Allocated Score: Difference between revisions

Full rewrite for clarity from the 0-5 Star Proportional Research Committee, including Keith Edmonds, and Sara Wolk following the approval of this method as the Equal Vote Coalition's recommendation for Proportional STAR.
(→‎Procedure: changed "rounds" to "round's")
(Full rewrite for clarity from the 0-5 Star Proportional Research Committee, including Keith Edmonds, and Sara Wolk following the approval of this method as the Equal Vote Coalition's recommendation for Proportional STAR.)
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[[Allocated Score]] is a sequential [[Multi-Member System|Multi-Winner]] [[Cardinal voting systems|Cardinal voting system]] using [[Score Voting|5 star ballots]]. Its public branding is ''Proportional STAR'' (Score Then Automatic Runoffs.) This branding is intended to align with[[Single-member district | single-winner]] [[STAR voting]].
 
Allocation is the default method of removingdesignating voters as represented and then reweighting ballots in a sequential [[Multi-Member System]]. Winners are selected in multiple rounds. Each round selectselects the candidate with the highest total score. After each selection, the Hare quota of ballots which scored thatthe candidatewinner the highest is allocated to this candidatethem, and as such those ballots are removed from subsequent rounds. Ballots on the cusp of the quota may only have their ballots partially allocated to ensure that voters who supported the winner equally are treated equally.
 
==Procedure==
Each voter scores all candidates on a [0,5] scale
 
# Select the candidate with the highest sum of score as thiseach round's winner.
# Set the ballot weight to zero for the [[Quotaquota]] of voters ballotswhose whichballots contributed the highest scores to that winner.
#* If several voters have contributed the same score to the winner at the threshold of the Quotaquota then [[Fractional Surplus Handling]] is applied to those voters
# Repeat this process until all the seats are filled.
 
[[Fractional Surplus Handling]]: When determining which ballots belong to a winner's quota, voter’s ballots are sorted by the score they contributed to the winner's total score.
'''Fractional Surplus Handling to break ties in exhaustion''': When calculating which ballots belong to a candidate's quota so they should be allocated to them, if for a particular score, including voters that gave that candidate that score in the quota would make the quota to large and excluding it would make it to small, then exhaust a portion of those voter's ballot weights such that the total weight of the exhausted ballots still equals the Hare quota. The reason why [[Fractional Surplus Handling]] is preferred is that it preserves the [[Independence of irrelevant alternatives]] and [[Monotonicity]] criteria. Note that this means that voters can have a fractional ballot weight and they can subsequently only contribute that fraction of the score they put on the ballot to the candidates during tabulation. Additionally, they are only counted as that fraction of a ballot during exhaustion.
 
When multiple voters contributed the same score to the winner it may be the case that allocating them all to the winner would cause the quota to be exceeded but not allocating them all would cause the quota not to be met. For these voters on the cusp, an equal fraction of their ballot weight is allocated.
 
Fractional Surplus Handling ensures that voters who supported a candidate equally will be treated equally, while ensuring that the total weight of the ballots allocated for each winner will not exceed the Hare quota. It also preserves the [[Independence of irrelevant alternatives|Independence of Irrelevant Alternatives]] and [[Monotonicity]] criteria.
 
Note that with Fractional Surplus Handling voters can have a fractional ballot weight and they can subsequently only contribute that fraction to the remaining candidates, both during subsequent score tabulation and allocation.
 
==Python Implementation==
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