Peak-Robust Voting Rules

This paper proposes new robustness criteria for social choice correspondences under single-peaked preferences, inspired by the concepts of robustness in statistical estimation, where robust estimators are designed to be resilient to both model misspecification and outliers. Motivated by robustness to model assumptions, we introduce peak-robustness: a voting rule is peak-robust if it never selects an alternative that is a majority loser relative to some unchosen alternative for any preference profile sharing the same peak profile. To capture robustness to outliers, we propose tail-invariance, which requires that variations in the tails of the peak distribution do not affect the collective decision. Our main result shows that the median voting rule is the unique efficient rule satisfying these robustness criteria. When peak-robustness is weakened, we characterize the broader class of quantile rules. Taken together, these results provide a robustness-based axiomatic foundation for median and quantile voting rules, independent of the traditional strategy-proofness approach.