 The impossibility theorem roughly says that there is no general way to rank a given set of (more than two) alternatives on the basis of (at least two) individual preferences, if one wants to respect three conditions: (Weak Pareto) unanimous preferences are always respected (if everyone prefers A to B, then A is better than B); (Independence of Irrelevant Alternatives) any subset of two alternatives must be ranked on the sole basis of individual preferences over this subset; (No-Dictatorship) no individual is a dictator in the sense that his strict preferences are always obeyed by the ranking, no matter what they and the other individuals’ preferences are. The impossibility holds when one wants to cover a great variety of possible profiles of individual preferences. When there is sufficient homogeneity among preferences, for instance when alternatives differ only in one dimension and individual preferences are based on the distance of alternatives to their preferred alternative along this dimension (think, for instance, of political options on the left-right spectrum), then consistent methods exist (the majority rule, in this example; Black 1958).