鲁棒稀疏投票
Robust Sparse Voting
AI总结：
本文定义鲁棒稀疏投票问题，提出一种限制单个投票者影响、可恢复跨尺度一致偏好的新型投票机制，并证明其 Lipschitz 韧性与一致偏好恢复条件。
摘要：
许多应用，例如内容审核和推荐，需要审查并评分大量备选方案。然而，要鲁棒地完成这项工作极具挑战性。事实上，投票者的输入不可避免地是稀疏的：大多数备选方案只由一小部分投票者评分。这种稀疏性会放大两类投票者的影响：一类是引入不公平性的有偏投票者，另一类是试图通过报告不诚实评分来操纵投票过程的恶意投票者。我们给出了鲁棒稀疏投票问题的精确定义，强调了其潜在技术挑战，并提出了一种解决该问题的新型投票机制。我们证明，使用该机制，任何投票者对每个备选方案评分的影响都不会超过一个可参数化的较小值；我们将这一性质称为 Lipschitz 韧性。我们还确定了投票者可比较性的条件，在这些条件下，即使每个投票者只提供稀疏评分，且其评分尺度可能与其他任何投票者的评分尺度截然不同，也能恢复任何一致偏好。证明这些性质要求我们引入、分析并仔细组合若干新型聚合原语，这些原语本身也可能具有独立价值。
英文摘要：
Many applications, such as content moderation and recommendation, require reviewing and scoring a large number of alternatives. Doing so robustly is however very challenging. Indeed, voters' inputs are inevitably sparse: most alternatives are only scored by a small fraction of voters. This sparsity amplifies the effects of biased voters introducing unfairness, and of malicious voters seeking to hack the voting process by reporting dishonest scores. We give a precise definition of the problem of robust sparse voting, highlight its underlying technical challenges, and present a novel voting mechanism addressing the problem. We prove that, using this mechanism, no voter can have more than a small parameterizable effect on each alternative's score; a property we call Lipschitz resilience. We also identify conditions of voters comparability under which any unanimous preferences can be recovered, even when each voter provides sparse scores, on a scale that is potentially very different from any other voter's score scale. Proving these properties required us to introduce, analyze and carefully compose novel aggregation primitives which could be of independent interest.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
