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.

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. 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, 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.

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:

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