Sequential proportional approval voting: Difference between revisions

'''Sequential proportional approval voting''' (SPAV) or reweighted approval voting (RAV) is an [[electoral system]] that extends the concept of [[approval voting]] to a multiple winner election. Proposed by Danish statistician [[Thorvald N. Thiele]] in the early 1900s,<ref>E. Phragmén (1899): "Till frågan om en proportionell valmetod." Statsvetenskaplig tidskrifts Vol. 2, No. 2: pp 87-95 [http://journals.lub.lu.se/index.php/st/article/view/1949/1528&usg=ALkJrhiuUQ1zCqZHnca_-iAmk1KpNqMtmg]</ref> it was used (with adaptations for party lists) in Sweden for a short period after 1909.<ref>Aziz, H., Brill, M., Conitzer, V., et al. (2014): "Justified Representation in Approval-Based Committee Voting", arXiv:1407.8269 p5 [https://arxiv.org/abs/1407.8269]</ref> If [[Score voting]] ballots are used then it is equivalent to [[Reweighted Range Voting|Reweighted Score Voting]].

This system converts AV into a multi-round rule,<ref name="Kilgour2010">{{cite book |last=Kilgour |first=D. Marc |editor1=Jean-François Laslier |editor2=M. Remzi Sanver |title=Handbook on Approval Voting |url=https://books.google.com/books?id=mQBEAAAAQBAJ&pg=PA114 |date=2010 |publisher=Springer |isbn=978-3-642-02839-7 |pages=105–124 |chapter=Approval Balloting for Multi-winner Elections}}</ref> selecting a candidate in each round and then reweighingre-weighing the approvals for the subsequent rounds. The first candidate elected is the AV winner (''w₁''). The value of all ballots that approve of ''w₁'' are reduced in value from 1 to 1/2 and the approval scores recalculated. Next, the unelected candidate who has the highest approval score is elected (''w₂''). Then the value of ballots that approve of both ''w₁'' and ''w₂'' are reduced in value to 1/3, and the value of all ballots that approve of either ''w₁'' or ''w₂'' but not both are reduced in value to 1/2.<ref>Steven J. Brams, D. Marc Kilgour (2009): "Satisfaction Approval Voting": p4 [http://www2.eco.uva.es/presad/SSEAC/documents/Tilburg09-Brams-Kilgour.pdf]</ref>

At each stage, the unelected candidate with the highest approval score is elected. Then the value of each voter’s ballot is set at ''<math>\frac{1/}{(1+m+1)''}</math> where ''m'' is the number of candidates approved on that ballot who were already elected, until the required number of candidates is elected.

The system disadvantages minority groups who share some preferences with the majority. In terms of [[tactical voting]], it is therefore desirable to [[ Free riding | free ride ]] by withholding approval from candidates who are likely to be elected in any case. With the standard [[Jefferson method]] based reweighing it favours large factions in an attempt to mitigate [[Free_riding#Vote_Management | vote management]]. On the other hand [[Sainte-Laguë method]] based reweighting is more fair to smaller factions.

== Example Code==

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==Notes ==

[[Category:Approval methodsvoting]]