McKelvey–Schofield chaos theorem

See McKelvey–Schofield chaos theorem

The theorem roughly implies that spatial models in more than one dimension can create Condorcet cycles, even when every voter prefers closer candidates to more distant ones. In one dimension, there's always a Condorcet winner under these conditions, but it stops being true with more dimensions.

Note that though the theorem holds that the Smith set will generally contain most of the alternatives, evidence seems to suggest otherwise in real-world political settings. See Condorcet paradox for more information.