Sequentially Spent Score: Difference between revisions

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[[File:SSS procedure (AT diagram).jpg|thumb|SSS procedure]]

It works by a four-step process:

Each voter starts with a ballot ~~weight~~ equal to the MAX possible score.

Each voter starts with a ballot a number of score points equal to the MAX possible score.

# Elect the candidate who is the [[Utilitarian winner]] (ie the candidate with the highest sum of score)

# Lower the ~~weight~~ of ~~the~~ ~~ballots~~ that had supported that candidate ~~in proportion to~~ how strongly they supported that candidate. ie (~~new~~ ~~weight~~) = (~~weight~~) - (score given to winner) (with surplus handling; see below)

# Lower the "remaining score points" for each voter that had supported that candidate by how strongly they supported that candidate. ie (remaining points) = (points) - (score given to winner) (with surplus handling; see below)

# For ~~ballots~~ that ~~lost~~ ~~weight~~ in the previous step, adjust the amount of score ~~they give~~ to the remaining candidates by '''capping''' it at the ~~reduced~~ ~~ballot~~ ~~weight~~. ie (new score) = min(score,weight)

# For voters that spent points in the previous step, adjust the amount of score given to the remaining candidates on the ballot by '''capping''' it at the remaining number of score points. ie (new score) = min(score,weight)

# Repeat these steps until all the necessary seats are filled.

===[[Surplus Handling]]===

For the second step, if that candidate had received more than a predefined threshold of points (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 that round's winner is to be reduced proportionally to ensure that only the equivalent in ballot weight of that predefined threshold of points is removed. This is known as [[Factional Surplus Handling]].

For the second step, if that candidate had received more than a predefined threshold of points (usually defined as a Hare or Droop [[Quota]] of the ballots multiplied by the maximum score), then the amount of score points to take away from the ballots supporting that round's winner is to be reduced proportionally to ensure that only the equivalent in ballot weight of that predefined threshold of points is removed. This is known as [[Factional Surplus Handling]].

Specifically, in the second step, the score given to the winner is divided by (the total score given to that winner) * (Total number of Winners)/ (Total number of voters). This is a number greater than 1 and hence reduces the amount spent on that winner.

Specifically, in the second step, the score given to the winner is divided by (the total score given to that winner) * (Total number of Winners)/ (Total number of voters). This is a number greater than 1 and hence reduces the amount spent on that winner by each voter.

==Python Implementation==