Satisfaction approval 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]
Description
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]
Example
10 voters, 4 candidates, 2 seats
4 voters: ab
3 voters: c
3 voters: d
Using the methodology used in PAV:
| AB | AC | AD | BC | BD | CD | |
|---|---|---|---|---|---|---|
| ab voters' satisfaction | 4 | 2 | 2 | 2 | 2 | 0 |
| c voters' satisfaction | 0 | 3 | 0 | 3 | 0 | 3 |
| d voters' satisfaction | 0 | 0 | 3 | 0 | 3 | 3 |
| total satisfaction | 4 | 5 | 5 | 5 | 5 | 6 |
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 | 3 | 0 |
| d voters - total vote | 0 | 0 | 0 | 3 |
| overall vote | 2 | 2 | 3 | 3 |
See also
References
- 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.