Approval voting is a voting system used for elections, in which each voter can vote for as many or as few candidates as the voter chooses. It is typically used for single-winner elections but can be extended to multiple winners. Approval voting is a limited form of range voting, where the range that voters are allowed to express is extremely constrained: accept or not.

Each voter may vote for as many options as they wish, at most once per option. This is equivalent to saying that each voter may "approve" or "disapprove" each option by voting or not voting for it, and it's also equivalent to voting +1 or 0 in a range voting system.

The votes for each option are tallied. The option with the most votes wins.

Suppose that Tennessee is holding an election on the location of its capital. The population is concentrated around four major cities. All voters want the capital to be as close to them as possible. The options are:

• Memphis, the largest city, but far from the others (42% of voters)
• Nashville, near the center of the state (26% of voters)
• Chattanooga, somewhat east (15% of voters)
• Knoxville, far to the northeast (17% of voters)

The preferences of each region's voters are:

Supposing that voters voted for their two favorite candidates, the results would be as follows (a more sophisticated approach to voting is discussed below):

• Memphis: 42 total votes
• Nashville: 68 total votes
• Chattanooga: 58 total votes
• Knoxville: 32 total votes

Approval voting passes a form of the monotonicity criterion, in that voting for a candidate never lowers that candidate's chance of winning. Indeed, there is never a reason for a voter to tactically vote for a candidate X without voting for all candidates he or she prefers to candidate X.

However, as approval voting does not offer a single method of expressing sincere preferences, but rather a plethora of them, voters are encouraged to analyze their fellow voters' preferences and use that information to decide which candidates to vote for.

A good strategy is to vote for every candidate the voter prefers to the leading candidate, and to also vote for the leading candidate if that candidate is preferred to the current second-place candidate. When all voters follow this strategy, the Condorcet winner is almost certain to win.

In the above election, if Chattanooga is perceived as the strongest challenger to Nashville, voters from Nashville will only vote for Nashville, because it is the leading candidate and they prefer no alternative to it. Voters from Chattanooga and Knoxville will withdraw their support from Nashville, the leading candidate, because they do not support it over Chattanooga. The new results would be:

• Memphis: 42
• Nashville: 68
• Chattanooga: 32
• Knoxville: 32

If, however, Memphis were perceived as the strongest challenger, voters from Memphis would withdraw their votes from Nashville, whereas voters from Chattanooga and Knoxville would support Nashville over Memphis. The results would then be:

• Memphis: 42
• Nashville: 58
• Chattanooga: 32
• Knoxville: 32

The effect of this system as an electoral reform is disputed. Instant-runoff voting advocates like the Center for Voting and Democracy argue that Approval Voting would lead to the election of "compromise candidates" disliked by few, and liked by few. A study by Approval advocates Steven Brams and Dudley R. Herschbach published in Science in 2000 argued that approval voting was "fairer" than preference voting on a number of criteria. They claimed that a close analysis shows that the hesitation to support a 'compromise candidate' to the same degree as one supports one's first choice (as approval voting requires) actually outweighs the extra votes that such second choices get. Accordingly, preference voting is more biased towards compromise candidates than approval voting - a non-obvious and surprising result. Citizens for Approval Voting was organized in December 2002 to promote the use of approval voting in all public single-winner elections.

Advocates of approval voting often note that a single simple ballot can serve for single, multiple, or negative choices. It requires the voter to think carefully about who or what they really accept, rather than trusting a system of tallying or compromising by formal ranking or counting. Compromises happen but they are explicit, and chosen by the voter, not by the ballot counting. Some features of approval voting include:

• Unlike Instant Runoff Voting and other methods that require ranking candidates, Approval voting does not require significant changes in ballot design, voting procedures or equipment, and it is easier for voters to use and understand. This reduces problems with mismarked ballots, disputed results and recounts.
• Increasing options for voters, when compared with the common First-past-the-post system, could increase voter turnout
• It provides less incentive for negative campaigning than many other systems.
• It allows voters to express tolerances but not preferences. This is considered by some political scientists a major advantage, especially where acceptable choices are more important than popular choices.
• Each voter may vote as many times as they wish, at most once per candidate. This is equivalent to saying that each voter may "approve" or "disapprove" each candidate by voting or not voting for them, and it's also equivalent to voting +1 or 0 in a range voting system.
• It is easily reversed as disapproval voting where a choice is disavowed, as is already required in other measures in politics (e.g. representative recall).

• In an Approval Vote election, the total number of approvals will add up to more than 100% of the number of voters, which may appear to some people as a breech of the "One Man One Vote" principle. It is not a breech, but how does one argue that it is not a breech?

• Suppose that a voter approves of candidates B and C; but approves of candidate B more than C. How does he cast his votes?
  • If he approves of only B, the lack of an approval vote for C may let A in.
  • If he approves of both B and C, then he has failed to express his preference for B over C.
  • It is thus impossible to simultaneously approve of two candidates which preferring one over the other.
  • Approval voting suffers the disadvantage that all approvals are of equal weight, even when the vote wishes to express unequal approvals.

• These two problems are resolved with Instant Runoff Voting.
  • With IRV, the total number of votes for each candidate at every stage of the count equals the number of votes orignally cast.
  • If a votes put B first, C second and A third, then the full value of his vote is set against B in the first round. Depending on how B and C score against eachother, either the second preferences of C go to B, or the second preferences of B go to C. No votes need be lost in the struggle between like minded B and C against the common enemy A.
  • In military terms, there is no "Division of Force" when a voter preferences B before C. No matter whether a votes remains with its original choice, or is redistributed to a lower choice, that vote always retains its full value, one man, one vote, one value.

• There is a problem with Instant Runoff Voting that in practice is no longer a problem.
  • With Approval Voting, Limited Voting, and the like, when a computer is used to tally the results, only the total score for each candidate need be recorded. This requires only a small Commodure 64 computer with 64k of memory.
  • With Instant Runoff Voting, it is necessary to store an image of every ballot; it there are N ballots, and M candidates per ballot, then a Pentium computer with N * M bytes or even double bytes of memory is required.
  • It can also be represented with much less memory. Just as the example above represented many voters with just four columns, you can get my with just counting how many ef each *unique* ballot exists. You only need M * (M!) entries, each entry able to count up to N. For M=4 candidates, this comes to 96 entries. For M=10 candidates, this comes to about 36 mega-entries.
  • If Department of Elections only has Commodore 64 computers at its disposal, then a computerised IRV may be out of the question.
  • A computerised count of and IRV election would also take much more time to process than an Approval Voting election.
  • How many people still use Commodore 64 computers?

The Citizens for Approval Voting website uses the following ballot paper as its logo:

• • [YES] Jefferson - a great president
  • [NO ] Stalin - a tyrant
  • [YES] Madison - a great president
  • [YES] Washington - a great president

Clearly, it does not matter which of these three great presidents wins, so long as Stalin loses.

But suppose the ballot was revised as follows:

• • [YES] Jefferson - a great president
  • [NO ] Stalin - a tyrant
  • [YES] Madison - a great president
  • [ ? ] Warren G. Harding - a ROTTEN president

Now the choice is less clear. We would want even Warren G. Harding to beat Stalin, but either Jefferson or Madison to beat Harding. This example shows a fundimental weakness of Approval Voting. Cumulative Voting does better, and Instant Runoff Voting better still.

Put simply, Approval Voting cannot simultaneously approve of multiple candidates and choose between them.

An even more telling ballot would be to place Stalin against the three worst presidents.

Approval Voting can be converted into a form of Instant Runoff Voting by replacing YES with "1" and NO with "2"

• [2] Joe Smith ----- Greens.
• [1] Henry Ford ---- Rural Republican
• [2] Jane Doe ------ Democrat
• [2] Fred Rubble --- Reform
• [1] Mary Hill ----- City Republican

Note how the numbers "1" and "2" are repeated.

If a voter desires to preference Ford ahead of Hill, while supporting both these Republicans against all others, then that voter would need to use the numbers "1", "2" and "3".

This "1" = "FULL YES", "2" = "PART YES", "3" = "NO"

• [3] Joe Smith ----- Greens.
• [1] Henry Ford ---- Rural Republican
• [3] Jane Doe ------ Democrat
• [3] Fred Rubble --- Reform
• [2] Mary Hill ----- City Republican

It would not be Rocket Science to devise a (computerised) system to allow a voter to use either Approval Voting or Instant Runoff Voting in the same election.

• [3] Joe Smith ----- Greens.
• [1] Henry Ford ---- Rural Republican
• [4] Jane Doe ------ Democrat
• [5] Fred Rubble --- Reform
• [2] Mary Hill ----- City Republican

A convential Instant Runoff Voting requires each square to be filled in by different consequtive numbers, which helps the electoral officials check for errors.

Approval voting can be extended to multiple winner elections, either as block approval voting, a simple variant on block voting where each voter can select an unlimited number of candidates and the candidates with the most approval votes win, or as proportional approval voting which seeks to maximise the overall satisfaction with the final result using approval voting.

A disadvantage of multiple winner voting, is that if there are N vacancies, voters must vote for N candidates, which is like N First Past the Post votes in parallel. The result if often a clean sweep by one major party or the other.

Limited Voting allows each voter M votes for N vacancies, where M < N, which reduces the likely of a clean sweep.

Cumulative Voting allows each voter M votes for N vacancies, where M <= N, but the voter can allocate those votes 1 each for M candidates or M votes for just 1 candidate, or something in between.

Approval ballots can be of at least four semi-distinct forms. The simplest form is a blank ballot where the names of supported candidates is written in by hand. A more structured ballot will list all the candidates and allow a mark or word to be made by each supported candidate. A more explicit structured ballot can list the candidates and give two choices by each. (Candidate list ballots can also include spaces for a write-in candidates as well)

All four ballots are interchangeable. The more structured ballots may aid voters in offering clear votes so they explicitly know all their choices. The Yes/No format can help to detect an "undervote" when a candidate is left unmarked, and allow the voter a second chance to confirm the ballot markings are correct.

• List of democracy and elections-related topics
• Borda count
• Bucklin voting
• First Past the Post electoral system (also called Plurality or Relative Majority)
• Instant-runoff voting
• Voting system - many other ways of voting

• Approval Voting Home Page
• Citizens for Approval Voting
• electionmethods.org on approval voting
• "The Science of Elections", Steven J. Brams and Dudley R. Herschbach, Science May 25, 2001: 1449.
• Rebuttal to "The Science of Elections", Center for Voting and Democracy.