Heavy Tails and the Shape of Modified Numerals

Abstract

The pattern of implicatures of the modified numeral “more than n” depends on the roundness of n. Cummins et al. (2012) present experimental evidence for the relation between roundness and implicature patterns and propose a pragmatic account of the phenomenon. More recently, Hesse and Benz (2020) present more extensive evidence showing that implicatures also depend on the magnitude of n and propose a novel explanation based on the approximate number system (Dehaene, 1999). Despite the wealth of experimental data, no formal account has yet been proposed to characterize the full posterior distribution over numbers of a listener after hearing “more than n.” We develop one such account within the Rational Speech Act framework, quantitatively reconstructing the pragmatic reasoning of a rational listener. We argue that world knowledge about the distribution of the true quantity has a substantial impact on the information conveyed by the modified numeral. We show that our pragmatic account in combination with a heavy‐tailed model of the participants' prior correctly predicts various features of the experimental data from Hesse and Benz (2020).

Questions About Quantifiers: Symbolic and Nonsymbolic Quantity Processing by the Brain

“…26 As a reviewer pointed out, one should also ask here about the potential role of implicit negation, as for instance, "at least seven" might be represented as "not less than seven." 27 See Carcassi and Szymanik (2022) for formalizing the use of modified numerals with a computational model based on a similar idea. 28 Possibly due to bias introduced by each quantifier, as suggested by Shikhare and colleagues; see Deschamps, Agmon, Loewenstein, and Grodzinsky (2015) for an extensive discussion of other possible explanations.…”

“…2727See Carcassi and Szymanik (2022) for formalizing the use of modified numerals with a computational model based on a similar idea.…”