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 |
Most, but not all, election methods that meet the [[Condorcet criterion]] or the [[Condorcet loser criterion]] use pairwise counting.<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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Revision as of 04:51, 21 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, but not all, election methods that meet the Condorcet criterion or the Condorcet loser criterion use pairwise counting.[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.