Abstract: For many decades, the United States has been conducting an extraordinary natural experiment: Randomly assigned three-judge panels on courts of appeals produce extensive evidence of the effect of judicial ideology on judges' votes. If the political party of the appointing president is treated as a rough proxy for ideology, then it becomes possible to test three hypotheses: (a) a judge's votes, in ideologically contested areas, can be predicted by the party of the appointing president; (b) a judge's ideological tendency, in such areas, will be amplified if the panel has two other judges appointed by an appointing president of the same political party; and (c) a judge's ideological tendency, in such areas, will be dampened if the panel has no other judge appointed by an appointing president of the same political party. All three hypotheses are confirmed in many areas, including affirmative action, campaign finance, sex discrimination, sexual harassment, piercing the corporate veil, disability discrimination, race discrimination, and review of environmental regulations. An important implication is that panel composition has a strong effect on likely outcomes, thus creating extremely serious problems for the rule of law. Taken as a whole, the evidence suggests that judges frequently issue collegial concurrences, that is, concurrences produced by the unanimous views of the other judges on the panel, and that judges are subject to group polarization, by which groups of like-minded people go to extremes. Notably, all three hypotheses are rejected in the areas of federalism, criminal appeals, and takings of private property, because Republican and Democratic appointees vote essentially alike. In the areas of abortion and capital punishment, the first hypothesis is confirmed, but the second and third are rejected, because judges vote their convictions, and are not affected by the composition of the panel. Disaggregating the data by circuit allows courts of appeals to be ranked along an ideological spectrum; it also shows striking differences between Republican appointees and Democratic appointees on different circuits. Normative implications are briefly explored.