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.

翻译：许多应用（如内容审核与推荐）需要审查并对大量备选项进行评分。然而，这一过程的鲁棒性极具挑战性。这是因为投票者的输入必然存在稀疏性：大多数备选项仅由少量投票者评分。这种稀疏性放大了偏见投票者引入不公平性的影响，以及恶意投票者通过提交不诚实分数试图操控投票过程的影响。我们给出了鲁棒稀疏投票问题的精确定义，揭示了其背后的技术挑战，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项分数的影响均不超过一个可参数化的小值——我们称此性质为Lipschitz弹性。我们还识别了投票者可比性条件，在此条件下，即使每个投票者提供稀疏评分（且评分尺度可能与其他投票者差异极大），任何一致偏好仍可被恢复。为证明这些性质，我们引入、分析并精心组合了可能具有独立价值的新型聚合原语。