Dominant mutual third set: Difference between revisions
Rephrase DMTBR as the previous definition was wrong, and fix the immunity to DH3 argument.
(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 ===
[[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>
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.
Dominant mutual third burial resistance grants immunity to
== Notes ==
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