Certain features of the legal system, such as litigant-driven appeals and random assignment of judges to cases, are supposed to prevent biased and error-prone decision-making by judges. I analyze a formal model illustrating this is not always true, even when judges are personally unbiased. First, an unbiased trial judge may make systematically biased judgments when that judge’s decisions can be appealed by a losing litigant. If the judge is sufficiently reversal averse, this bias favors higher resource litigants. Second, litigant-driven appeals allow unbiased judges to put less effort into resolving cases correctly. Third, when unbiased judges are assigned randomly to cases, they will produce more errors than a case assignment system allowing trial judges more freedom to select cases. The results confirm one contention of “team models” of judicial hierarchy (that litigant behavior is important) while also demonstrating the limits of another (that judicial hierarchies minimize adjudication errors).