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{{wikipedia}}
'''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]].
==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
At each stage, the unelected candidate with the highest approval score is elected. Then the value of each voter’s ballot is set at
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
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
<syntaxhighlight lang="python" line="">
import pandas
ballots = [
{"Red": 1, "Green": 0, "Yellow": 0, "Blue": 1},
{"Red": 0, "Green": 1, "Yellow": 0, "Blue": 1},
{"Red": 1, "Green": 0, "Yellow": 1, "Blue": 0},
{"Red": 1, "Green": 0, "Yellow": 1, "Blue": 1},
{"Red": 0, "Green": 1, "Yellow": 0, "Blue": 1},
{"Red": 1, "Green": 0, "Yellow": 1, "Blue": 1},
{"Red": 1, "Green": 1, "Yellow": 0, "Blue": 1},
{"Red": 0, "Green": 1, "Yellow": 0, "Blue": 1},
{"Red": 1, "Green": 0, "Yellow": 0, "Blue": 1},
]
seats = 4
seated = []
max_score = 1
#reweight
def reweight(ballot):
seated_scores = [
ballot[candidate] for candidate in ballot if candidate in seated
]
weight = 1/(1+sum(seated_scores)/max_score)
return {candidate: weight*ballot[candidate] for candidate in ballot}
def nextRound(ballots):
reweightedBallots = [reweight(ballot) for ballot in ballots]
winner = pandas.DataFrame(reweightedBallots).sum().drop(seated).idxmax()
print(pandas.DataFrame(reweightedBallots).sum())
seated.append(winner)
return reweightedBallots
while len(seated) < seats:
nextRound(ballots)
print(seated)
</syntaxhighlight>
Red 6.0
Green 4.0
Yellow 3.0
Blue 8.0
dtype: float64
['Blue']
Red 3.5
Green 2.0
Yellow 2.0
Blue 4.0
dtype: float64
['Blue', 'Red']
Red 2.166667
Green 1.833333
Yellow 1.166667
Blue 3.166667
dtype: float64
['Blue', 'Red', 'Green']
Red 2.083333
Green 1.250000
Yellow 1.166667
Blue 2.583333
dtype: float64
['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>
In the same way that [[Approval voting]] is considered by almost nobody to be worse than [[FPTP]], though some question the magnitude of the improvement, many find SPAV to be unambiguously better than [[SNTV]]. This is because it satisfies a stronger [[Weak forms of PSC|weak form of PSC]], which allows solid coalitions to gain proportional representation with less need for coordinated strategy. This makes it less likely to result in anomalous results (i.e. less likely that a minority wins a majority of seats using [[
==See also==
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{{reflist}}
[[Category:Approval PR methods]]
[[Category:Approval
[[Category:Highest averages-reducing voting methods]]
[[Category:Adjustable-proportionality voting methods]]
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