# Single-Peaked Opinion Updates

arXiv: https://arxiv.org/abs/2204.14094 · HTML: https://mlsanity.com/paper/2204.14094/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Apr 2022.

## Built on by (most cited first, 1 of 1)

- [Diversity of Structured Domains via k-Kemeny Scores](https://mlsanity.com/paper/2509.15812/) (2025)

## Abstract (arXiv)

We consider opinion diffusion for undirected networks with sequential updates when the opinions of the agents are single-peaked preference rankings. Our starting point is the study of preserving single-peakedness. We identify voting rules that, when given a single-peaked profile, output at least one ranking that is single peaked w.r.t. a single-peaked axis of the input. For such voting rules we show convergence to a stable state of the diffusion process that uses the voting rule as the agents' update rule. Further, we establish an efficient algorithm that maximises the spread of extreme opinions.