# Swap distance minimization shapes the order of subject, object and verb in languages of the world

arXiv: https://arxiv.org/abs/2604.26726 · HTML: https://mlsanity.com/paper/2604.26726/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 30 references that are in the map.
- First posted on arXiv 29 Apr 2026.

## Builds on (most cited first, 5 of 5)

- [Universal Dependencies v2: An Evergrowing Multilingual Treebank Collection](https://mlsanity.com/paper/2004.10643/) (2020)
- [Kauffman's adjacent possible in word order evolution](https://mlsanity.com/paper/1512.05582/) (2015)
- [Swap distance minimization in SOV languages. Cognitive and mathematical foundations](https://mlsanity.com/paper/2312.04219/) (2023)
- [Swap distance minimization beyond entropy minimization in word order variation](https://mlsanity.com/paper/2404.14192/) (2024)
- [How to measure the optimality of word or gesture order with respect to the principle of swap distance minimization](https://mlsanity.com/paper/2604.01938/) (2026)

## Abstract (arXiv)

Languages of the world vary concerning the order of subject (S), object (O) and verb (V). The most frequent dominant orders are SOV and SVO, and researchers have tailored models to this fact. However, there are still languages whose dominant order does not conform to these expectations or even lack a dominant order. Here we approach word order variation through swap distance, namely the distance between orders in the permutohedron, a graph where the vertices are the six possible orders of S, O and V, and two orders are connected if they differ by a swap of adjacent constituents. Then word order variation becomes a problem of assigning probabilities to word orders so as to minimize the average swap distance. Although previous work suggests that swap distance minimization may influence synchronic and diachronic variation as well as word order acceptability, here we provide large-scale cross-linguistic evidence across families, macroareas and sources that word order variation within languages is shaped by the principle of swap distance minimization, even when the dominant order is not SOV/SVO and even when a dominant order is lacking.