Learning Unanimously Acceptable Lotteries via Queries

TL;DR

This paper investigates algorithms for finding lotteries acceptable to all stakeholders using minimal binary feedback, balancing efficiency and certainty in high-stakes AI decision-making.

Contribution

It introduces new algorithms that efficiently identify or certify the impossibility of acceptable lotteries with adaptive and randomized strategies, including learning-augmented methods.

Findings

Deterministic and randomized algorithms can find or certify infeasibility of acceptable lotteries.

Adaptive and randomized approaches reduce the number of stakeholder queries needed.

Learning-augmented algorithms improve efficiency when predictions about stakeholders are accurate.

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.