I’ve implemented my own versions of Bucklin PR / EAR, and there are various alternatives one can consider.

When implemented as Bucklin, it is a ranked method. However, Bucklin with equal rating allowed and gaps in ranking allowed can also be viewed as a median rating method.

If you use ratings instead of rankings, equal rating allowed, then the candidate who wins each seat is chosen from among those with the highest number of ballots at or above the current approval threshold. As in EAR/Bucklin the threshold starts at the highest rating, then is sequentially lowered until at least one candidate’s totals (upward) exceed the quota.

With a Bucklin-style scheme, the tie-breaker is simply the at-and-above-threshold total number of weighted ballots. This reduces to ER-Bucklin-ratings in the limiting case of single winner (with Droop quota).

But there are alternatives, among which are a Majority Judgment style in which the pairs (rating, total-at-and-above that rating) are sorted in order of increasing distance from the quota. This reduces to MJ in the single winner case.

Another alternative would be to use the average score in just the top two quota blocks. In other words, if S[r,c] is the number of ballots giving candidate c a cardinal rating of r, then let T[r,c] be the sum of S[r,c] from score r up to the maximum rating, and let W[r,c] be the sum of r * S[r,c] from rating r up to the maximum rating. Then, for candidate c find r2q such that T[r2q,c] > 2 * quota. And the two-quota score average is then (T[r2q+1,c] + (T[r2q,c] - 2*quota) * r2q) / (2 * quota). The qualifying candidate with the highest two-quota average score is the winner.

In this last case, the method reduces to median-rating // Score in the single winner case, using a Droop quota of Nvotes/(Nseats + 1). That is, the score winner tie-breaker among those candidates with highest median rating.