Satisfaction approval voting
Satisfaction approval voting (SAV) is an electoral 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]
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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: vote for both Alice and Bob (each of these two candidates with get half a vote from each of these four voters)
3 voters: vote only for Carol (this candidate gets a whole vote from each of these three voters)
3 voters: vote only for Dan (this candidate gets a whole vote from each of these three voters)
Using the methodology used in PAV:
| Potential winners of the two seats | ||||||
|---|---|---|---|---|---|---|
| Alice and Bob | Alice and Carol | Alice and Dan | Bob and Carol | Bob and Dan | Carol and Dan | |
| Voters' satisfaction for Alice and Bob | 4 | 2 | 2 | 2 | 2 | 0 |
| Voters' satisfaction for Carol | 0 | 3 | 0 | 3 | 0 | 3 |
| Voters' satisfaction for Dan | 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:
| Alice | Bob | Carol | Dan | |
|---|---|---|---|---|
| Alice and Bob voters – total vote | 2 | 2 | 0 | 0 |
| Carol voters – total vote | 0 | 0 | 3 | 0 |
| Dan voters – total vote | 0 | 0 | 0 | 3 |
| overall vote | 2 | 2 | 3 | 3 |
References
- 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 (eds.). 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 (2014). "Computational Aspects of Multi-Winner Approval Voting". Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems. pp. 107–115. arXiv:1407.3247v1. ISBN 978-1-4503-3413-6.CS1 maint: multiple names: authors list (link)