Concerned about widespread incompetence among voters in democratic societies, epistocrats propose quasi-democratic electoral systems that amplify the voices of competent voters while silencing (or perhaps just subduing) the voices of those deemed incompetent. In order to amplify the voices of the competent we first need to know what counts as political competence, and then we need a way of identifying those who possess the relevant characteristics. After developing an account of what it means to be politically competent, I argue that there is no way for the epistocrat to identify such persons. Therefore, epistocracy cannot be implemented.