Dominant mutual third set: Difference between revisions
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It can be proven that several other [[:Category:Condorcet-IRV hybrid methods|Condorcet-IRV hybrid methods]] pass dominant mutual third burial resistance. For example, with [[Benham's method]], since at least one member of the smallest DMT set is guaranteed to be one of the two final remaining candidates after eliminating the rest, there is no incentive for a voter who honestly prefers that DMT member over the other final remaining candidate to not vote that preference i.e. the same incentive for honest voting exists as if it was a [[runoff]]. This is one major reason cited by those who prefer Condorcet-IRV methods, as they claim that most elections feature a DMT set (i.e. perhaps because the voters are polarized into two sides, and with one side being majority-preferred to the other), and therefore these methods will be more [[Strategic voting|strategically resistant]] in practice than many others. |
It can be proven that several other [[:Category:Condorcet-IRV hybrid methods|Condorcet-IRV hybrid methods]] pass dominant mutual third burial resistance. For example, with [[Benham's method]], since at least one member of the smallest DMT set is guaranteed to be one of the two final remaining candidates after eliminating the rest, there is no incentive for a voter who honestly prefers that DMT member over the other final remaining candidate to not vote that preference i.e. the same incentive for honest voting exists as if it was a [[runoff]]. This is one major reason cited by those who prefer Condorcet-IRV methods, as they claim that most elections feature a DMT set (i.e. perhaps because the voters are polarized into two sides, and with one side being majority-preferred to the other), and therefore these methods will be more [[Strategic voting|strategically resistant]] in practice than many others. |
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Any voting method that is "DMT-efficient" will be [[Smith-efficient]] when the [[Smith set]] is a subset of the DMT set. All [[Smith-efficient]] [[Condorcet methods]] are DMT-efficient. |
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== Notes == |
== Notes == |
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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). |
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). |
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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: |
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: |
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33 A>B>C |
33 A>B>C |
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