I build a citizen-candidate model in which one candidate, the incumbent, can selectively eliminate other citizen-candidates. I apply it to study candidate elimination in competitive autocracies. I find that the incumbent either eliminates all competitive challengers to win the election, removes a smaller subset of challengers to select a preferable successor, or organizes a free and fair election and loses power. In a free and fair election, the median voter result does not hold. For a large range of parameters, the successor selected by the incumbent can be more moderate than any candidate that would emerge from a free and fair election. Consequently, compared to a free and fair election, the median voter may be better off in a rigged election.