Benham's method: Difference between revisions

Benham's method is a [[Generalized Condorcet criterion|Smith-efficient]] [[Condorcet method]]. This is because there will always be a point in the count where at least one [[Smith set]] member is uneliminated, and that candidate must beat all other candidates by virtue of being in the Smith Set. (It is also possible that once some members of the Smith set are eliminated, one of the multiple remaining members wins by virtue of beating every remaining candidate, including those in the Smith set. In fact, any voting method that operates by eliminating one at a time until there is a Condorcet winner is Smith-efficient.) Benham's method passes mono-add-plump, unlike several Condorcet-IRV hybrids. It fails [[ISDA]], however.<ref>{{Cite web|url=http://www.votingmatters.org.uk/ISSUE29/I29P1.pdf|title=Four Condorcet-Hare Hybrid Methods for Single-Winner Elections|date=|access-date=|website=|last=Green-Armytage|first=James|archive-url=|archive-date=|url-status=live}}</ref>

Benham's method can be thought of as a [[Tideman's Alternative methods|Tideman alternative method]] that uses the Condorcet winner as its "set". Benham's method can also be thought of as an advanced version of IRV which interprets "majority" to mean "candidate who can win a majority [[Pairwise counting|pairwise]] against all other uneliminated candidates" rather than "majority's 1st choice among all uneliminated candidates". Because the latter is always equivalent to the former (a candidate who is a majority's 1st choice is always a Condorcet winner), Benham's method will never require more rounds of counting (eliminations, ignoring the discovery of the [[Pairwise counting|pairwise counting]] table) than plain IRV, and will often require none (when there is a Condorcet winner).