Cardinal-weighted pairwise comparison

Cardinal-weighted pairwise

"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 (rating) information in addition to ordinal (ranking) 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.

Approval-weighted pairwise

"Approval weighted pairwise", or "AWP", 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.

External resources

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