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Deliberation among individuals online plays a key role in shaping the opinions that drive votes, purchases, donations and other critical offline behavior. Yet, the determinants of opinion-change via persuasion in deliberation online remain largely unexplored. Our research examines the persuasive power of $\textit{ethos}$ -- an individual's "reputation" -- using a 7-year panel of over a million debates from an argumentation platform containing explicit indicators of successful persuasion. We identify the causal effect of reputation on persuasion by constructing an instrument for reputation from a measure of past debate competition, and by controlling for unstructured argument text using neural models of language in the double machine-learning framework. We find that an individual's reputation significantly impacts their persuasion rate above and beyond the validity, strength and presentation of their arguments. In our setting, we find that having 10 additional reputation points causes a 31% increase in the probability of successful persuasion over the platform average. We also find that the impact of reputation is moderated by characteristics of the argument content, in a manner consistent with a theoretical model that attributes the persuasive power of reputation to heuristic information-processing under cognitive overload. We discuss managerial implications for platforms that facilitate deliberative decision-making for public and private organizations online.