# The Enmity Paradox

arXiv: https://arxiv.org/abs/2304.10076 · HTML: https://mlsanity.com/paper/2304.10076/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2023.

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

- [In-Group Love, Out-Group Hate: A Framework to Measure Affective Polarization via Contentious Online Discussions](https://mlsanity.com/paper/2412.14414/) (2024)

## Abstract (arXiv)

The "friendship paradox" of social networks states that, on average, "your friends have more friends than you do." Here, we theoretically and empirically explore a related and overlooked paradox we refer to as the "enmity paradox." We use empirical data from 24,687 people living in 176 villages in rural Honduras. We show that, for a real negative undirected network (created by symmetrizing antagonistic interactions), the paradox exists as it does in the positive world. Specifically, a person's enemies have more enemies, on average, than a person does. Furthermore, in a mixed world of positive and negative ties, we study the conditions for the existence of the paradox, both theoretically and empirically, finding that, for instance, a person's friends typically have more enemies than a person does. We also confirm the "generalized" enmity paradox for nontopological attributes in real data, analogous to the generalized friendship paradox (e.g., the claim that a person's enemies are richer, on average, than a person is). As a consequence, the naturally occurring variance in the degree distribution of both friendship and antagonism in social networks can skew people's perceptions of the social world.