The Condorcet paradox tells us that, even though it is impossible to satisfy all of Arrow's properties of a desirable voting system, pairwise majority voting will always satisfy transitivity.

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The Condorcet paradox actually demonstrates a situation where pairwise majority voting can lead to intransitive results, meaning that even if candidate A is preferred over B, and B is preferred over C, it does not necessarily follow that A is preferred over C.

The Condorcet Paradox Tells Us That, Even Though It Is