McKelvey–Schofield chaos theorem: Difference between revisions

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See [[w:McKelvey–Schofield chaos theorem]]
See [[w:McKelvey–Schofield chaos theorem]]

The theorem roughly implies that spatial models in more than one dimension can create [[Condorcet cycle]]s, 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.
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.

Revision as of 18:46, 18 July 2022

See w: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.