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Cardinal-weighted pairwise comparison: Difference between revisions
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'''Cardinal-weighted pairwise comparison''' (also known as "'''Cardinal pairwise'''"
== History==
Cardinal pairwise differs from traditional pairwise count methods ([[Condorcet method|Condorcet methods]]) in that it uses cardinal (ratings) information in addition to ordinal information.▼
This method was first proposed by [[James Green-Armytage]] in June of 2004.<ref>Author:
James Green-Armytage (jarmyta at antioch-college.edu), [http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-June/013280.html Thread: "approval vs. IRV: false claim about MMC examples?"], Publisher: [[election-methods list]], Date: Sun Jun 6 18:57:01 PDT 2004</ref> Green-Armytage then published a paper in [[Voting Matters]] in November 2004.<ref>[[James Green-Armytage|Green-Armytage, James]], "''Cardinal-weighted pairwise comparison''", Date: November 2004, Journal-issue: [https://www.votingmatters.org.uk/ISSUE19/INDEX.HTM Voting Matters: Volume 19], Publisher: [[Voting Matters]], Current link: https://www.votingmatters.org.uk/ISSUE19/I19P2.PDF , Old link: <nowiki>http://www.mcdougall.org.uk/VM/ISSUE19/I19P2.PDF</nowiki></ref>
== Definition ==
{{Distinguish|Rated pairwise preference ballot}}
▲Cardinal pairwise differs from traditional pairwise count methods ([[Condorcet method
CWP uses the ''ordinal'' information to determine the ''direction'' of pairwise defeats, exactly as most Condorcet methods do. However, it uses the ''cardinal'' information to determine the ''strength'' of the pairwise defeats.
Thus, in essence, CWP can be thought of as a
'''For each voter who ranks A over B, and only for these voters, subtract
This is akin to a cardinal version of [[winning votes]], since only the preferences of voters who prefer the winner of the matchup are counted.
The name "cardinal pairwise" also implies that a [[Smith-efficient]], [[:Category:Defeat-dropping Condorcet methods|defeat-dropping]] base method will be used, for example [[
===Ballot types===
1. One way to ballot for CWP is to have a separate ordinal and cardinal ballot, and to require that if a voter gives candidate R a higher rating than candidate S, then that voter must also give candidate R a higher ranking than candidate S.
2. A simpler way to ballot for CWP is to use only a cardinal ballot, and to derive the ordinal information from the cardinal information. The only disadvantage of this is that it creates an additional [[tactical voting|compromising-compression]] incentive not found in the first version. However, this additional incentive should be extremely minor if the scale is sufficiently fine.
For example, assume that the scale consists of integers from 0 to 100. If my sincere preferences are J>K>L, and I want to make the J>K defeat as weak as possible while making the K>L defeat as strong as possible, I can vote J:100, K:99, L:0. There is only a very small temptation to vote J: 100, K:100, L:0. This temptation can be reduced even further by allowing decimal ratings, e.g. J:100, K:99.99, L:0. It can be mostly eliminated by allowing voters to use an [[approval threshold]] to indicate their cardinal support.
==Approval-weighted pairwise==
"'''Approval weighted pairwise'''", "'''AWP'''", or "'''approval pairwise'''" is the special case of cardinal pairwise in which the only available ratings are 0 and 1. AWP can use a ranked ballot with an approval cutoff.
== Example ==
▲'''For each voter who ranks A over B, and only for these voters, subtract B’s rating from A’s rating, to get the rating differential. Sum these rating differentials to get the defeat strength.'''
10 A:10 B:2
9 B:10 A:0
▲The name "cardinal pairwise" also implies that a Smith-efficient, defeat-dropping base method will be used, for example [[beatpath]], [[ranked pairs]], or [[river]].
A [[Pairwise beat]]<nowiki/>s B 10 voters to 9, and has a rating differential of 80 points (equivalent to 8 votes on a scale of 0 to 10) against B.
==
<references/>
[[Category:Single-winner voting methods]]
[[Category:Condorcet methods]]
[[Category:Cardinal voting methods]]
[[Category:Condorcet-cardinal hybrid methods]]
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