy—bounds that cannot be improved upon. Empirical evaluations demonstrate that the proposed approach significantly outperforms exhaustive enumeration strategies.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Mechanism Design
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

Many high-stakes AI deployments proceed only if every stakeholder deems the system acceptable relative to their own minimum standard. With randomization over a finite menu of options, this becomes a feasibility question: does there exist a lottery over options that clears all stakeholders' acceptability bars? We study a query model where the algorithm proposes lotteries and receives only binary accept/reject feedback. We give deterministic and randomized algorithms that either find a unanimously acceptable lottery or certify infeasibility; adaptivity can avoid eliciting many stakeholders' constraints, and randomization further reduces the expected elicitation cost relative to full elicitation. We complement these upper bounds with worst-case lower bounds (in particular, linear dependence on the number of stakeholders and logarithmic dependence on precision are unavoidable). Finally, we develop learning-augmented algorithms that exploit natural forms of advice (e.g., likely binding stakeholders or a promising lottery), improving query complexity when predictions are accurate while preserving worst-case guarantees.

Problem

• unanimous acceptability
• lottery
• stakeholder constraints
• feasibility
• query model

Innovation

• query complexity
• randomized algorithms
• learning-augmented algorithms
• stakeholder consensus
• lottery design