Benham's method: Difference between revisions
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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//2014-April/097948.html|title= |
'''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=Benham's method looks best, among the Smith + CD methods|last=Ossipoff|first=Michael|date=2014-04-28|website=Election-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. |
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Between two candidates X and Y, X pairwise beats Y if more ballots rank X over Y than rank Y over X. |
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: |
Example: |
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{{ballots| |
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34: A>B>C |
34: A>B>C |
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32: B>A |
32: B>A |
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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. |
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. |