Abstract: A key tenet of representative democracy is that politicians' discourse and policies should follow voters' preferences. In the median voter theorem, this outcome emerges as candidates strategically adjust their platform to get closer to their opponent. Despite its importance in political economy, we lack direct tests of this mechanism. In this paper, we show that candidates converge to each other both in ideology and rhetorical complexity. We build a novel dataset including the content of 9,000 primary and general election websites of candidates for the U.S. House of Representatives, 2002-2016, as well as 57,000 campaign manifestos issued by candidates running in the first and second round of French parliamentary and local elections, 1958-2022. We first show that candidates tend to converge to the center of the ideology and complexity scales and to diversify the set of topics they cover, between the first and second round, reflecting the broadening of their electorate. Second, we exploit cases in which the identity of candidates qualified for the second round is quasi-random, by focusing on elections in which they narrowly win their primary (in the U.S.) or narrowly qualify for the runoff (in France). Using a regression discontinuity design, we find that second-round candidates converge to the platform of their actual opponent, as compared to the platform of the runner-up who did not qualify for the last round. We conclude that politicians behave strategically and that the convergence mechanism underlying the median voter theorem is powerful.