Dominant mutual third set: Difference between revisions

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(Add implication about DMTBR protecting the method from the worst DH3 outcome.)
(Rephrase DMTBR as the previous definition was wrong, and fix the immunity to DH3 argument.)
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=== Complying methods ===
=== Complying methods ===
[[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=Benham, Chris}}</ref> raising a candidate not in the smallest dominant mutual third set cannot make that candidate the IRV winner.
[[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=Benham, Chris}}</ref> voters who prefer some candidate X to the current winner can't get X elected by burying the current winner under someone not in the smallest dominant mutual third set.


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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Reversal symmetry and Condorcet are incompatible with [[Dominant mutual third|dominant mutual third burial resistance]].<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2018-April/001760.html|title=Condorcet and Reversal Symmetry are incompatible with DMTBR|website=Election-methods mailing list archives|date=2018-04-03|first=Kristofer|last=Munsterhjelm}}</ref> Requiring reversal symmetry will thus weaken a Condorcet method's resistance to strategy, all other things equal.
Reversal symmetry and Condorcet are incompatible with [[Dominant mutual third|dominant mutual third burial resistance]].<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2018-April/001760.html|title=Condorcet and Reversal Symmetry are incompatible with DMTBR|website=Election-methods mailing list archives|date=2018-04-03|first=Kristofer|last=Munsterhjelm}}</ref> Requiring reversal symmetry will thus weaken a Condorcet method's resistance to strategy, all other things equal.


Dominant mutual third burial resistance grants immunity to the worst outcome of the [[Dark horse plus 3 rivals]] scenario. Since the smallest DMT set does not contain the dark horse, burial (raising the dark horse) can't make him win. However, the burial might still partially succeed - depending on the method, one of the burying factions might still get its preferred candidate elected by burying the competing candidates, if that faction's preferred candidate is part of the smallest DMT set.
Dominant mutual third burial resistance grants immunity to the [[Dark horse plus 3 rivals]] scenario, as long as the dark horse is not initially part of the innermost dominant mutual third set, as no faction preferring someone else to the current winner can benefit from burying the winner under the dark horse.


== Notes ==
== Notes ==
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