Dominant mutual third set: Difference between revisions
Try to rewrite the compliance section to show that Benham showed DMTCBR, not full DMTBR. (I'm not completely satisfied with the phrasing, but it'll have to do for now...)
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(Try to rewrite the compliance section to show that Benham showed DMTCBR, not full DMTBR. (I'm not completely satisfied with the phrasing, but it'll have to do for now...)) |
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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=Green-Armytage, James}}</ref>
The '''DMT criterion''' or property is that a voting method must always elect a candidate in the DMT set. A related criterion, the '''DMT candidate criterion''' is that the method must do so when the set consists of a single candidate.
=== 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 Smith,IRV also meets DMTCBR.<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-April/081042.html|title='Weak Burial Resistance' criterion|website=Election-methods mailing list archives|date=2005-04-21|author=Benham, Chris}}</ref><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.▼
▲It can be proven that several
Since the Smith set is a subset of the smallest DMT set, all [[Smith-efficient]] [[Condorcet methods]] are DMT-efficient. Smith does not necessarily imply dominant mutual third burial resistance, however; for instance, [[Schulze]] fails DMTBR.
Even if a method M passes DMTBR, Condorcet composite versions (e.g. Smith,M) may still fail. However, they automatically pass
If there is a single candidate in the DMT set (i.e. a Condorcet winner with at least a third of the first preferences), and no voters change their votes between the first and second round, then [[Runoff voting]] elects that candidate. [[Runoff voting]] thus passes DMTCBR, but it does not pass the DMT criterion in full generality.
== Implications ==
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