ER-Bucklin

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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 exampe, 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

See also

Bucklin voting