Benham's method: Difference between revisions
Added clone independent category and explanation, rephrased strategy susceptibility paragraph
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'''Benham's method''' is a variation of [[instant-runoff voting]] independently invented by Chris Benham, David Hill, and Robert Loring.<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><ref>{{cite web | title=Loring One Winner Rule | website=Accurate Democracy Voting Rules | last=Loring | first=Robert | date=2000-08-16 | url=https://www.accuratedemocracy.com/l_lor1.htm#LOR | access-date=2022-04-23}}</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.
▲Between two candidates X and Y, X pairwise beats Y if more ballots rank X over Y than rank Y over X.}}
An alternative way of describing it is: "Elect the [[Condorcet winner]] (if there is one), otherwise eliminate the candidate ranked the highest by the fewest voters, and repeat". This can be further rephrased to also work as a variant of STV, in the following way: "Eliminate the candidate ranked the highest by the fewest voters unless that candidate is the [[Condorcet winner]], in which case eliminate the candidate ranked highest by the second fewest voters".
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Example:
{{ballots|
34: A>B>C
32: 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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Because Benham's method is just IRV with the possibility of ending in an earlier round, it is possible to figure out who the Benham winner would be if given the full results of an IRV election (the round-by-round breakdown) and the pairwise comparison table for that election.
Like other
Benham is cloneproof for the same reason that IRV is: suppose the winner is X and is cloned. Then these clones can't have higher first preference counts than X itself, and so all appear after X. When all of these clones but one has been eliminated, then X still wins. The introduction of clones may lead to Benham needing more rounds to determine the winner, however.
== References ==
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[[Category:Smith-efficient Condorcet methods]]
[[Category:Condorcet-IRV hybrid methods]]
[[Category:Clone-independent electoral systems]]
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