Approval Voting

A voting system in profile

Tomas McIntee
Aug 6 · 7 min read

There are many credible alternatives to plurality voting. Of those, the simplest is approval voting, which has support from both prominent voting theorists as well as activists who advocate for voting reforms.

The way approval voting works is simple: A voter considers a list of candidates, and either approves or disapproves of each candidate. Usually, approving of a candidate means marking the bubble next to their name, while disapproving a candidate means leaving the bubble blank. The candidate with the largest number of voters behind them wins.

There are two main drawbacks of approval voting. The first is that it can sometimes end up looking a lot like a plurality vote. The second is that if some voters act strategically and some do not, the results can be very unusual — although they are unlikely to be very bad. These weaknesses are tied to the fact that approval voting is flexible, but does not resolve different levels of support.

A brief history of approval voting

Given the simplicity of the method, it should come as no surprise that it has been used in some historic elections. Most notably, approval ballots were used to select popes.

Cover of the book titled “Approval Voting” by Stephen Brams and Peter Fishburn. Fair use without permission.

Modern voting theorists rediscovered approval voting in the 1970s. It is not clear who came up with the idea first, as it appears in print in works that were authored concurrently. The most notable inventors are Stephen Brams and Peter Fishburn, who authored an early definitive book simply titled Approval Voting. In the preface to that book, they recognize as other inventors Guy Ottewell, John Kellett and Kenneth Mott, Robert Weber, and Richard Morin.

Stephen Brams vigorously championed the adoption of approval voting, notably including an effort to try to get approval voting enacted in New Hampshire’s presidential primary. While Brams did not succeed in New Hampshire, approval voting was soon adopted by a number of professional societies.

Notable adopting societies included one of the professional societies most closely linked to the study of voting systems (Society for Social Choice and Welfare), the major mathematical societies (American Mathematical Society, Mathematical Association of America, and American Statistical Association) and the Institute of Electrical and Electronic Engineers, one of the largest professional associations in America.

More recently, the city of Fargo, North Dakota adopted approval voting for use in municipal elections, while the city of St Louis, Missouri has adopted approval voting for use in a preliminary round, followed by a final majority runoff election.

The benefits of approval voting

An approval vote using marbles in early 20th century Greece. From source.

Approval voting is arguably the simplest possible voting method if voters approach it sincerely, without attempting to strategize: Simply approve or disapprove of each option independently, without comparing options directly or considering how other voters might act.

In terms of cognitive complexity, this is simpler than a plurality vote, especially for voters who think there is really only one important issue, e.g., abortion, climate change, and gun control. A voter can look at each candidate’s positions and give a quick thumbs-up or thumbs-down.

Approval voting really shines in preliminary elections with a large number of candidates — e.g., the New Hampshire presidential primary. Ranking large numbers of poorly-known candidates is very difficult, and plurality voting simply performs worse with more candidates. (The types of strategic voting that occur in approval voting also become less of a concern in a preliminary election, where multiple candidates will advance to the next round.)

If all voters behave like this, approval voting winners tend to have exceptionally broad coalitions of voters behind them — much more than a simple majority. This has made approval voting a natural fit for elections where a supermajority is required, and is probably one reason why approval voting was used for several centuries in papal conclaves. (A two thirds supermajority has usually been required in papal elections.)

Relationships with other voting systems and criteria

In a combined approval vote, this ballot would be counted as +1 vote for Jonald Triden and Pike Marris, -1 vote against Donald Bump, Harala Kence, and Bernsi Gabbers, but would add 0 votes to Tulie Sandard.

Mathematically (but not psychologically), approval voting is equivalent to a system known negative voting, which counts the number of voters who disapprove of a candidate. This method was used briefly in some local Soviet elections in 1987; it’s worth noting that many of the modern discoverers of approval voting started with the negative version of the system.

One major criticism of approval voting is that it does not allow voters to express fine distinctions between candidates. A more sophisticated variation that counts both “yes” and “no” votes separately is called combined approval voting. In this case, voters can leave a line blank in order to express their indifference towards a candidate. Another natural variation allowing to allow voters to express much finer distinctions (e.g., a 0–10 rating) is known as range voting or score voting.

Approval voting winners are likely to be Condorcet winners and not Condorcet losers, though this is not guaranteed. If voters make full use of their ability to approve or disapprove any number of candidates, and there is no correlation between the raw number of candidates approved and preferences of the voter, approval voting results will, on average, match Borda count results.

How and when an approval vote looks like a plurality vote

In 2002, the IEEE decided to return to using plurality voting. The stated justification for this was that most voters only voted for one candidate anyway. (The full story is slightly more complex; the short version is that the political reasons for adopting approval voting involved trying to avoid the election of a particularly irksome candidate, who was no longer a factor.)

Theoretically, an approval vote can give worse results than a plurality vote. Very unusual results can occur if groups of voters with different preferences approach the ballot in ways that are consistent within the groups, but different across the groups. A more common concern is that an approval ballot will fail to make a meaningful difference when it replaces a plurality ballot. There are three common ways in which an approval vote may end up giving similar results to plurality voting.

Bullet voting

Voters can choose to fill out an approval ballot just as if it were a plurality ballot, casting a “bullet vote.” It is possible for an approval election’s ballots to mostly or entirely consist of “bullet” votes that look just like plurality votes.

Plurality ballot or approval ballot? How do you know?

Voters accustomed to plurality voting may “bullet vote” in an approval election either out of habit or out of ignorance, even if they would benefit from approving of multiple candidates. It is easy to simply glance at a ballot and mark it in the manner one is accustomed to doing.

This can also occur as the result of strategic behavior in certain circumstances. Unlike in a plurality vote, voters should always vote for their favorite candidate on an approval ballot, even if they think their favorite is unlikely to win. A voter has a real strategic incentive to only vote for their favorite candidate either if they optimistically believe that their favorite candidate has a good chance, or if they simply don’t see any differences among the other candidates.

If most voters meet one of those two criteria, then most voters may strategically choose to vote for only their favorite candidate, leading to an election that looks very much like a sincere plurality vote.

Other strategic voting

Finally, another scenario in which approval voting does not deviate from the plurality winner can occur when voters mostly vote strategically … and share a common opinion of which two candidates are most likely to win. Each voter has a strategic incentive to vote for one of those top two candidates. In this case, the top two candidates may end up with the exact same number of votes they would have gotten in a plurality election.

This is a result similar but not identical to a plurality vote. While the winner of the election may be the same candidate with the same number of voters, third-place and lower candidates will likely receive considerably more votes. Voters whose favorite candidates were not elected still have the opportunity to show support for their favorite candidate.

Recap

Approval voting is a very simple alternate method of voting, arguably even simpler than plurality voting. It has support from both theoreticians and activists. The quality of results from an approval ballot can vary significantly depending on how voters choose to approach the ballot.

In general, an approval vote is a clear upgrade from a plurality vote. It is especially well-suited for preliminary elections or primary elections, where there are a large number of candidates, voters may have limited information about candidates, and two or more candidates can advance to the next round of elections.

If voters make full use of the flexible capabilities of their ballots and tend to be equally likely to approve or disapprove of candidates, the results can be very good. The main risk of approval voting is that, either because of strategic behavior or voters habituated to it ends up closely approximating a plurality vote. Even in this case, however, we can at least be reassured that the results we get tell us more information about what voters really want.

Basic Voting Theory

How different methods of voting work