ER-Bucklin

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

See also

Bucklin voting