Satisfaction approval voting

Approval voting Proportional approval voting Electoral system

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]


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:

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:

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


  1. ^ a b 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.
  2. ^ 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.
  3. ^ 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)