Pairwise counting: Difference between revisions
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(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. |
'''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. |
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Most election methods that meet the [[Condorcet 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> |
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== Example == |
== Example == |
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* Number of voters who have no preference for B versus C |
* Number of voters who have no preference for B versus C |
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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>{{ |
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. |
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{| class="wikitable" |
{| class="wikitable" |
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|+Pairwise counts |
|+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. |
In cases where only some pairwise counts are of interest, those pairwise counts can be displayed in a table with fewer table cells. |
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==Notes== |
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{{reflist|group=nb}} |
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== References == |
== References == |
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