Swap distance minimization beyond entropy minimization in word order variation

TL;DR

This paper explores how natural language word order is influenced by entropy minimization and swap distance minimization, introducing a new metric and providing evidence for both principles across different linguistic structures.

Contribution

It introduces average swap distance as a novel measure and demonstrates its significance alongside entropy minimization in shaping word order frequencies.

Findings

Strong evidence for entropy and swap distance minimization in linguistic data

Average swap distance effectively captures word order preferences

Swap distance minimization effects persist beyond entropy considerations

Abstract

Consider a linguistic structure formed by $n$ elements, for instance, subject, direct object and verb ($n=3$) or subject, direct object, indirect object and verb ($n=4$). We investigate whether the frequency of the $n!$ possible orders is constrained by two principles. First, entropy minimization, a principle that has been suggested to shape natural communication systems at distinct levels of organization. Second, swap distance minimization, namely a preference for word orders that require fewer swaps of adjacent elements to be produced from a source order. We present average swap distance, a novel score for research on swap distance minimization. We find strong evidence of pressure for entropy minimization and swap distance minimization with respect to a die rolling experiment in distinct linguistic structures with $n=3$ or $n=4$. Evidence with respect to a Polya urn process is strong for $n=4$ but weaker for $n=3$. We still find evidence consistent with the action of swap distance minimization when word order frequencies are shuffled, indicating that swap distance minimization effects are beyond pressure to reduce word order entropy.