ER-Bucklin: Difference between revisions
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ER-Bucklin is an old name for [[Majority Choice Approval]] (MCA). Please see that article, which mostly supersedes the following. |
''ER-Bucklin is an old name for [[Majority Choice Approval]] (MCA). Please see that article, which mostly supersedes the following.'' |
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== Definition == |
== Definition == |
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It is a rated version of [[Bucklin voting]] that allows voters to give equal rankings to some candidates. There are at least two main versions of ER-Bucklin; these are '''ER-Bucklin(whole)''' and '''ER-Bucklin(fractional)'''. |
It is a rated version of [[Bucklin voting]] that allows voters to give equal rankings to some candidates. There are at least two main versions of ER-Bucklin; these are '''ER-Bucklin (whole)''' and '''ER-Bucklin (fractional)'''. |
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''If a ballot lists n candidates as tied in kth place, count that ballot as a whole point for all n candidates beginning in the kth round.'' |
''If a ballot lists n candidates as tied in kth place, count that ballot as a whole point for all n candidates beginning in the kth round.'' |
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Note: A candidate is ranked in kth place on a given ballot if there are k-1 candidates who are ranked strictly higher. For |
Note: A candidate is ranked in kth place on a given ballot if there are k-1 candidates who are ranked strictly higher. For example, a ballot marked A>B=C=D>E>F=G=H=I>J should be considered to rank A to in 1st place, B, C, and D in 2nd place, E in 5th place, F, G, H, and I in 6th place, and J in 10th place. Thus, the ballot would not count in favor of E until the 5th round, and it would not count in favor of J until the 10th round. |
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This rule is perhaps unique in that it satisfies both the "[[favorite betrayal]]" criterion and the [[Majority criterion for solid coalitions]]. |
This rule is perhaps unique in that it satisfies both the "[[favorite betrayal]]" criterion and the [[Majority criterion for solid coalitions]]. |
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== ER-Bucklin(fractional) == |
== ER-Bucklin (fractional) == |
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''If a ballot lists n candidates as tied in kth place, count that ballot as 1/n point for all n candidates in the kth round, adding another 1/n point in each subsequent round until the ballot has contributed 1 point to all n candidates.'' |
''If a ballot lists n candidates as tied in kth place, count that ballot as 1/n point for all n candidates in the kth round, adding another 1/n point in each subsequent round until the ballot has contributed 1 point to all n candidates.'' |
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== Example == |
== Example == |
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:::''or'': |
:::''or'': |
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{| border=1 |
{| class="wikitable" border="1" |
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!# |
!# |
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!1st |
!1st |
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|} |
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=== ER-Bucklin(whole) tally === |
=== ER-Bucklin(whole) tally === |
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{| border=1 |
{| class="wikitable" border="1" |
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!candidate |
!candidate |
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!round 1 |
!round 1 |
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|30 |
|30 |
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|} |
|} |
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There is a tie between B1 and B2. |
There is a tie between B1 and B2. |
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=== ER-Bucklin(fractional) tally === |
=== ER-Bucklin(fractional) tally === |
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{| border=1 |
{| class="wikitable" border="1" |
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!candidate |
!candidate |
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!round 1 |
!round 1 |
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A wins. |
A wins. |
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'' |
''Work in progress'' |
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== See also == |
== See also == |
Revision as of 20:36, 8 August 2019
ER-Bucklin is an old name for Majority Choice Approval (MCA). Please see that article, which mostly supersedes the following.
Definition
It is a rated version of Bucklin voting that allows voters to give equal rankings to some candidates. There are at least two main versions of ER-Bucklin; these are ER-Bucklin (whole) and ER-Bucklin (fractional).
ER-Bucklin (whole)
If a ballot lists n candidates as tied in kth place, count that ballot as a whole point for all n candidates beginning in the kth round.
Note: A candidate is ranked in kth place on a given ballot if there are k-1 candidates who are ranked strictly higher. For example, a ballot marked A>B=C=D>E>F=G=H=I>J should be considered to rank A to in 1st place, B, C, and D in 2nd place, E in 5th place, F, G, H, and I in 6th place, and J in 10th place. Thus, the ballot would not count in favor of E until the 5th round, and it would not count in favor of J until the 10th round.
This rule is perhaps unique in that it satisfies both the "favorite betrayal" criterion and the Majority criterion for solid coalitions.
ER-Bucklin (fractional)
If a ballot lists n candidates as tied in kth place, count that ballot as 1/n point for all n candidates in the kth round, adding another 1/n point in each subsequent round until the ballot has contributed 1 point to all n candidates.
Example
- 36 voters: A>B1=B2>C
- 34 voters: B1=B2>C>A
- 30 voters: C>A>B1=B2
- or:
# | 1st | 2nd | 3rd | 4th |
---|---|---|---|---|
36 | A | B1&B2 | C | |
34 | B1&B2 | C | A | |
30 | C | A | B1&B2 |
ER-Bucklin(whole) tally
candidate | round 1 | round 2 |
---|---|---|
A | 36 | 66 |
B1 | 34 | 70 |
B2 | 34 | 70 |
C | 30 | 30 |
There is a tie between B1 and B2.
ER-Bucklin(fractional) tally
candidate | round 1 | round 2 |
---|---|---|
A | 36 | 66 |
B1 | 17 | 52 |
B2 | 17 | 52 |
C | 30 | 30 |
A wins.
Work in progress