Pairwise counting: Difference between revisions

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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.


Election methods that always meet the [[Condorcet winner]] criterion or the [[Condorcet loser criterion]] use pairwise counting.
Election methods that always meet the [[Condorcet winner]] criterion or the [[Condorcet loser criterion]] use pairwise counting.
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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


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>{{Citation|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 these counts are arranged in a table such as below.
{| class="wikitable"
{| class="wikitable"
|+Pairwise counts
|+Pairwise counts
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!C
!C
|-
|-
|A
!A
|
|
|A > B
|A > B
|A > C
|A > C
|-
|-
|B
!B
|B > A
|B > A
|
|
|B > C
|B > C
|-
|-
|C
!C
|C > A
|C > A
|C > B
|C > B
|
|
|}
|}

== References ==
<references />

Revision as of 18:28, 16 January 2020

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.

Election methods that always meet the Condorcet winner criterion or the Condorcet loser criterion use pairwise counting.

Example

As an example, if pairwise counting is used in an election that has three candidates named A, B, and C, the following pairwise counts are produced:

  • Number of voters who prefer A over B
  • Number of voters who prefer B over A
  • Number of voters who have no preference for A versus B
  • Number of voters who prefer A over C
  • Number of voters who prefer C over A
  • Number of voters who have no preference for A versus C
  • Number of voters who prefer B over C
  • Number of voters who prefer C over B
  • Number of voters who have no preference for B versus C

Often these counts are arranged in a pairwise comparison matrix[1] or outranking matrix[2] table such as below.

Pairwise counts
A B C
A A > B A > C
B B > A B > C
C C > A C > B

References

  1. ↑ Mackie, Gerry. (2003). Democracy defended. Cambridge, UK: Cambridge University Press. p. 6. ISBN 0511062648. OCLC 252507400.
  2. ↑ Nurmi, Hannu (2012), Felsenthal, Dan S.; Machover, Moshé (eds.), "On the Relevance of Theoretical Results to Voting System Choice", Electoral Systems, Springer Berlin Heidelberg, pp. 255–274, doi:10.1007/978-3-642-20441-8_10, ISBN 978-3-642-20440-1, retrieved 2020-01-16
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