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

Human languages expand vocabularies by combining existing morphemes rather than inventing arbitrary forms. Communicative efficiency shapes lexical systems at multiple levels (Gibson et al., 2019), yet morphological composition -- combining morphemes through compounding or affixation -- has rarely been modeled as a historically situated speaker choice among competing morpheme sequences, leaving unanswered why a language settles on one morpheme combination over other plausible alternatives. We ask whether a trade-off between listener recoverability and speaker production cost can predict attested compositions over contemporaneously available alternatives. Here we show, within the Rational Speech Act (RSA) framework (Frank & Goodman, 2012; Goodman & Frank, 2016) using a time-indexed lexicon constructed from Corpus of Historical American English (COHA) and Corpus of Contemporary American English (COCA), that across 4323 naturally occurring English compounds and derivations spanning 1820--2019, attested compositions are systematically ranked above unattested alternatives generated from contemporaneously available morphemes. Models integrating semantic informativeness with production cost outperform semantic-only and cost-only baselines on Mean Reciprocal Rank (MRR) and top-k accuracy (Acc@k), with the advantage of the Pragmatic Speaker model ($S_1$) over the semantic-only baseline growing as the candidate set expands, where meaning alone leaves morphological choice underdetermined. These findings suggest that lexicalization reflects a communicative trade-off between expressiveness and efficiency, extending rational accounts of communication from utterance-level choice to the internal structure of words.

Human recursive numeral systems (i.e., counting systems such as English base-10 numerals), like many other grammatical systems, are highly regular. Following prior work that relates cross-linguistic tendencies to biases in learning, we ask whether regular systems are common because regularity facilitates learning. Adopting methods from the Reinforcement Learning literature, we confirm that highly regular human(-like) systems are easier to learn than unattested but possible irregular systems. This asymmetry emerges under the natural assumption that recursive numeral systems are designed for generalisation from limited data to represent all integers exactly. We also find that the influence of regularity on learnability is absent for unnatural, highly irregular systems, whose learnability is influenced instead by signal length, suggesting that different pressures may influence learnability differently in different parts of the space of possible numeral systems. Our results contribute to the body of work linking learnability to cross-linguistic prevalence.

The structure of naming systems in natural languages hinges on a trade-off between high informativeness and low complexity. Focusing on the domain of kinship naming, we analyze such trade-off while addressing simplifying assumptions of prior work, namely: (i) universal communicative need across languages, and (ii) optimal listeners. To that aim, we collect data from four different languages, and analyze how different communicative needs and variations in the listener model influence the informativeness--complexity trade-off. Adopting a referential game setup from emergent communication, we further show that trade-off optimality is not only theoretically achievable but also emerges empirically in learned communication systems.