Pairwise counting: Difference between revisions

Clarify that not all methods that pass CW or CL use pairwise matrices.
(Added clarification based on request in discussion page.)
(Clarify that not all methods that pass CW or CL use pairwise matrices.)
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'''Pairwise counting''' is the process of considering a set of items, comparing one pair of items at a time, and for each pair counting the comparison results.
 
ElectionMost election methods that always meet the [[Condorcet winnercriterion]] criterion or the [[Condorcet loser criterion]] use pairwise counting, but not all.<ref group=nb>[[Nanson's method|Nanson]] meets the [[Condorcet criterion]] and [[Instant-runoff voting]] meets the [[Condorcet loser criterion]].</ref>
 
== Example ==
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* Number of voters who have no preference for B versus C
 
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>{{CitationCite 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
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|}
In cases where only some pairwise counts are of interest, those pairwise counts can be displayed in a table with fewer table cells.
 
==Notes==
{{reflist|group=nb}}
 
== References ==
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