Equally Weighted Vote: Difference between revisions
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=== Voting methods which ensure an Equally Weighted Vote ===
Voting Methods which ensure an Equally Weighted Vote with any number of candidates include Approval Voting, Score Voting, STAR Voting, as well as a number of others. In general Cardinal Voting methods ensure an Equally Weighted Vote for each voter. Many Condorcet methods (most that can be calculated only with the [[Pairwise counting|pairwise counting]] matrix, most Condorcet-cardinal hybrids, etc.) also pass the criterion.
Choose One Plurality Voting only satisfies the Equal Vote Criterion in elections with two candidates only. Instant Runoff Voting (often referred to as Ranked Choice Voting) does not satisfy and the Equal Vote Criterion.
== Notes ==
Some voting methods which pass the Equal Vote Criterion (which has also been called "Frohnmayer balance" in reference to its creator) don't pass a generalized form which refers to more than two voters being able to cancel each other out.
STAR may or may not pass the generalized criterion depending on how it is defined. Example:<blockquote>Example modeled off of <nowiki>https://rangevoting.org/TobyCondParadox.html</nowiki>:
3 A:5>B:4>C:0
2 B:5>A:4>C:0
2 B:5>C:4>A:0
2 C:5>A:4>B:0
Scores are A 31, B 32, C 18, with A pairwise beating B and thus being the STAR winner. Removing 6 votes that constitute a cycle and a kind of pairwise tie and a definite scored tie for A, B, and C (2 A:5>B:4>C:0, 2 B:5>C:4>A:0, 2 C:5>A:4>B:0 votes, which give a total of 9 points to A, B, and C, and create a [[Condorcet cycle]] between the three where A>B, B>C, and C>A are all matchups of 4 to 2) yields:
1 A>B>C
2 B>A>C
Without even looking at the scores, B must win here, since A and B are unanimously preferred as the top 2 candidates and a majority prefers B>A. <ref>https://www.reddit.com/r/EndFPTP/comments/f51ww6/the_meaning_of_one_person_one_vote/fhwk752/</ref></blockquote>If it is considered a kind of "pairwise tie" for there to be a Condorcet cycle between the three candidates where each candidate's pairwise matchups are either 4 to 2 or 2 to 4, then STAR fails. But if one requires the pairwise tie to be an exact pairwise tie between all candidates, then this example doesn't show a failure for STAR.
The passing or failure of Condorcet methods of this generalization is also similarly dependent on how a pairwise tie is interpreted (shown in https://rangevoting.org/TobyCondParadox.html).
Approval voting and Score voting pass the generalized form of the criterion, since removing any number of votes that constitute a scored tie for all candidates won't change the difference in scores between any candidates, thus since the winner must have originally had more approvals/points than all other candidates, they will still have more and thus still win.
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