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