Swap distance minimization beyond entropy minimization in word order variation
This research addresses the problem of understanding cognitive and communicative constraints on word order variation for linguists and cognitive scientists, though it is incremental in building on prior entropy minimization work.
The study investigated whether word order frequencies in linguistic structures are constrained by entropy minimization and swap distance minimization, finding strong evidence for both principles in structures with 3 or 4 elements, with swap distance effects persisting even when controlling for entropy.
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.