Definition
Young Score ( COMSOC)
The Young score is the minimum number of voters whose removal makes an alternative
a Condorcet winner. For a profile of complete, strict rankings, Here
retains only the voters in . Delete whole ballots; do not change their rankings or remove alternatives. The majority threshold is recomputed using , the number of retained voters. Every candidate is evaluated separately from the original profile. If no retained electorate makes
a Condorcet winner, set its score to . A score of zero means already wins every pairwise contest.
Intuition
Unlike Dodgson, Young deletes whole ballots. Each deletion changes both support counts and the majority threshold; a tie still does not suffice. Use the same three-voter profile below, starting afresh for each candidate.
Candidate A: no deletions
Voters 1 and 2 give
a majority against both opponents. Delete nobody. Thus
.
Candidate C: delete one opponent, then the other
loses to by . Keep its sole supporter, voter 3; delete voter 1, who opposes against both alternatives. The remaining
tie against is insufficient. Delete voter 2, the remaining supporter of over . Both contests are now won. One deletion could only tie the original
loss, so .
Candidate B: the necessary deletions still fail
loses both contests by . Only voter 3 supports it against . Keep voter 3 and first delete voter 2, who opposes in both contests. To break the tie against
, delete voter 1—even though this removes ‘s only supporter against . Only this electorate lets
beat , but it loses to . Deleting everyone gives no strict majority either. Hence .
The Young winner is
Deleting ballots cannot create new preferences; this is why swaps can repair
Score Convention
Young scores are also commonly expressed as the maximum number of voters retained, which is maximised rather than minimised. When a successful retained electorate exists, the two objectives satisfy
Keep the convention explicit when comparing sources.