According to Arrow's impossibility theorem, it is impossible to find a social ordering that is complete, reflexive, and transitive.

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Arrow's impossibility theorem states that no rank-order voting system can be designed that always satisfies three fairness criteria (unrestricted domain, non-dictatorship, and independence of irrelevant alternatives), not that it's impossible to find a social ordering that is complete, reflexive, and transitive.

According to Arrow's Impossibility Theorem, It Is Impossible to Find