Pairwise counting: Difference between revisions
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'''Pairwise champion''': Also known as a beats-all winner or [[Condorcet winner]], it is a candidate who pairwise beats every other candidate. Due to pairwise ties (see above) and pairwise cycling (see below), there is not always a pairwise champion.
'''Pairwise cycling:''' Also known as a [[Condorcet cycle]], it is when within a set of candidates, each candidate has at least one pairwise defeat (when looking only at the matchups between the candidates in the set). Note that some cycles can be symmetrical i.e. you can swap the candidates' names without changing the result. (See the [[Condorcet paradox]] article for an example, and the [[Neutrality criterion|neutrality criterion]] for more information). Such cycles are sometimes called ties.
'''Minimal pairwise dominant set''': Also known as the [[Smith set]], it is the smallest group of candidates who pairwise beat all others. The [[Pairwise champion|pairwise champion]] will always be the only member of this set when they exist.
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