Satisfaction approval voting

Satisfaction approval voting

Description

Example

References

Description

Example

See Also

References

Voting systems
Part of the Politics series
Plurality/Majoritarian Simple majoritarianism Limited voting Single non-transferable vote Plurality First-past-the-post Two-round Exhaustive ballot Preferential/ranked/ordinal systems Borda count Bucklin voting Condorcet methods (Copeland's, Dodgson's, Kemeny-Young, Minimax, Nanson's, Ranked pairs, Schulze) Coombs' method Instant-runoff (alternative vote) Contingent vote Oklahoma primary electoral system Cardinal/graded/rated systems Approval voting Proportional approval voting Sequential proportional approval voting Satisfaction approval voting Majority judgment Range voting
Proportional Representation Party-list (Open lists, Closed lists, Local lists) Highest averages (D'Hondt, Sainte-Laguë) Largest remainder (Hare, Droop, Imperiali, Hagenbach-Bischoff) Single transferable vote (CPO-STV, Gregory, Schulze STV, Wright)
Mixed-Member Mixed-member proportional Majority bonus system Additional member system Scorporo, Av+ Parallel voting Majoritarian representation Plurality-at-large Preferential block voting General ticket
Other Proxy voting Delegable voting Delegated voting Random selection Sortition Random ballot Social choice theory Arrow's theorem Gibbard–Satterthwaite theorem Voting system criteria Public choice theory (separate but related) Multiple Ballot Voting Cumulative voting
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Satisfaction approval voting (SAV) is a voting system that extends the concept of approval voting to a multiple winner election. It was proposed by Steven Brams and Marc Kilgour in 2010.^[1]

Satisfaction approval voting aims to maximise the electorate's satisfaction, rather like proportional approval voting (PAV), however SAV calculates a voter's satisfaction differently to the way used in PAV. The satisfaction gained by a voter when a candidate they approve of is elected is equal to 1/n where n is the number of candidates that they voted for.^[2] This has the effect of giving everyone a single vote that they split between the n candidates that they vote for. This makes calculating the winners much easier than for PAV,^[3] as a voter's satisfaction gained for each elected candidate under this method is independent of how many of their choices have been elected, making satisfaction additive.^[1]

10 voters, 4 candidates, 2 seats

4 voters: ab

3 voters: c

3 voters: d

Using the methodology used in PAV:

Therefore C and D win

Alternatively, making use of the system's additive satisfaction property:

	A	B	C	D
ab voters - total vote	2	2	0	0
c voters - total vote	0	0	9	0
d voters - total vote	0	0	0	9
overall vote	2	2	9	9

1 2 Brams, Steven J.; Kilgour, D. Marc (2010). "Satisfaction Approval Voting" (PDF). Paper presented at the Annual National Conference of the Midwest Political Science Association, Chicago, Illinois, in April 2010.
↑ Brams, Steven J.; D. Marc Kilgour (2014). "Satisfaction Approval Voting". In Rudolf Fara, Dennis Leech, Maurice Salles. Voting Power and Procedures: Essays in Honour of Dan Felsenthal and Moshe Machover. Springer. pp. 322–346. doi:10.1007/978-3-319-05158-1_18. ISBN 978-3-319-05158-1.
↑ Aziz, Haris; Serge Gaspers, Joachim Gudmundsson, Simon Mackenzie, Nicholas Mattei, Toby Walsh. "Computational Aspects of Multi-Winner Approval Voting" (PDF). Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems. pp. 107–115. ISBN 978-1-4503-3413-6.

Voting systems

Part of the Politics and Election series

Single-winner voting system	Approval voting Borda count Bucklin voting Contingent vote Coombs' method Copeland's method Exhaustive ballot First-past-the-post voting Instant-runoff voting Kemeny–Young method Simple majoritarianism Minimax Condorcet Nanson's method Plurality Positional voting system Range voting Ranked pairs Schulze method Two-round system

Proportional representation	Mixed-member Party-list Single transferable vote Schulze STV CPO-STV Highest averages method Sainte-Laguë D'Hondt Largest remainder method Alternative vote Plus Closed list Open list Overhang seat Underhang seat

Semi-proportional representation	Parallel voting Single non-transferable vote Cumulative voting Limited voting Proportional approval voting Sequential proportional approval voting Satisfaction approval voting

Usage	Table of voting systems by country

Voting system criterion	Condorcet criterion Condorcet loser criterion Consistency criterion Independence of clones Independence of irrelevant alternatives Independence of Smith-dominated alternatives Later-no-harm criterion Majority criterion Majority loser criterion Monotonicity criterion Mutual majority criterion Pareto efficiency Participation criterion Plurality criterion Resolvability criterion Reversal symmetry Smith criterion

Voting system quotas	Droop quota Hagenbach-Bischoff quota Hare quota Imperiali quota

Other	Ballot Vote counting system Election threshold First-preference votes Spoilt vote Sortition

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ab voters' satisfaction

c voters' satisfaction

d voters' satisfaction

total satisfaction