Sequentially Spent Score

Sequentially Spent Score (SSS), also known as Sequentially Subtracted Score or Unitary Cardinal Voting, is sequential Multi-Winner Cardinal voting 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

Procedure

It works by a four-step process: Each voter starts with a ballot weight equal to the MAX possible score.

1. Elect the candidate who is the Utilitarian winner (ie the candidate with the highest sum of score)
2. Weaken the weight of the ballots that had supported that candidate in proportion to how strongly they supported that candidate, and
3. Adjust the amount of support each ballot gives to the remaining candidates by capping it at the reduced score
4. Repeat these steps until all the necessary seats are filled.

Surplus Handling

For the second step, if that candidate had received a surplus 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 supporting the winner. This is known as Factional Surplus Handling.

Variants

Scaling

A variant of this method can be made by scaling instead of capping to adjust ballot support for 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 (a score of 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.

Quota of Ballot Selection

In the first step one need not choose the Utilitarian winner. A reasonable alternative is the take the winner as the candidate who has the highest sum of score in the top Hare (or Droop ) quota of Ballots.

Related Systems

It is the natural extension of the Hamilton method which is used in Partisan Systems to Multi-Member System.