McKelvey-Schofield Chaos Theorem

The McKelvey-Schofield chaos theorem is a result in social choice theory stating that when political preferences are defined over a policy space with more than one dimension, decisions made by majority rule become unstable. In most such settings there's no Condorcet winner, and any outcome can be reached from any starting point through some sequence of votes, so the order in which options are put to a vote can be used to steer the process toward almost any result. Richard McKelvey proved an early version of the theorem in 1976 for preferences based on Euclidean distance, Norman Schofield proved a further version in 1978 for differentiable preferences, and the result is often read as showing that Arrow's impossibility theorem keeps binding once preferences are allowed more than one dimension, unlike the single-dimensional case covered by the median voter theorem.