Robust Sparse Voting

TL;DR

This work tackles robust sparse voting, where only a small fraction of voters rate a large set of alternatives and inputs may be biased or malicious. It defines two core properties—$L$-Lipschitz resilience and sparse unanimity—and introduces aggregation primitives, Quadratically Regularized Median and Lipschitz-Robustified Mean, to support them. Building on these primitives, the Mehestan algorithm performs local normalization, collaborative scaling, translation alignment, and robust aggregation to produce bounded, scale-invariant scores. The authors prove Mehestan achieves $L$-Lipschitz resilience, sparse unanimity under suitable conditions, and nontrivial outputs, while offering empirical evidence of robustness under sparsity and adversarial perturbations. The work advances robust aggregation design for large-scale, sparse, and potentially adversarial decision-making contexts with practical implications for content moderation, recommendations, and surveys.

Abstract

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.

Figures (5)

• Figure 1: Performance of Mehestan under sparsity, with and without malicious voters.
• Figure 2: Performance of Mehestan under sparsity, with and without malicious voters (Uniform distribution of $\theta_*$)
• Figure 3: Performance of Mehestan under sparsity, with and without malicious voters. (Gaussian distribution of $\theta_*$)
• Figure 4: Performance of Mehestan under sparsity, with and without malicious voters. (Cauchy distribution of $\theta_*$)
• Figure 5: Performance of Mehestan depending on the sparsity bias.

Theorems & Definitions (75)

• Definition 1: Lipschitz resilience
• Definition 2: Sparse unanimity
• Example
• Definition 3: Nontriviality
• Proposition 1
• Theorem 1
• proof : Sketch of proof
• Theorem 2
• proof : Sketch of proof
• Theorem 3