Condorcet's paradox corresponds to non-orientability of a surface homeomorphic to the Klein bottle or real projective plane in a generalized topological model of strict ordinal preferences.
A one-shot proof of Arrow’s impossibility theorem
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Condorcet's Paradox as Non-Orientability
Condorcet's paradox corresponds to non-orientability of a surface homeomorphic to the Klein bottle or real projective plane in a generalized topological model of strict ordinal preferences.