THEORY-472: A speaker who chooses words to minimise the information lost about a single intended referent, with words' literal meanings uniform over their extensions, picks each true word with probability inversely proportional to a power of its extension, so the size principle follows from informative communication; in one betting experiment, learners who knew the referent bet on a novel word's meaning in line with the inversion of that speaker (r = .93 on condition means), and in one free-description study speakers' word use followed it only weakly (r = .19)

Source

Frank, Goodman, Lai and Tenenbaum (2009), LIT-824 (Proceedings of CogSci 31, pp. 1228–1233), read in full in NOTE-627 from the authors’ posted copy. The derivations of Eqs. 8–10 and 12 were checked by hand.

What was actually shown

The speaker (Eqs. 4–6). Meanings are distributions over the objects in a context C. A word’s literal meaning w̃_C is uniform over its extension. The speaker chooses w with P(w | M_S, C) ∝ exp(α U), where U = −D_KL(M_S ‖ w̃_C) + F, and F (other costs) is 0 here.

The size principle (Eqs. 8–10; C1, a derivation). If the intended meaning is a point mass on the referent, D_KL(M_S ‖ w̃_C) = log |w|, so P(w | M_S, C) = |w|^(−α) / Σ |w′|^(−α) over the words true of the referent, and 0 for false ones.

The learner (Eq. 12). A learner who knows the referent, with two features and two candidate lexicons under a uniform prior, infers that the word names f₁ with probability |f₁|⁻¹ / (|f₁|⁻¹ + |f₂|⁻¹): 2/3 for “red” in the display with one red object and two circles.

Experiment 1 (C2, moderate). 700 participants from MIT mailing lists split $100betweentwocandidatemeaningsofanovelwordacrosssix-objectdisplays.Meanbetsagainsttheparameter-freemodel(\alpha =1):Pearsonr=.93,Spearman.92.Betssatnear$50 when the features were equally frequent, and the Figure 1 case gave $70againstapredicted$67.

Experiment 2 (C3, weak). 44 participants wrote descriptions of 50 of 304 Flickr superball photos so that someone could pick each out. Use of a ball’s tag-words against Eq. 10: r = .19 overall, .51 without basic colour terms, .02 for colour terms alone (p = .63). A Google-Images frequency estimate of F moves these to .22 and .52.

What could have come out otherwise. Bets could have ignored feature frequency, and speakers could have used words with no relation to their extension. The first did not happen. The second nearly did for colour terms.

What this does not say

• That learners reason about the speaker. With point referents and uniform literal meanings, the informative-speaker learner and a plain size-principle learner make the same predictions “by construction” (NOTE-627, Open questions). Experiment 1 fits both. No competing model was fitted, and the within-condition spread in Figure 2 is not addressed.
• That speakers are informative. Experiment 2 is the record’s only test of production on this model, and it is weak: one album owner’s tags as features, extensions counted over all 304 photos though each ball was described alone, bag-of-words scoring, and a post-hoc account of the colour failure (C4, a conjecture).
• Anything about listeners inferring a referent. There is one speaker and a learner who inverts it once, with the referent given. The listener who infers a referent, and the recursion, are Frank and Goodman 2012 (LIT-821) and the papers behind THEORY-172.
• That the framework covers implicature or anaphora. Claimed in the discussion (C5), not modelled.

Connections

• THEORY-172 (listeners invert an informative speaker, so a fixed form’s interpretation depends on the alternatives) is the later and wider account. This is its precursor, in the word-learning form: the lexicon is inferred given the referent. Experiment 1’s evidence is of the kind that THEORY’s promote_when says cannot settle it. THEORY-172 extends this account: the same mechanism, widened from the lexicon to the referent. It does not cite this paper among its sources.
• Grice’s maxim of Quantity (LIT-1041, read only at pp. 45–47) is the informal ancestor the paper names. Grice himself calls the second Quantity maxim “disputable”.
• The companion Psychological Science paper (LIT-815) infers referential intentions and has no informative speaker. NOTE-627 confirms that RSA work cites this paper, not that one, for the informative speaker.

Note of 2026-10-20: the wider claim, filed Proposed

Under ADR-047 v4 the narrowing-loss sweep (batch 072) filed THEORY-816 as Proposed, extending this entry. It carries the claim this entry’s title gave up when batch 025 narrowed it: that word learners reason about an informative speaker when they infer a novel word’s meaning, so the size principle in word learning is a consequence of that inference, as Frank, Goodman, Lai and Tenenbaum propose. This entry is its evidence and is not changed by the filing.