Cardinal-weighted pairwise comparison: Difference between revisions

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"Cardinal pairwise" and "CWP" are shorter names for "cardinal-weighted pairwise comparison", a method first proposed by James Green-Armytage in June of 2004.

Cardinal pairwise differs from traditional pairwise count methods (Condorcet methods) in that it uses cardinal (ratings) information in addition to ordinal information.

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 definition of defeat strength. If A pairwise defeats B, the strength of the defeat is defined as follows:

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.

The name "cardinal pairwise" also implies that a Smith-efficient, defeat-dropping base method will be used, for example beatpath, ranked pairs, or river.

External resources

Cardinal pairwise paper in html or pdf. (The latter as published by Voting Matters.)
Initial proposal on election methods list.

@@ Line 5: / Line 5: @@
 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 definition of defeat strength.
+Thus in essence, CWP can be thought of as a definition of defeat strength. If A pairwise defeats B, the strength of the defeat is defined as follows:
+'''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.'''
-If A pairwise defeats B, the strength of the defeat is defined as follows:
-'''For each voter who ranks A over B, and only for those voters, subtract B’s rating from A’s rating, to get the rating differential. Sum these rating differentials to get the defeat strength.'''
 The name "cardinal pairwise" also implies that a Smith-efficient, defeat-dropping base method will be used, for example [[beatpath]], [[ranked pairs]], or [[river]].