Dominant mutual third set: Difference between revisions

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In many voting methods that pass DMT, if there are two DMT-like sets (i.e. over 1/3rd of voters [[solidly support]] Democrats and over 1/3rd for Republicans, with the Democrat solid coalition being pairwise-dominant), then one of the candidates in each set will be the winner and runner-up (i.e. a Democrat will win and a Republican will be the runner-up).

Note that DMT can be used to simplify or shorten the explanation of how some voting methods compute their result. For example, in IRV, the usual approach to show a result is to repeatedly eliminate candidates until one has a majority. However, a DMT-based way is to show whether the candidate with the most votes in a round has over 1/3rd of 1st choices and pairwise beats all other uneliminated candidates, and if not, only then eliminate candidate(s). This never requires more rounds of counting (ignoring the discovery of the [[pairwise comparison matrix]]), because a candidate with a majority of votes has both over 1/3rd of the votes and is guaranteed to pairwise beat all other uneliminated candidates (except possibly if [[Equal-ranking methods in IRV|equal-ranking]] is allowed).

Note that DMT can be used to simplify or shorten the explanation of how some voting methods compute their result; specifically, for Dr-compliant voting methods that use eliminations, the election after each elimination can yield a DMT set i.e. after eliminating some candidate, suddenly some set of candidates becomes [[Solidly support|solidly suppor]]<nowiki/>ted by over 1/3rd of the voters in relation to other uneliminated candidates. For example, in IRV, the usual approach to show a result is to repeatedly eliminate candidates until one has a majority. However, a DMT-based way is to show whether the candidate with the most votes in a round has over 1/3rd of 1st choices and pairwise beats all other uneliminated candidates, and if not, only then eliminate candidate(s). This never requires more rounds of counting (ignoring the discovery of the [[pairwise comparison matrix]]), because a candidate with a majority of votes has both over 1/3rd of the votes and is guaranteed to pairwise beat all other uneliminated candidates (except possibly if [[Equal-ranking methods in IRV|equal-ranking]] is allowed). Example:

33 A>B>C

35 B

32 C>B

No candidate has a majority of votes, so under the usual IRV depiction, C would be eliminated, and then B would have a majority. But because B is the only candidate in the DMT set, the DMT-based approach can terminate without eliminating anyone, and automatically identify B as the winner.

== References ==