Dominant mutual third set: Difference between revisions
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The '''dominant mutual third set''' (DMT set) is a set of candidates such that every candidate within the set [[Pairwise beat|pairwise-beats]] every candidate outside the set, and more than one-third of the voters prefer the members of the set to every non-member of the set i.e. it is a [[solid coalition]].
It was first defined by James Green-Armytage as a more particular version of the mutual majority set.<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-June/078580.html|title=IRV vs. approval: dominant mutual third|website=Election-methods mailing list archives|date=2004-06-06|author=James Green-Armytage}}</ref>
One implication is that when all but one candidate in the DMT set is eliminated, the remaining candidate will be a [[Condorcet winner]] and have over 1/3rd of all 1st choice votes. This is notable in the context of [[IRV]] because any candidate who has over 1/3rd of the active votes in any round of [[IRV]] is guaranteed to be one of the final two remaining candidates if
[[Instant-runoff voting]] always elects a winner from the smallest dominant mutual third set, just like it does from the smallest mutual majority set. Chris Benham later determined that [[Instant-runoff voting|IRV]] and Smith,IRV also meet '''dominant mutual third burial resistance''' (DMTBR):<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-November/121408.html|title=Re: Why I Prefer IRV to Condorcet|website=Election-methods mailing list archives|date=2008-11-25|author=Chris Benham}}</ref> raising a candidate not in the smallest dominant mutual third set cannot make that candidate the IRV winner.
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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