Benham's method: Difference between revisions
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'''Definition of Benham's method:''' |
'''Definition of Benham's method:''' |
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{{definition|Do IRV, but before each elimination check if there is an un-eliminated candidate who beats |
{{definition|Do [[IRV]], 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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the other un-eliminated candidates, and elect them if they exist. |
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X 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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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." When voters are allowed to equally rank candidates, Benham's method can either be implemented by equally splitting each voter's vote between each candidate they equally ranked highest, or giving each equally-highest-ranked candidate one vote. |
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| ⚫ | 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 |
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| ⚫ | 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. Benham's method fails [[ISDA]], however. <ref>http://www.votingmatters.org.uk/ISSUE29/I29P1.pdf</ref> |
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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 be thought of as a [[Tideman's Alternative methods|Tideman alternative method]] that uses the Condorcet winner as its "set". |
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Revision as of 19:14, 25 February 2020
Definition of Benham's method:
Do IRV, but before each elimination check if there is an un-eliminated candidate who 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.
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." When voters are allowed to equally rank candidates, Benham's method can either be implemented by equally splitting each voter's vote between each candidate they equally ranked highest, or giving each equally-highest-ranked candidate one vote.
Benham's method is a 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. Benham's method fails ISDA, however. [1]
Benham's method can be thought of as a Tideman alternative method that uses the Condorcet winner as its "set".
For more information, go to the Woodall's method article.