From the perspective of social anthropology, this paper examines the collection and analysis of census data on ethnic group membership. It identifies a fundamental problem lying in the census's attempt to enumerate a subjective identity. The problem is seen as exacerbated by allowing census respondents to report membership in more than one ethnic group. This not only contradicts the census's own definition of ethnic group, and steers respondents toward a racial conception of ethnicity, but involves the census in the arbitrary re-allocation of respondent's answers. The paper then reviews two influential social science analyses of census data on ethnic group membership and finds that the analysts concerned impose their own quite different definitions of ethnic groups onto the data. It is concluded that the whole process of collecting and analysing census data of ethnic group membership is subjective and arbitrary from start to finish.