Sequentially Spent Score: Difference between revisions

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'''Sequentially Spent Score''' ('''SSS''')~~, also known as Sequentially Subtracted Score or Unitary Cardinal Voting,~~ is a sequential [[Multi-Member System|Multi-Winner]] [[Cardinal voting systems|Cardinal voting system]] ~~built~~ on [[Score voting]] ballots. Each round's winner is the candidate who has the highest sum of score. ~~Between~~ ~~each round~~ 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]]~~. Sequentially Spent Score was invented by [[Keith Edmonds]] and [[Vote Unitarity]] was defined to describe this underlying theory~~.

'''Sequentially Spent Score''' ('''SSS''') is a sequential [[Multi-Member System|Multi-Winner]] [[Cardinal voting systems|Cardinal voting system]]. Voters score candidates, generally from 0-5, using [[Score voting]] ballots. Each round's winner is the candidate who has the highest sum total score. When tabulating the ballots, each voter begins with 5 stars to spend in order to gain representation and voters spend those stars when a candidate they supported is elected. If a voter scored a candidate 3 stars, that voter could only spend up to three stars to help elect that candidate.-- Voters cannot influence subsequent rounds more than the stars they have remaining. This property of spending stars is a particular implementation of [[Vote Unitarity]].

== Background ==

Sequentially Spent Score was invented by [[Keith Edmonds]] and is also known as Sequentially Subtracted Score or Unitary Cardinal Voting. The concept of [[Vote Unitarity]] was defined to describe this underlying theory.

==Procedure==

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

Each voter starts with 5 stars, (the max possible score which can be given to any candidate.) Depending on the number of seats up for election, each seat also has a set max cost.

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It works by a four-step process:

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

* Max cost to win a seat = (number of voters) x 5 / number of seats up for election

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# Elect the candidate ~~who is~~ the ~~[[Utilitarian~~ ~~winner]]~~

#:*ie the candidate with the highest sum of score)

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'''Sequentially Spent Score works by a four-step process:'''

# 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)

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# Elect the candidate with the highest total sum of score.

# 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.

# Each voter spends the amount of stars they gave the elected candidate. Voters may get some "change" back if the candidate received more support than needed.

#:*ie (new score) = min(score,remaining points)

#* If a voter had given the winner 3 stars they would spend all 3 stars. If a voter had given the winner 1 star they only spend 1.

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

#* If the set of voters supporting the highest scoring candidate collectively put up more than the max cost to elect a candidate, some "change" (surplus handling) is returned to those voters.

# For ballots which spent stars to elect a candidate, the amount of stars available for remaining candidates is then capped at the number of stars that voter has left, (max possible score remaining). Recalculate the sum total for each candidate using the capped ballot scores.

#* Max possible score remaining = 5 - (stars given to winner) + change

#* Capped ballot scores = 5 - score spent in preceding rounds, or, the original score given, whichever is higher.

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# Repeat until all the necessary seats are filled.

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