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An alternatives account of 'most’ and 'more than half’

Paper · 2021 · Fausto Carcassi and Jakub Szymanik

Summary

Under the standard analysis, 'most' and 'more than half' have identical truth conditions. Speakers nonetheless use 'more than half' for proportions just above 50% and 'most' for noticeably larger ones. Earlier explanations either give the two expressions different literal meanings or invoke pragmatic enrichment without spelling it out. Solt (2016), the main lexical account, links them to ratio versus semi-ordered scales. Carcassi and Szymanik build a fully specified pragmatic account that keeps the semantics equal. It rests on two mechanisms that are already motivated elsewhere:

  • In similarity-structured domains, listeners choose interpretations that minimize the expected distance to the speaker's actual observation.
  • The alternatives an utterance competes with follow from the conceptual structure of that utterance (the structural theory of alternatives).

The authors formalize the account in the Rational Speech Act (RSA) framework. They also run a quantifier production experiment modelled on Pezzelle et al. (2018) and fit a hierarchical Bayesian model to the data. The version with structural alternatives fits better than a minimally different version without them. The broader point is that synonymous expressions can diverge in typical use through pragmatics and concept structure alone, with no semantic difference.

Key points

  • The formal baseline follows Hackl (2009). 'Most' means |A∩B| > |A−B|, while 'more than half' means |A∩B| > ½|A|.
  • Solt's COCA data come from occurrences with an explicit percentage: 54 for 'more than half' and 141 for 'most'.
    • 'More than half' clusters around 50–65%.
    • 'Most' spreads more evenly over 50–100% but rarely appears below 60%.
  • The model is built in three parts:
    • an RSA speaker/listener;
    • structurally derived alternatives, where 'more than half' competes with finer fractions such as 'more than three quarters' and 'most' mainly with 'all';
    • a listener who minimizes expected distance.
  • The fitting code (PyMC3) and anonymized data are public at github.com/thelogicalgrammar/mostVsMoreThanHalf.
  • Several questions remain open:
    • what the model predicts under negation, where Denić & Szymanik find the threshold for 'most' stays higher;
    • how it behaves with larger utterance sets;
    • whether it extends to modified numerals such as 'more than 100' vs 'more than 101'.

Interesting ideas

  • I1. In graded domains such as proportions, colours or numbers, communication succeeds by being close rather than exactly right, so a good listener picks a central guess within the region the utterance allows.
  • I2. Each expression's set of alternatives comes from its own conceptual structure. Fraction-based phrases compete with other fractions, while 'most' competes with 'all', so equivalent phrases yield different upper-bound implicatures.
  • I3. Keep truth conditions and typical usage as separate layers: two phrases can verify the same situations yet carry different expected values.
  • I4. Support a theory by comparing it against a minimally different model that lacks only the mechanism in question.
  • I5. The same machinery can run in reverse: a speaker model chooses whichever of two synonymous expressions best signals the actual proportion.

For Mova

How these ideas could serve Mova, our small open language model — its files, stages and tests:

  • I1 (world): when a text says "most of the apples", the world model could store a typical proportion plus an admissible interval instead of a bare ">50%", which gives downstream reasoning a realistic estimate.
  • I2 (frames): the implicature module could generate scalar alternatives from the internal makeup of the quantifier phrase, so that "more than half" implies "not more than three quarters" but "most" only implies "not all".
  • I3 (answer): word-problem and QA readers could check logical consistency with the strict meaning, but use the usage layer when a question asks for a likely amount or plausibility.
  • I4 (learn): when adding a repair rule or pragmatic component, always evaluate against an ablated twin on the same data, so any gain can be credited to that single component.
  • I5 (back): generation could say "more than half" for values near 52% and "most" for values near 80%, so that regenerated text keeps the reader's inferred proportion close to the one in the meaning graph.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

🎓University of AmsterdamAmsterdam · Netherlands89 works · 81,337 citations

📚 Shelves 6The field of science this work belongs to (OpenAlex fields).Computer Science · 9,086 worksArtificial Intelligence · 8,889 worksArts and Humanities · 9,296 worksLanguage and Linguistics · 9,206 worksPsychology · 798 worksExperimental and Cognitive Psychology · 463 works

Cite

Cite as Fausto Carcassi and Jakub Szymanik. 2021. An alternatives account of 'most’ and 'more than half’. Glossa: a journal of general linguistics.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.16995/glossa.5764

@article{carcassi2021alternatives,
  title = {{An alternatives account of 'most’ and 'more than half’}},
  author = {Fausto Carcassi and Jakub Szymanik},
  journal = {Glossa: a journal of general linguistics},
  year = {2021},
  doi = {10.16995/glossa.5764},
  url = {https://doi.org/10.16995/glossa.5764}
}

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