Well there are several ways to answer that question, but I'll start off by clarifying. What I was referring to was the social construction of race, and in the social processes of race issues and relations, a good deal of it is indeed arbitrary. For example, in the US, in order for a newborn to be deemed "white", both parents must be "white". Different countries have different means of determining race, so somebody who is of one social race in one country may be considered a different one elsewhere. There is no universal system of classifying race in this sense, because it has cultural origins with respect to given regions. And of course cultural concepts are arbitrary in their very natures.