# New Characterizations of Strategy-Proofness under Single-Peakedness

arXiv: https://arxiv.org/abs/2102.11686 · HTML: https://mlsanity.com/paper/2102.11686/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Feb 2021.

## Built on by (most cited first, 2 of 2)

- [Strategyproof and Proportionally Fair Facility Location](https://mlsanity.com/paper/2111.01566/) (2021)
- [Facility Location Games with Scaling Effects](https://mlsanity.com/paper/2402.18908/) (2024)

## Abstract (arXiv)

We provide novel simple representations of strategy-proof voting rules when voters have uni-dimensional single-peaked preferences (as well as multi-dimensional separable preferences). The analysis recovers, links and unifies existing results in the literature such as Moulin's classic characterization in terms of phantom voters and Barber`a, Gul and Stacchetti's in terms of winning coalitions ("generalized median voter schemes"). First, we compare the computational properties of the various representations and show that the grading curve representation is superior in terms of computational complexity. Moreover, the new approach allows us to obtain new characterizations when strategy-proofness is combined with other desirable properties such as anonymity, responsiveness, ordinality, participation, consistency, or proportionality. In the anonymous case, two methods are single out: the -- well know -- ordinal median and the -- most recent -- linear median.