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.

Condorcet Paradox

The Condorcet Paradox is a concept in voting theory where individual preferences cannot be aggregated into a consistent collective decision without creating contradictions.

Arrow's Properties

A set of criteria designed by economist Kenneth Arrow to assess the social welfare or collective decision-making functions, ensuring fairness, unanimity, and independence of irrelevant alternatives.

Pairwise Majority Voting

A voting system where candidates are compared in pairs, with each pair being voted on separately, to determine the most preferred option by majority decision.