 The Pareto criterion has a strong intuitive appeal. If everyone agrees that a state x is preferred to a state y, certainly the collective assessment must rank x more highly than y. The Pareto criterion moreover appears to be weak, i.e., to impose few constraints on social choice. After all, each member of the society will only rarely rank two alternatives as every other member of the society. Nevertheless, the Pareto criterion has strong implications for the aggregation of individual judgments. Indeed, as summarized below, the Pareto criterion is inconsistent with a large number of other principles, each of which also has strong intuitive appeal. 