Learning Unanimously Acceptable Lotteries via Queries

Davin Choo; Paul W. Goldberg; Nicholas Teh

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arXiv · 2604.17505

Learning Unanimously Acceptable Lotteries via Queries

Davin Choo·Paul W. Goldberg·Nicholas Teh

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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.

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BibTeX RIS

Davin Choo, Paul W. Goldberg, Nicholas Teh. 2026-04-19. Learning Unanimously Acceptable Lotteries via Queries. https://arxiv.org/abs/2604.17505

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