User:Marylander/Sequentially Represented Groups

Sequentially Represented Groups is a sequential multiwinner Cardinal voting system that uses score ballots.

Selection
Each round, elect the candidate that can reach one Hare quota of points on the fewest ballots, counted by weight. Note that the best order in which to add ballots will always be by adding ballots that give the candidate a higher score first. So first all the scores of 5 are added, then 4, etc. (If adding all ballots that give the candidate the same score would cause the quota to be exceeded, then an equal portion of each ballot giving the candidate that score is counted as contributing to the quota.)

Reweighting
A total of one Hare quota is removed from the ballots. Each ballot pays weight in proportion to the score it contributed.

Steps for when no one meets quota
One procedure for when no one meets quota is to elect the candidate that is closest to meeting quota, then charge each ballot enough that a full quota is met. Some ballots will be charged more than they can pay. Then the unpaid cost goes to the ballots scoring the elected candidate the highest.