Pairwise counting: Difference between revisions

== Cardinal methods ==

[[File:Pairwise relations Score.png|thumb|Pairwise matchups done using Score voting to indicate strength of preference in each matchup.]]

Cardinal methods can be counted using pairwise counting, by looking at the difference in scores between each candidate. The Smith set is then always full of candidates who are at least weak Condorcet winners i.e. tied for having the most points/approvals. Note that this is not the case if voters are allowed to have preferences that wouldn't be writeable on a cardinal ballot i.e. if the max score is 5, and a voter indicates their 1st choice is 5 points better than their 2nd choice, and that their 2nd choice is 5 points better than their 3rd choice, then this would not be an allowed preference in cardinal methods, and thus it would be possible for a Condorcet cycle to occur. Also, if a voter indicates their 1st choice is 2 points better than their 2nd choice, that this likely automatically implies their 1st choice must be at least 2 points better than their 3rd choice, etc. So there seems to be a transitivity of strength of preference, just as there is a transitivity of preference for rankings. <ref>https://www.reddit.com/r/EndFPTP/comments/fcexg4/score_but_for_every_pairwise_matchup/</ref>