Dominant mutual third set: Difference between revisions
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(Add note that Smith-DMTBR methods are not necessarily DMTBR themselves.) |
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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.
Even if a method M passes DMTBR, Condorcet composite methods (e.g. Smith,M) may still fail it. However, they automatically pass when the DMT set consists of a single candidate.<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>
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.
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