Predicting focal colors with a rational model of representativeness

Predicting focal colors with a rational model of representativeness Joshua T. Abbott (joshua.abbott@berkeley.edu) Department of Psychology, University of California, Berkeley, CA 94720 USA Terry Regier (terry.regier@berkeley.edu) Department of Linguistics, Cognitive Science Program, University of California, Berkeley, CA 94720 USA Thomas L. Griffiths (tom griffiths@berkeley.edu) Department of Psychology, University of California, Berkeley, CA 94720 USA Abstract They argued that color categories are not defined around uni- versal foci, but are instead defined at their boundaries by local linguistic convention, which varies across languages. They proposed: “Once a category has been delineated at the bound- aries, exposure to exemplars may lead to the abstraction of a central tendency so that observers behave as if their categories have prototypes” (p. 395). On this view, best examples do not reflect a universal cognitive or perceptual substrate, but are merely an after-effect of category construction by language: best examples are derived from language-specific boundaries, rather than boundaries from universal best examples. A proposal by Jameson and D’Andrade (1997) has the po- tential to reconcile these two opposed stances. This proposal holds that there are genuine universals of color naming, but they do not stem from a small set of focal colors. Instead, universals of color naming may stem from irregularities in the overall shape of perceptual color space, which is partitioned into categories by language in a near-optimally informative way. This proposal has been shown to explain universal ten- dencies in the boundaries of color categories (Regier et al., 2007). However it has not yet provided an account of best examples of these categories, which lie at the heart of the de- bate. Here, we address this open issue, completing the reconcil- iation of the two standardly opposed views. We suggest that best examples are largely universal (in line with the universal- foci view), but nonetheless derived from category boundaries (in line with the relativist view). Specifically, given the in- dependent explanation of category boundaries in terms of the shape of color space, we propose that universal tendencies of best examples are derived from those of boundaries, rather than the other way around as has been traditionally assumed. Moreover, we propose that best examples are derived from category boundaries in an optimal manner, echoing the opti- mal or near-optimal partition of color space into categories. To pursue this idea, we draw on previous work on a rational model of representativeness, and ask whether the best exam- ples of color categories can be well-predicted as those colors that are most representative of a given category. The remainder of the paper proceeds as follows. In the next section, we discuss the previous work on representative- ness on which we draw, and contrast it with other approaches to that problem. We then describe the color naming data we consider, and a set of competing models that predict the foci Best examples of categories lie at the heart of two major de- bates in cognitive science, one concerning universal focal col- ors across languages, and the other concerning the role of rep- resentativeness in inference. Here we link these two debates. We show that best examples of named color categories across 110 languages are well-predicted by a rational model of repre- sentativeness, and that this model outperforms several natural competitors. We conclude that categorization in the contested semantic domain of color may be governed by general princi- ples that apply more broadly in cognition, and that these prin- ciples clarify the interplay of universal and language-specific forces in color naming. Keywords: Language and perception; semantic universals; color naming; representativeness; Bayesian inference. Introduction Do the world’s languages reflect a universal repertoire of cog- nitive and perceptual categories? Or do different languages partition the experienced world in fundamentally different ways? These questions have been pursued in depth in the do- main of color naming and cognition (e.g. Berlin & Kay, 1969; Kay & McDaniel, 1978; Lindsey & Brown, 2006; Rober- son, Davidoff, Davies, & Shapiro, 2005; Roberson, Davies, & Davidoff, 2000), and current findings suggest an inter- estingly mixed picture. There are clear universal tendencies of color naming across languages, but there is also substan- tial cross-language variation (e.g. Regier, Kay, & Khetarpal, 2007), more than is suggested by traditional universalist ac- counts. At the center of this debate is the disputed role of focal colors, or the best examples of named color categories. It has long been claimed that color naming across lan- guages is constrained by six universal privileged points, or foci, in color space, corresponding to the best examples of what would be described in English as white, black, red, yel- low, green, and blue. This view has received empirical sup- port: the best examples of color terms across languages tend to cluster near these six points (Berlin & Kay, 1969; Regier, Kay, & Cook, 2005), and these colors have also been found to be cognitively privileged (Heider, 1972; but see Roberson et al., 2000). A natural and influential proposal (Kay & Mc- Daniel, 1978) is that these privileged colors constitute a uni- versal foundation for color naming, such that languages dif- fer in their color naming systems primarily by grouping these universal foci together into categories in different ways. Roberson et al. (2000) advanced a diametrically opposed view of color naming, and of the role of best examples in it.