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. |
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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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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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Revision as of 23:48, 19 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.
Most election methods that meet the Condorcet criterion or the Condorcet loser criterion use pairwise counting, but not all.[nb 1]
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.
| A | B | C | |
|---|---|---|---|
| A | A > B | A > C | |
| B | B > A | B > C | |
| C | C > A | C > B |
In cases where only some pairwise counts are of interest, those pairwise counts can be displayed in a table with fewer table cells.
Notes
- ↑ Nanson meets the Condorcet criterion and Instant-runoff voting meets the Condorcet loser criterion.
References
- ↑ Mackie, Gerry. (2003). Democracy defended. Cambridge, UK: Cambridge University Press. p. 6. ISBN 0511062648. OCLC 252507400.
- ↑ Nurmi, Hannu (2012). Felsenthal, Dan S.; Machover, Moshé (eds.). "On the Relevance of Theoretical Results to Voting System Choice". Electoral Systems. Springer Berlin Heidelberg: 255–274. doi:10.1007/978-3-642-20441-8_10. ISBN 978-3-642-20440-1. Retrieved 2020-01-16.