Sequentially Subtracted Score

Sequentially Subtracted Score (SSS), also known as Sequentially Spent Score or Unitary Cardinal Voting, is a sequential semi-proportional method that can be used with Approval or Score ballots. It works by a four-step process: elect the candidate with the most support (points or votes), then weaken the weight of the ballots that had scored that candidate in proportion to how highly they scored that candidate, and use either capping or scaling (more information on this in the next paragraph) to adjust the amount of support each ballot gives to the remaining candidates, and then repeat these teps until all the necessary seats are filled. For the second step, if that candidate had received more than a certain amount of support (usually defined as a Hare or Droop Quota of the ballots multiplied by the maximum score), then the amount of weight to take away from the ballots supporting the winner is to be reduced proportionally to ensure that only the equivalent in ballot weight of that certain amount of support is removed from all ballots scoring the winner.

The third step of SSS varies depending on whether capping or scaling are used for adjusting ballot support for various candidates after the ballot's weight has been adjusted. Capping is when, if a ballot's weight has been reduced by a certain amount, a ballot that gives a candidate more support than its weight allows is edited to give that candidate only as much support as its ballot weight. In other words, if a ballot is at 70% weight (70% power), yet it gives a candidate 80% support (an 8 out of 10, for example), it is adjusted to give that candidate 70% support instead.

Scaling is when the amount of support a ballot gives a candidate is proportionally adjusted by how much weight it has remaining. In other words, a ballot with 50% weight that originally gave a candidate 70% support when it had full weight will now give that candidate 35% support.

Sequentially Subtracted Score is sequential Multi-Member System built on Score voting ballots. Each winner is that candidate who has the highest sum of score. Between each election rounds the ballots are adjusted such that a candidate cannot influence subsequent rounds more than the score they have remaining. This property of spending score is a particular implementation of Vote Unitarity