Sequential proportional approval voting: Difference between revisions

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Revision as of 23:46, 11 April 2022 (view source) Fsargent (talk \| contribs) m (Backling to Reweighted Score Voting) Tag: Visual edit ← Older edit		Latest revision as of 09:56, 16 August 2022 (view source) RobLa (talk \| contribs) (Renamed Category:Approval methods to Category:Approval voting)
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Line 4: ==Description== [[File:SPAV Flow Chart.png\|thumb\|Flow chart of SPAV]] 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 ~~reweighing~~re-weighing the approvals for the subsequent rounds. The first candidate elected is the AV winner (''w<sub>1</sub>''). The value of all ballots that approve of ''w<sub>1</sub>'' 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 (''w<sub>2</sub>''). Then the value of ballots that approve of both ''w<sub>1</sub>'' and ''w<sub>2</sub>'' are reduced in value to 1/3, and the value of all ballots that approve of either ''w<sub>1</sub>'' or ''w<sub>2</sub>'' 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. It is however a much computationally simpler algorithm than (and can be considered a sequential form of) [[proportional approval voting]], permitting votes to be counted either by hand or by computer, rather than requiring a computer to determine the outcome of all but the simplest elections.<ref name="AzizGaspers2014">{{Cite book\|title=Proceedings of the 2015 International Conference on Autonomous Agents & Multiagent Systems: May, 4 - 8, 2015, Istanbul, Turkey\|date=2015\|publisher=ACM\|editor-last=International Foundation for Autonomous Agents and Multiagent Systems\|location=New York, NY\|chapter=Computational Aspects of Multi-Winner Approval Voting \|chapterurl=https://arxiv.org/pdf/1407.3247v1.pdf \|pages=107–115 \|isbn=978-1-4503-3413-6}}</ref> == Example Code== <syntaxhighlight lang="python" line=""> import pandas Line 77: ['Blue', 'Red', 'Green', 'Yellow'] ==Notes == SPAV's [[party list case]] is [[D'Hondt]], because its reweighting is based on D'Hondt's divisors.<ref name="Janson 2016">{{cite arXiv \| last=Janson \| first=Svante \| title=Phragmén's and Thiele's election methods \| date=2016-11-27 \| eprint=1611.08826\|class=math.HO}}</ref> Line 90: {{reflist}} [[Category:Approval PR methods]] [[Category:Approval ~~methods~~voting]] [[Category:Highest averages-reducing voting methods]] [[Category:Adjustable-proportionality voting methods]]