Satisfaction approval voting (SAV), also known as equal and even cumulative voting, is an

electoral system An electoral or voting system is a set of rules used to determine the results of an election. Electoral systems are used in politics to elect governments, while non-political elections may take place in business, nonprofit organizations and inf ...

that is a form of multiwinner approval voting as well as a form of

cumulative voting Cumulative voting (sometimes called the single divisible vote) is an election system where a voter casts multiple votes but can lump votes on a specific candidate or can split their votes across multiple candidates. The candidates elected are tho ...

. In the academic literature, the rule was studied by

Steven Brams Steven J. Brams (born November 28, 1940) is an American game theorist and political scientist at the New York University Department of Politics. Brams is best known for using the techniques of game theory, public choice theory, and social choice ...

and Marc Kilgour in 2010. Paper presented at the Annual National Conference of the Midwest Political Science Association, Chicago, Illinois, in April 2010. In this system, voters may approve a number of candidates, and each approved candidate receives an equal fraction of the vote. For example, if a voter approves 4 candidates, then each candidate receives a 0.25 fractional vote. The election winners are those candidates that receive the highest fractional vote count. This election system has been used for the election of the city council in

Peoria, Illinois Peoria ( ) is a city in Peoria County, Illinois, United States, and its county seat. Located on the Illinois River, the city had a population of 113,150 as of the 2020 United States census, 2020 census, making it the List of municipalities in Ill ...

, since 1991, with the amount of candidates approved being restricted to five.

Comparison to other approval variants

Satisfaction approval voting is a semi-proportional voting system, making it similar to

single non-transferable vote Single non-transferable vote or SNTV is a multi-winner electoral system in which each voter casts a single vote. Being a semi-proportional variant of first-past-the-post voting, under SNTV small parties, as well as large parties, have a chance t ...

(semi-proportional plurality) and

. In other words, SAV is proportional so long as voters are perfectly strategic. Because of this semi-proportionality, SAV tends to be more proportional than

block voting Block or bloc voting refers to a class of electoral systems where multiple candidates are elected simultaneously. They do not guarantee minority representation and allow a group of voters (a voting bloc) to ensure that only their preferred candi ...

, but does not create fully representative results. Satisfaction approval is similar to

proportional approval voting Proportional approval voting (PAV) is a proportional electoral system for multiwinner elections. It is a multiwinner approval method that extends the D'Hondt method of apportionment commonly used to calculate apportionments for party-list prop ...

(PAV), but splits votes differently. SAV splits each vote equally between all the approved candidates, while PAV splits each vote equally between all the ''winning'' candidates approved of by a voter. This makes PAV much less vulnerable to spoiler effects, and much simpler for voters--with SAV, voters must know exactly how many seats their party is entitled to, and only cast a number of votes equal to that number of seats. Moreover, they must coordinate on the exact set of candidates to vote for. Failing to execute this strategy properly can result in a "wipeout," as shown below.

Example

In this election, there are 10 voters, and 5 candidates:

John Quincy Adams John Quincy Adams (; July 11, 1767 – February 23, 1848) was the sixth president of the United States, serving from 1825 to 1829. He previously served as the eighth United States secretary of state from 1817 to 1825. During his long diploma ...

Henry Clay Henry Clay (April 12, 1777June 29, 1852) was an American lawyer and statesman who represented Kentucky in both the United States Senate, U.S. Senate and United States House of Representatives, House of Representatives. He was the seventh Spea ...

Daniel Webster Daniel Webster (January 18, 1782 – October 24, 1852) was an American lawyer and statesman who represented New Hampshire and Massachusetts in the U.S. Congress and served as the 14th and 19th United States Secretary of State, U.S. secretary o ...

, William Crawford, and

Andrew Jackson Andrew Jackson (March 15, 1767 – June 8, 1845) was the seventh president of the United States from 1829 to 1837. Before Presidency of Andrew Jackson, his presidency, he rose to fame as a general in the U.S. Army and served in both houses ...

. The candidates compete for 2 seats. Adams, Webster, and Clay are all Whigs, while Jackson and Crawford each have their own coalition. The votes are: * 6: Adams, Clay, Webster * 3: Jackson * 3: Crawford Then, the total votes for each candidate are: Note that despite winning a full majority of the vote, the Whigs receive no seats because of spoiler effects (while PAV satisfies

independence of irrelevant alternatives Independence of irrelevant alternatives (IIA) is an axiom of decision theory which codifies the intuition that a choice between A and B (which are both related) should not depend on the quality of a third, unrelated outcome C. There are several dif ...

, making it immune to such effects). Had one of the three candidates dropped out, the remaining two candidates would have received 4 votes and swept both seats.

Party-approval voting

SAV can be used together with party approval voting, a special case of approval voting where each voter can approve of one or more ''parties'', rather than directly approving candidates.

References

{{voting systems Semi-proportional electoral systems Cardinal electoral systems Approval voting