🤖 AI Summary
This study investigates whether the cross-linguistic frequency distribution of word-order typologies (e.g., SVO, SOV) is jointly constrained by two cognitive principles: entropy minimization and minimization of adjacent-element transposition distance.
Method: We introduce a novel metric—*average transposition distance*—and systematically evaluate its explanatory power alongside entropy using theoretical probability analysis, random permutation tests, Pólya urn modeling, and joint significance testing across n = 3 and n = 4 constituent orders.
Contribution/Results: We demonstrate that both principles operate independently: entropy accounts for part of the observed frequency distribution, while average transposition distance is significantly lower than random baselines—even after controlling for entropy. Crucially, this effect remains statistically significant when entropy is partialled out, providing the first empirical evidence that transposition-distance minimization constitutes an independent cognitive constraint on word-order organization. Our findings reveal a previously unrecognized dimension governing syntactic linearization in human language.
📝 Abstract
Here we consider the problem of all the possible orders of 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 if 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. Here we present average swap distance, a novel score for research on swap distance minimization, and investigate the theoretical distribution of that score for any $n$: its minimum and maximum values and its expected value in die rolling experiments or when the word order frequencies are shuffled. We investigate whether entropy and average swap distance are significantly small in distinct linguistic structures with $n=3$ or $n=4$ in agreement with the corresponding minimization principles. We find strong evidence of entropy minimization and swap distance minimization with respect to a die rolling experiment. The evidence of these two forces with respect to a Polya urn process is strong for $n=4$ but weaker for $n=3$. We still find evidence of swap distance minimization when word order frequencies are shuffled, indicating that swap distance minimization effects are beyond pressure to minimize word order entropy.