Dominant mutual third set: Difference between revisions
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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> |
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> |
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The '''DMT criterion''' or property is that a voting method must always elect a candidate in the DMT set. |
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. |
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=== Complying methods === |
=== Complying methods === |
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[[Instant-runoff voting]] always elects a winner from the smallest dominant mutual third set, just like it does from the smallest [[mutual majority]] set. |
[[Instant-runoff voting]] always elects a winner from the smallest dominant mutual third set, just like it does from the smallest [[mutual majority]] set. By passing both [[later-no-help]] and [[later-no-harm]], IRV is completely immune to [[burial]] and thus meets the '''dominant mutual third burial resistance''' (DMTBR) criterion: 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 thus also passes this criterion limited to a single candidate, '''dominant mutual third candidate burial resistance''' (DMTCBR). |
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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> |
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⚫ | It can be proven that several |
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⚫ | 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. |
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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. |
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. |
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Even if a method M passes DMTBR, Condorcet composite versions (e.g. Smith,M) may still fail. However, they automatically pass |
Even if a method M passes DMTBR, Condorcet composite versions (e.g. Smith,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> |
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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]] does not pass the DMT criterion in full generality. |
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. |
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== Implications == |
== Implications == |