A Condorcet winner defeats every other alternative by a strict majority in pairwise voting. It is unique when it exists. For an odd electorate with single-peaked preferences, the median peak is a Condorcet winner: alternatives on either side lose to the majority whose peaks lie at or beyond the median in the other direction. With an even electorate ties may prevent a strict winner.
A weak Condorcet winner is never defeated by a strict pairwise majority, allowing ties. For even electorates with single-peaked preferences, all alternatives between the two middle peaks have this property. A single-valued selection requires a tie convention; arbitrary tie selection is not automatically strategyproof.
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