Several scholars have recently entertained proposals for "epistocracy," a political regime in which decision-making power is concentrated in the hands of a society's most informed and competent citizens. These proposals rest on the claim that we can expect better political outcomes if we exclude incompetent citizens from participating in political decisions because competent voters are more likely to vote "correctly" than incompetent voters. We develop what we call the objection from selection bias to epistocracy: a procedure that selects voters on the basis of their observed competence---as epistocracy does---will often be "biased" in the sense that competent voters will be, on average, more likely than incompetent voters to possess certain attributes that reduce the probability of voting correctly. Our objection generalizes the "demographic objection" discussed in previous literature, showing that the range of realistic scenarios in which epistocracy is vulnerable to selection bias is substantially broader than previous discussions appreciate. Our discussion also shows that previous discussions have obscured the force of the threat of selection bias. Since we lack reasons to believe that epistocratic proposals can avoid selection bias, we have no reason to seriously entertain epistocracy as a practical proposal.