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* Number of voters who have no preference for B versus C
Alternatively, the words "Number of voters who prefer A over B" can be interpreted as "The number of votes that help A beat (or tie) B in the A versus B [[Pairwise matchup|pairwise matchup]]".
Note that more generally, for example, the pairwise count "Number of voters who prefer B over C" can be thought of as "the number of votes helping B beat or tie C in the B vs. C [[Pairwise matchup|pairwise matchup]]". Also, in order to know the number of voters who have no preference between two candidates, the only values that need be known are the number of voters who prefer the first over the second, the number of voters that prefer the second over the first, and the number of total voters in the election. This is done by subtracting the first two categories (which together are the number of voters who have any preference between the two candidates) from the number of total voters.
If the number of voters who have no preference between two candidates is not supplied, it can be calculated using the supplied numbers. Specifically, start with the total number of voters in the election, then subtract the number of voters who prefer the first over the second, and then subtract the number of voters who prefer the second over the first.
In general, for N candidates, there are 0.5*N*(N-1) pairwise matchups to consider. So for 1 candidate, there are 0 matchups, 2 candidates, 1 matchup, 3 candidates, 3 matchups, 4 candidates, 6 matchups, 5 candidates, 10 matchups, 6 candidates, 15 matchups, 7 candidates, 21 matchups, etc. ▼
▲In general, for N candidates, there are 0.5*N*(N-1) pairwise matchups to consider. SoFor example, for 12 candidate,candidates there areis 0one matchupsmatchup, 2for 3 candidates , 1there matchup,are 3 candidatesmatchups, 3 matchups,for 4 candidates , there are 6 matchups, for 5 candidates , there are 10 matchups, for 6 candidates , there are 15 matchups, and for 7 candidates , there are 21 matchups , etc.
Often these counts are arranged in a ''pairwise comparison matrix''<ref name=":0">{{Cite book|url=https://books.google.com/?id=q2U8jd2AJkEC&lpg=PA6&pg=PA6|title=Democracy defended|last=Mackie, Gerry.|date=2003|publisher=Cambridge University Press|isbn=0511062648|location=Cambridge, UK|pages=6|oclc=252507400}}</ref> or ''outranking matrix<ref>{{Cite journal|title=On the Relevance of Theoretical Results to Voting System Choice|url=http://link.springer.com/10.1007/978-3-642-20441-8_10|publisher=Springer Berlin Heidelberg|work=Electoral Systems|date=2012|access-date=2020-01-16|isbn=978-3-642-20440-1|pages=255–274|doi=10.1007/978-3-642-20441-8_10|first=Hannu|last=Nurmi|editor-first=Dan S.|editor-last=Felsenthal|editor2-first=Moshé|editor2-last=Machover}}</ref>'' table such as below. ▼
▲Often theseThese counts arecan be arranged in a ''pairwise comparison matrix''<ref name=":0">{{Cite book|url=https://books.google.com/?id=q2U8jd2AJkEC&lpg=PA6&pg=PA6|title=Democracy defended|last=Mackie, Gerry.|date=2003|publisher=Cambridge University Press|isbn=0511062648|location=Cambridge, UK|pages=6|oclc=252507400}}</ref> or ''outranking matrix<ref>{{Cite journal|title=On the Relevance of Theoretical Results to Voting System Choice|url=http://link.springer.com/10.1007/978-3-642-20441-8_10|publisher=Springer Berlin Heidelberg|work=Electoral Systems|date=2012|access-date=2020-01-16|isbn=978-3-642-20440-1|pages=255–274|doi=10.1007/978-3-642-20441-8_10|first=Hannu|last=Nurmi|editor-first=Dan S.|editor-last=Felsenthal|editor2-first=Moshé|editor2-last=Machover}}</ref>'' table such as below.
{| class="wikitable"
|+Pairwise counts
In cases where only some pairwise counts are of interest, those pairwise counts can be displayed in a table with fewer table cells.
Note that since a candidate can't be pairwise compared to themselves (i.e.for example candidate BA can't be compared to candidate B, since there's only one candidate in the comparisonA), the cell that doesindicates sothis comparison is always empty.
WhenTo it is only desired to knowidentify which candidate wins thea specific pairwise matchup, say,such as between candidates A and B, one can subtract the value of B>A from A>B. If the resulting value is positive, itthen meanscandidate A won the matchup,. and ifIf it is 0zero, it meansthen there is a pairwise tie;. otherwiseIf itthe meansresult is negative, then candidate B won the matchup. (See the [[Pairwise counting#Terminology|Terminology]] section) for details.)
== Example with numbers ==
|