# The one-dimensional Euclidean domain: Finitely many obstructions are not enough

arXiv: https://arxiv.org/abs/1506.03838 · HTML: https://mlsanity.com/paper/1506.03838/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2015.

## 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 show that one-dimensional Euclidean preference profiles can not be characterized in terms of finitely many forbidden substructures. This result is in strong contrast to the case of single-peaked and single-crossing preference profiles, for which such finite characterizations have been derived in the literature.