# Satisfaction approval voting

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