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The non-partisan two-round system is commonly used to elect public officials in large cities throughout the United States. When the first-round vote-getter of a multi-candidate contest does not win a majority, a runoff election is triggered to decide between the top two finishers. How does an additional stage of competition affect the quality of representation in a polity? In this paper, I develop a formal model and provide an equilibrium analysis which suggests that holding runoffs improves the quality of political representation, ceteris paribus. Intuitively, choice reduction mitigates the negative effects of strategic voting and majority group vote-splitting endemic to multi-candidate competition. To test the model's implications, I leverage a novel set of data: Chicago City Council election returns from 1923-present. Using a regression discontinuity design, I compare the future electoral performance of winners who barely win decisively in the first round with winners who win an election in which a runoff was barely triggered. Runoff winners are more likely than their counterparts to run, face fewer challengers, obtain higher vote shares, and win in future elections -- suggesting that these representatives are more well-suited to their districts than are those whose path to office is less arduous.