How communicatively optimal are exact numeral systems? Once more on lexicon size and morphosyntactic complexity

Chundra Cathcart, Arne Rubehn, Katja Bocklage, Luca Ciucci, Kellen Parker van Dam +5 more
2/23/2026
cs.CL

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Abstract

Recent research argues that exact recursive numeral systems optimize communicative efficiency by balancing a tradeoff between the size of the numeral lexicon and the average morphosyntactic complexity (roughly length in morphemes) of numeral terms. We argue that previous studies have not characterized the data in a fashion that accounts for the degree of complexity languages display. Using data from 52 genetically diverse languages and an annotation scheme distinguishing between predictable and unpredictable allomorphy (formal variation), we show that many of the world's languages are decisively less efficient than one would expect. We discuss the implications of our findings for the study of numeral systems and linguistic evolution more generally.

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Cite this paper

@article{cathcart2026communicatively,
  title  = {How communicatively optimal are exact numeral systems? Once more on lexicon size and morphosyntactic complexity},
  author = {Chundra Cathcart and Arne Rubehn and Katja Bocklage and Luca Ciucci and Kellen Parker van Dam and Alžběta Kučerová and Jekaterina Mažara and Carlo Y. Meloni and David Snee and Johann-Mattis List},
  year   = {2026},
  eprint = {2602.20372},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2602.20372v1}
}

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