Does optimal partitioning of color space account for universal color categorization?

A 2007 study by Regier, Kay, and Khetarpal purports to show that universal categories emerge as a result of optimal partitioning of color space. Regier, Kay, and Khetarpal only consider color categorizations of up to six categories. However, in most industrialized societies eleven color categories are observed. This paper shows that when applied to the case of eleven categories, Regier, Kay, and Khetarpal's optimality criterion yields unsatisfactory results. Applications of the criterion to the intermediate cases of seven, eight, nine, and ten color categories are also briefly considered and are shown to yield mixed results. We consider a number of possible explanations of the failure of the criterion in the case of eleven categories, and suggest that, as color categorizations get more complex, further criteria come to play a role, alongside Regier, Kay, and Khetarpal's optimality criterion.