Dominant mutual third set: Difference between revisions
m
Add reddit thread explaining DMTBR immunity to DH3, for further information
(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...)) |
m (Add reddit thread explaining DMTBR immunity to DH3, for further information) |
||
| (2 intermediate revisions by the same user not shown) | |||
Line 6:
=== Complying methods ===
[[Instant-runoff voting]] elects from the DMT set. Since the Smith set is a subset of the smallest DMT set, all [[Smith-efficient]] [[Condorcet methods]] are DMT-efficient as well. Every method that passes the [[Condorcet criterion]] passes the DMT candidate criterion, as do the partial generalizations of [[fpA-fpC]].
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>▼
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.
=== Burial resistance ===
The DMT and DMT candidate criteria have been discussed on the election-methods list in context of burial resistance. Chris Benham defined a weak burial resistance criterion,<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> which is the three-candidate case of the more general
'''Dominant mutual third candidate burial resistance''' or '''DMTCBR''' criteron: voters who prefer some candidate X to the current winner W can't get X elected by burying W if W is the sole member of the DMT set.
By analogy to the DMT criterion, one may also define:
'''Dominant mutual third burial resistance''' or '''DMTBR''': voters who prefer some candidate X to the current winner W can't get X elected by lowering W below candidates who are not in the DMT set.
Even though Condorcet methods can't be completely invulnerable to burial (since the [[Condorcet criterion]] is incompatible with [[later-no-help]] and [[later-no-harm]]), some Condorcet methods pass the burial resistance criteria above.
▲[[Instant-runoff voting]] passes the DMTBR criterion because it passes the DMT criterion and is completely immune to burial. Chris Benham later determined that Smith,IRV
It can be proven that several [[:Category:Condorcet-IRV hybrid methods|Condorcet-IRV hybrid methods]] pass the full dominant mutual third burial resistance criterion. 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.
Even if a method M passes DMTBR, Condorcet composite versions (e.g. [[Smith set|Smith]],M or [[Uncovered set|Landau]]//M) may still fail. However, they automatically pass DMTCBR.<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2022-March/003707.html|title=Re: Condorcet-composite method DMTBR disproof|date=2022-03-25|last=Munsterhjelm|first=Kristofer|website=Election-methods mailing list archives}}</ref>
When [[Runoff voting]] passes the DMT candidate criterion, it also passes DMT candidate burial resistance because the selection of finalists is based only on first preferences, which are not affected by burial.
▲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.
The partial generalizations of [[fpA-fpC]] pass the DMTC and DMTC burial resistance criteria, and are also monotone (unlike [[instant-runoff voting]]). However, no method has yet been found to pass full DMT, DMT burial resistance, and monotonicity.
== Implications ==
Line 29 ⟶ 46:
As with any other set criterion, an elimination method that passes the DMT criterion can be halted once there's only one uneliminated candidate left in the set: that candidate must be the winner. Whether doing so is faster than running the elimination method to completion depends on the complexity of the method in question.
== See also ==
[https://www.reddit.com/r/EndFPTP/comments/o9o93w/comment/h3dw743/ Explanation of DMTBR providing immunity to Dark horse plus 3 rivals]
== References ==
| |||