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Benham's method: Difference between revisions

Add possibly earliest EM post describing Benham's method
m (Remove note about the inventor of Benham as that's now explained in the first paragraph)
(Add possibly earliest EM post describing Benham's method)
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'''Benham's method''' is a variation of [[instant-runoff voting]] invented by Chris Benham.<ref>{{Cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2006-October/116721.html|title=Condorcet + IRV completion? |last=Benham|first=Chris|date=2006-10-16|website=Election-methods mailing list|url-status=live|access-date=2022-03-28}}</ref><ref>{{Cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2014-April/097948.html|title=[EM] Benham's method looks best, among the Smith + CD methods|last=Ossipoff|first=Michael|date=Mon Apr 28 22:42:39 PDT 2014-04-28|website=electionElection-methods mailing list|url-status=live|access-date=2022-01-11}}</ref> The method calls for tabulating the first-choice of all voters on all ballots (as done with instant-runoff), but before each elimination check if there is an un-eliminated candidate who [[pairwise counting#Terminology|pairwise beats]] all other un-eliminated candidates, and elect them if they exist.
 
Between two candidates X and Y, X pairwise beats Y if more ballots rank X over Y than rank Y over X.
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Example:
 
{{ballots|
34: A>B>C
 
32: B>A
34: C>B>A }}
 
34: C>B>A
 
Regular IRV eliminates B and elects A here, whereas Benham elects B for being the Condorcet winner ([[Pairwise beat|pairwise beats]] A and C 66 to 34 each). This is an example of an averted [[Center squeeze effect|center squeeze]] instance. Note that had B had a few more 1st choices, they would've had over 1/3rd of all 1st choice votes, and thus been guaranteed to win in IRV as well.
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