Approval voting - AbsoluteAstronomy.com

Approval voting is a single-winner voting system used for election

Election

An election is a formal decision-making process by which a population chooses an individual to hold public office. Elections have been the usual mechanism by which modern representative democracy operates since the 17th century. Elections may fill offices in the legislature, sometimes in the...

s. Each voter may vote for (or 'approve' of) as many of the candidates as the voter wishes. The winner is the candidate receiving the most votes. Each voter may vote for any combination of candidates and may give each candidate at most one vote.

The system was described in 1976 by Guy Ottewell and also by Robert J. Weber

Robert J. Weber

Robert J. Weber is the Frederic E. Nemmers Distinguished Professor of Decision Sciences at the J.L. Kellogg Graduate School of Management, Northwestern University.-Education:...

, who coined the term "approval voting." It was more fully published in 1978 by political scientist Steven Brams

Steven Brams

Steven J. Brams is a game theorist and political scientist at the New York University Department of Politics. Brams is best known for using the techniques of game theory and public choice to research voting systems and fair division. He is one of the independent discoverers of approval voting...

and mathematician Peter Fishburn.

Theory

Approval voting can be considered a form of range voting

Range voting

Range voting is a voting system for one-seat elections under which voters score each candidate, the scores are added up, and the candidate with the highest score wins.A form of range voting was apparently used in...

, with the range restricted to two values, 0 and 1, or a form of Majority Judgment

Majority Judgment

Majority Judgment is a single-winner voting system proposed by Michel Balinski and Rida Laraki. Voters freely grade each candidate in one of several named ranks, for instance from "excellent" to "bad", and the candidate with the highest median grade is the winner. If more than one candidate has the...

, with the grades restricted to "Good" and "Poor". Approval voting can also be compared to plurality voting

Plurality voting system

The plurality voting system is a single-winner voting system often used to elect executive officers or to elect members of a legislative assembly which is based on single-member constituencies...

, without the rule that discards ballots which vote for more than one candidate.

Ballots which mark every candidate the same (whether yes or no) have no effect on the outcome of the election. Each ballot can therefore be viewed as a small "delta" which separates two groups of candidates, or a single-pair of ranks (e.g. if a ballot indicates that A & C are approved and B & D are not, the ballot can be considered to convey the ranking [A=C]>[B=D]).

Uses

Approval voting has been adopted by the Mathematical Association of America

Mathematical Association of America

The Mathematical Association of America is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists;...

(1986), the Institute of Management Sciences (1987) (now the Institute for Operations Research and the Management Sciences

Institute for Operations Research and the Management Sciences

The Institute for Operations Research and the Management Sciences is an international society for practitioners in the fields of operations research and management science...

), the American Statistical Association

American Statistical Association

The American Statistical Association , is the main professional US organization for statisticians and related professions. It was founded in Boston, Massachusetts on November 27, 1839, and is the second oldest, continuously operating professional society in the United States...

(1987), and the Institute of Electrical and Electronics Engineers

Institute of Electrical and Electronics Engineers

The Institute of Electrical and Electronics Engineers is a non-profit professional association headquartered in New York City that is dedicated to advancing technological innovation and excellence...

(1987). According to Steven J. Brams and Peter C. Fishburn, the IEEE board in 2002 rescinded its decision to use approval voting. IEEE Executive Director Daniel J. Senese stated that approval voting was abandoned because "few of our members were using it and it was felt that it was no longer needed." Approval voting also was used for Dartmouth Alumni Association elections for seats on the College Board of Trustees, but after some controversy it was replaced with traditional runoff elections by an alumni vote of 82% to 18% in 2009. Dartmouth students used approval voting to elect their student body president in 2011; the winner secured the support of 41% of voters against several write-in candidates.

Historically, several voting methods which incorporate aspects of approval voting have been used:

Approving voting was used for papal conclave
Papal conclave
A papal conclave is a meeting of the College of Cardinals convened to elect a Bishop of Rome, who then becomes the Pope during a period of vacancy in the papal office. The Pope is considered by Roman Catholics to be the apostolic successor of Saint Peter and earthly head of the Roman Catholic Church...

s between 1294 and 1621, with an average of about forty cardinals engaging in repeated rounds of voting until one candidate was listed on at least two-thirds of ballots.
In the 13th through 18th centuries, the Republic of Venice
Republic of Venice
The Republic of Venice or Venetian Republic was a state originating from the city of Venice in Northeastern Italy. It existed for over a millennium, from the late 7th century until 1797. It was formally known as the Most Serene Republic of Venice and is often referred to as La Serenissima, in...

elected the Doge of Venice
Doge of Venice
The Doge of Venice , often mistranslated Duke was the chief magistrate and leader of the Most Serene Republic of Venice for over a thousand years. Doges of Venice were elected for life by the city-state's aristocracy. Commonly the person selected as Doge was the shrewdest elder in the city...

using a multi-stage process that featured random selection and voting which allowed approval of multiple candidates and required a supermajority.
According to Steven J. Brams, approval voting was used in 19th century England.
The selection of the Secretary-General
United Nations Secretary-General
The Secretary-General of the United Nations is the head of the Secretariat of the United Nations, one of the principal organs of the United Nations. The Secretary-General also acts as the de facto spokesperson and leader of the United Nations....

of the United Nations
United Nations
The United Nations is an international organization whose stated aims are facilitating cooperation in international law, international security, economic development, social progress, human rights, and achievement of world peace...

has involved rounds of approval polling to help discover and build a consensus before a formal vote is held in the Security Council.

Effect on elections

Approval voting advocates Steven Brams

Steven Brams

and Dudley R. Herschbach

Dudley R. Herschbach

Dudley Robert Herschbach is an American chemist at Harvard University. He won the 1986 Nobel Prize in Chemistry jointly with Yuan T. Lee and John C...

predict that approval voting should increase voter participation, prevent minor-party candidates from being spoilers, and reduce negative campaigning. The effect of this system as an electoral reform

Electoral reform

Electoral reform is change in electoral systems to improve how public desires are expressed in election results. That can include reforms of:...

measure is not without critics, however. FairVote

FairVote

FairVote is a U.S. non-profit organization based in Takoma Park, Maryland, whose mission is to achieve universal access to participation, a full spectrum of meaningful ballot choices and majority rule with fair representation for all...

has a position paper arguing that approval voting has three flaws that undercut it as a method of voting and political vehicle. They argue that it can result in the defeat of a candidate who would win an absolute majority in a plurality system, can allow a candidate to win who might not win any support in a plurality elections, and has incentives for tactical voting

Tactical voting

In voting systems, tactical voting occurs, in elections with more than two viable candidates, when a voter supports a candidate other than his or her sincere preference in order to prevent an undesirable outcome.It has been shown by the Gibbard-Satterthwaite theorem that any voting method which is...

.

One study showed that approval voting would not have chosen the same two winners
as plurality voting (Chirac and Le Pen) in France's presidential election of 2002

French presidential election, 2002

The 2002 French presidential election consisted of a first round election on 21 April 2002, and a runoff election between the top two candidates on 5 May 2002. This presidential contest attracted a greater than usual amount of international attention because of Le Pen's unexpected appearance in...

(first round) - it instead would have chosen Chirac and Jospin as the top two to proceed to a runoff. Le Pen lost by a very high margin in the runoff, 82.2% to 17.8%, a sign that the true top two had not been found. Straight approval voting without a runoff, from the study, still would have selected Chirac, but with an approval percentage of only 36.7%, compared to Jospin at 32.9%. Le Pen, in that study, would have received 25.1%. In the real primary election, the top three were Chirac, 19.9%, Le Pen, 16.9%, and Jospin, 16.2%.

A generalized version of the Burr dilemma

Burr dilemma

The Burr dilemma is a term coined by Jack H. Nagel to describe the likelihood of ties between two or more candidates in the misuse of approval voting as a multi-member method. According to Nagel, "Problems of multicandidate races in U.S...

applies to approval voting when two candidates are appealing to the same subset of voters. Although approval voting differs from the voting system used in the Burr dilemma, approval voting can still leave candidates and voters with the generalized dilemma of whether to compete or cooperate.

While in the modern era there have been relatively few competitive approval voting elections where tactical voting is more likely, Brams argues that approval voting usually elects Condorcet winners

Condorcet criterion

The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared with every other candidate, is preferred by more voters. Informally, the Condorcet winner is the person who would win a two-candidate election against each of the other candidates...

in practice. Critics of the use of approval voting in the alumni elections for the Dartmouth Board of Trustees in 2009 placed its ultimately successful repeal before alumni voters, arguing that the system has not been electing the most centrist candidates. The Dartmouth editorialized that "When the alumni electorate fails to take advantage of the approval voting process, the three required Alumni Council candidates tend to split the majority vote, giving petition candidates an advantage. By reducing the number of Alumni Council candidates, and instituting a more traditional one-person, one-vote system, trustee elections will become more democratic and will more accurately reflect the desires of our alumni base."

Sincere voting

Approval voting experts describe sincere votes as those "... that directly reflect the true preferences of a voter, i.e. , that do not report preferences 'falsely.'" They also give a specific definition of a sincere approval vote in terms of the voter's ordinal preferences

Preference

-Definitions in different disciplines:The term “preferences” is used in a variety of related, but not identical, ways in the scientific literature. This makes it necessary to make explicit the sense in which the term is used in different social sciences....

as being any vote that, if it votes for one candidate, it also votes for any more preferred candidate. This definition allows a sincere vote to treat strictly preferred candidates the same, ensuring that every voter has at least one sincere vote. The definition also allows a sincere vote to treat equally preferred candidates differently. When there are two or more candidates, every voter has at least three sincere approval votes to choose from. Two of those sincere approval votes do not distinguish between any of the candidates: vote for none of the candidates and vote for all of the candidates. When there are three or more candidates, every voter has more than one sincere approval vote that distinguishes between the candidates.

Examples

Based on the definition above, if there are four candidates, A, B, C, and D, and a voter has a strict preference order, preferring A to B to C to D, then the following are the voter's possible sincere approval votes:

vote for A, B, C, and D
vote for A, B, and C
vote for A and B
vote for A
vote for no candidates

If the voter instead equally prefers B and C, while A is still the most preferred candidate and D is the least preferred candidate, then all of the above votes are sincere and the following combination is also a sincere vote:

vote for A and C

The decision between the above ballots is equivalent to deciding an arbitrary "approval cutoff." All candidates preferred to the cutoff are approved, all candidates less preferred are not approved, and any candidates equal to the cutoff may be approved or not arbitrarily.

Strategy with ordinal preferences

A sincere voter with multiple options for voting sincerely still has to choose which sincere vote to use. Voting strategy

Tactical voting

is a way to make that choice, in which case strategic approval voting includes sincere voting, rather than being an alternative to it. This differs from other voting systems that typically have a unique sincere vote for a voter.

When there are three or more candidates, the winner of an approval voting election can change, depending on which sincere votes are used. In some cases, approval voting can sincerely elect any one of the candidates, including a Condorcet winner and a Condorcet loser, without the voter preferences changing. To the extent that electing a Condorcet winner and not electing a Condorcet loser is considered desirable outcomes for a voting system, approval voting can be considered vulnerable to sincere, strategic voting. In one sense, conditions where this can happen are robust and are not isolated cases. On the other hand, the variety of possible outcomes has also been portrayed as a virtue of approval voting, representing the flexibility and responsiveness of approval voting, not just to voter ordinal preferences, but cardinal utilities as well.

Dichotomous preferences

Approval voting avoids the issue of multiple sincere votes in special cases when voters have dichotomous preferences. For a voter with dichotomous preferences, approval voting is strategy-proof (also known as strategy-free). When all voters have dichotomous preferences and vote the sincere, strategy-proof vote, approval voting is guaranteed to elect the Condorcet winner, if one exists. However, having dichotomous preferences when there are three or more candidates is not typical. It is an unlikely situation for all voters to have dichotomous preferences when there are more than a few voters.

Having dichotomous preferences means that a voter has bi-level preferences for the candidates. All of the candidates are divided into two groups such that the voter is indifferent between any two candidates in the same group and any candidate in the top-level group is preferred to any candidate in the bottom-level group. A voter that has strict preferences between three candidates—prefers A to B and B to C—does not have dichotomous preferences.

Being strategy-proof for a voter means that there is a unique way for the voter to vote that is a strategically best way to vote, regardless of how others vote. In approval voting, the strategy-proof vote, if it exists, is a sincere vote.

Approval threshold

Another way to deal with multiple sincere votes is to augment the ordinal preference model with an approval or acceptance threshold. An approval threshold divides all of the candidates into two sets, those the voter approves of and those the voter does not approve of. A voter can approve of more than one candidate and still prefer one approved candidate to another approved candidate. Acceptance thresholds are similar. With such a threshold, a voter simply votes for every candidate that meets or exceeds the threshold.

With threshold voting, it is still possible to not elect the Condorcet winner and instead elect the Condorcet loser when they both exist. However, according to Steven Brams, this represents a strength rather than a weakness of approval voting. Without providing specifics, he argues that the pragmatic judgements of voters about which candidates are acceptable should take precedence over the Condorcet criterion

Condorcet criterion

and other social choice criteria.

Strategy with cardinal utilities

Voting strategy under approval is guided by two competing features of approval voting. On the one hand, approval voting fails the later-no-harm criterion

Later-no-harm criterion

The later-no-harm criterion is a voting system criterion formulated by Douglas Woodall. The criterion is satisfied if, in any election, a voter giving an additional ranking or positive rating to a less preferred candidate cannot cause a more preferred candidate to lose.- Complying methods :Single...

, so voting for a candidate can cause that candidate to win instead of a more preferred candidate. On the other hand, approval voting satisfies the monotonicity criterion

Monotonicity criterion

The monotonicity criterion is a voting system criterion used to analyze both single and multiple winner voting systems. A voting system is monotonic if it satisfies one of the definitions of the monotonicity criterion, given below.Douglas R...

, so not voting for a candidate can never help that candidate win, but can cause that candidate to lose to a less preferred candidate. Either way, the voter can risk getting a less preferred election winner. A voter can balance the risk-benefit trade-offs by considering the voter's cardinal utilities, particularly via the von Neumann–Morgenstern utility theorem

Von Neumann–Morgenstern utility theorem

In 1947, John von Neumann and Oskar Morgenstern exhibited four relatively modest axioms of "rationality" such that any agent satisfying the axioms has a utility function...

, and the probabilities of how others will vote.

A rational voter model described by Myerson

Roger Myerson

Roger Bruce Myerson is an American economist and Nobel laureate recognized with Leonid Hurwicz and Eric Maskin for "having laid the foundations of mechanism design theory." A professor at the University of Chicago, he has made contributions as an economist, as an applied mathematician, and as a...

and Weber specifies an approval voting strategy that votes for those candidates that have a positive prospective rating. This strategy is optimal in the sense that it maximizes the voter's expected utility, subject to the constraints of the model and provided the number of other voters is sufficiently large.

An optimal approval vote will always vote for the most preferred candidate and not vote for the least preferred candidate. However, an optimal vote can require voting for a candidate and not voting for a more preferred candidate if there 4 candidates or more.

Other strategies are also available and will coincide with the optimal strategy in special situations. For example:

Vote for the candidates that have above average utility. This strategy coincides with the optimal strategy if the voter thinks that all pairwise ties are equally likely
Vote for any candidate that is more preferred than the expected winner and also vote for the expected winner if the expected winner is more preferred than the expected runner-up. This strategy coincides with the optimal strategy if there are three or fewer candidates or if the pivot probability for a tie between the expected winner and expected runner-up is sufficiently large compared to the other pivot probabilities.
Vote for the most preferred candidate only. This strategy coincides with the optimal strategy when there is only one candidate with a positive prospective rating.

Another strategy is to vote for the top half of the candidates, the candidates that have an above-median utility. When the voter thinks that the others will balance their votes randomly and evenly, the strategy will maximize the voter's power or efficacy, meaning that it will maximize the probability that the voter will make a difference in deciding which candidate wins.

Optimal strategic approval voting fails to satisfy the Condorcet criterion

Condorcet criterion

and can elect a Condorcet loser

Condorcet loser criterion

In single-winner voting system theory, the Condorcet loser criterion is a measure for differentiating voting systems. It implies the majority loser criterion....

. Strategic approval voting can guarantee electing the Condorcet winner in some special circumstances. For example, if all voters are rational and cast a strategically optimal vote based on a common knowledge of how all the other voters vote except for small-probability, statistically independent errors in recording the votes, then the winner will be the Condorcet winner, if one exists.

Strategy examples

In the example election described here, assume that the voters in each faction share the following von Neumann-Morgenstern utilities, fitted to the interval between 0 and 100. The utilities are consistent with the rankings given earlier and reflect a strong preference each faction has for choosing its city, compared to weaker preferences for other factors such as the distance to the other cities.

Voter utilities for each candidate city
	\| Candidates
Fraction of Voters (living close to)	Memphis	Nashville	Chattanooga	Knoxville	Average
Memphis (42%)	100	15	10	0	31.25
Nashville (26%)	0	100	20	15	33.75
Chattanooga (15%)	0	15	100	35	37.5
Knoxville (17%)	0	15	40	100	38.75

Using these utilities, voters will choose their optimal strategic votes based on what they think the various pivot probabilities are for pairwise ties. In each of the scenarios summarized below, all voters share a common set of pivot probabilities.

Approval Voting Results
for scenarios using optimal strategic voting
			\| Candidate Vote Totals
Strategy Scenario	Winner	Runner-up	Memphis	Nashville	Chattanooga	Knoxville
Zero-info	Memphis	Chattanooga	42	26	32	17
Memphis leading Chattanooga	Three-way tie		42	58	58	58
Chattanooga leading Knoxville	Chattanooga	Nashville	42	68	83	17
Chattanooga leading Nashville	Nashville	Memphis	42	68	32	17
Nashville leading Memphis	Nashville	Memphis	42	58	32	32

In the first scenario, voters all choose their votes based on the assumption that all pairwise ties are equally likely. As a result, they vote for any candidate with an above-average utility. Most voters vote for only their first choice. Only the Knoxville faction also votes for its second choice, Chattanooga. As a result, the winner is Memphis, the Condorcet loser, with Chattanooga coming in second place.

In the second scenario, all of the voters expect that Memphis is the likely winner, that Chattanooga is the likely runner-up, and that the pivot probability for a Memphis-Chattanooga tie is much larger than the pivot probabilities of any other pair-wise ties. As a result, each voter will vote for any candidate that is more preferred than the leading candidate and will also vote for the leading candidate if that candidate is more preferred than the expected runner-up. Each of the remaining scenarios follows a similar pattern of expectations and voting strategies.

In the second scenario, there is a three-way tie for first place. This happens because the expected winner, Memphis, was the Condorcet loser and was also ranked last by any voter that did not rank it first.

Only in the last scenario does the actual winner and runner-up match the expected winner and runner-up. As a result, this can be considered a stable strategic voting scenario. In the language of Game Theory

Game theory

Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...

, this is an "equilibrium." In this scenario, the winner is also the Condorcet winner.

Compliance with voting system criteria

Most of the mathematical criteria by which voting systems are compared were formulated for voters with ordinal preferences. In this case, approval voting requires voters to make an additional decision of where to put their approval cutoff (see examples above). Depending on how this decision is made, approval voting satisfies different sets of criteria.

There is no ultimate authority on which criteria should be considered, but the following are some criteria that are accepted and considered to be desirable by many voting theorists:

Majority criterion
Majority criterion
The majority criterion is a single-winner voting system criterion, used to compare such systems. The criterion states that "if one candidate is preferred by a majority of voters, then that candidate must win"....

—If there exists a majority that ranks (or rates) a single candidate higher than all other candidates, does that candidate always win?
Monotonicity criterion
Monotonicity criterion
The monotonicity criterion is a voting system criterion used to analyze both single and multiple winner voting systems. A voting system is monotonic if it satisfies one of the definitions of the monotonicity criterion, given below.Douglas R...

—Is it impossible to cause a winning candidate to lose by ranking him higher, or to cause a losing candidate to win by ranking him lower?
Consistency criterion
Consistency criterion
A voting system is consistent if, when the electorate is divided arbitrarily into two parts and separate elections in each part result in the same choice being selected, an election of the entire electorate also selects that alternative...

—If the electorate is divided in two and a choice wins in both parts, does it always win overall?
Participation criterion
Participation criterion
The participation criterion is a voting system criterion. It is also known as the "no show paradox". It has been defined as follows:* In a deterministic framework, the participation criterion says that the addition of a ballot, where candidate A is strictly preferred to candidate B, to an existing...

—Is voting honestly always better than not voting at all? (This is grouped with the distinct but similar Consistency Criterion in the table below.)
Condorcet criterion
Condorcet criterion
The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared with every other candidate, is preferred by more voters. Informally, the Condorcet winner is the person who would win a two-candidate election against each of the other candidates...

—If a candidate beats every other candidate in pairwise comparison
Condorcet method
A Condorcet method is any single-winner election method that meets the Condorcet criterion, which means the method always selects the Condorcet winner if such a candidate exists. The Condorcet winner is the candidate who would beat each of the other candidates in a run-off election.In modern...

, does that candidate always win? (This implies the majority criterion, above)
Condorcet loser criterion
Condorcet loser criterion
In single-winner voting system theory, the Condorcet loser criterion is a measure for differentiating voting systems. It implies the majority loser criterion....

—If a candidate loses to every other candidate in pairwise comparison, does that candidate always lose?
Independence of irrelevant alternatives
Independence of irrelevant alternatives
Independence of irrelevant alternatives is an axiom of decision theory and various social sciences.The word is used in different meanings in different contexts....

—Is the outcome the same after adding or removing non-winning candidates?
Independence of clone candidates
Strategic nomination
Strategic nomination is the manipulation of an election through its candidate set...

—Is the outcome the same if candidates identical to existing candidates are added?
Reversal symmetry
Reversal symmetry
Reversal symmetry is a voting system criterion which requires that if candidate A is the unique winner, and each voter's individual preferences are inverted, then A must not be elected. Methods that satisfy reversal symmetry include Borda count, the Kemeny-Young method, and the Schulze method...

—If individual preferences of each voter are inverted, does the original winner never win?

	Majority Majority criterion The majority criterion is a single-winner voting system criterion, used to compare such systems. The criterion states that "if one candidate is preferred by a majority of voters, then that candidate must win"....	Monotone Monotonicity criterion The monotonicity criterion is a voting system criterion used to analyze both single and multiple winner voting systems. A voting system is monotonic if it satisfies one of the definitions of the monotonicity criterion, given below.Douglas R...	Consistency Consistency criterion A voting system is consistent if, when the electorate is divided arbitrarily into two parts and separate elections in each part result in the same choice being selected, an election of the entire electorate also selects that alternative... & Participation Participation criterion The participation criterion is a voting system criterion. It is also known as the "no show paradox". It has been defined as follows:* In a deterministic framework, the participation criterion says that the addition of a ballot, where candidate A is strictly preferred to candidate B, to an existing...	Condorcet Condorcet criterion The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared with every other candidate, is preferred by more voters. Informally, the Condorcet winner is the person who would win a two-candidate election against each of the other candidates...	Condorcet loser Condorcet loser criterion In single-winner voting system theory, the Condorcet loser criterion is a measure for differentiating voting systems. It implies the majority loser criterion....	IIA Independence of irrelevant alternatives Independence of irrelevant alternatives is an axiom of decision theory and various social sciences.The word is used in different meanings in different contexts....	Clone independence	Reversal symmetry Reversal symmetry Reversal symmetry is a voting system criterion which requires that if candidate A is the unique winner, and each voter's individual preferences are inverted, then A must not be elected. Methods that satisfy reversal symmetry include Borda count, the Kemeny-Young method, and the Schulze method...
Inherently dichotomous preferences	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Arbitrary cutoff	No	Yes	Yes	No	No	Yes	Yes	Yes
Strong Nash equilibrium Strong Nash equilibrium A strong Nash equilibrium is a Nash equilibrium in which no coalition, taking the actions of its complements as given, can cooperatively deviate in a way that benefits all of its members... (Perfect information, rational voters, and perfect strategy)	Yes	Yes	No	Yes	No	No	Yes	Yes

Other issues and comparisons

Approval voting can allow voters to cast a compromise vote without abandoning their favorite candidate as long as voters accept the potential of that compromise vote resulting in the defeat of their favorite. Plurality voting can lead to voters abandoning their first choice in order to help a "lesser of evils" to win.
Counting ballots in approval vote is faster than some other alternative voting methods, such as ordinal systems, and can be completed at the local level.
If voters are sincere, approval voting would elect centrists at least as often as moderates of each extreme. If backers of relatively extreme candidates are insincere and "bullet vote" for that first choice, they can help that candidate defeat a compromise candidate who would have won if every voter had cast sincere preferences.
If voters are sincere, candidates trying to win an approval voting election might need to get as much as 100% approval to beat a strong competitor, and would have to find solutions that are fair to everyone in order to do so, whereas a candidate may win a plurality
Plurality voting system
The plurality voting system is a single-winner voting system often used to elect executive officers or to elect members of a legislative assembly which is based on single-member constituencies...

race by promising many perks to a simple majority or even a plurality of voters at the expense of the smaller voting groups.
Approval voting fails the majority criterion
Majority criterion
The majority criterion is a single-winner voting system criterion, used to compare such systems. The criterion states that "if one candidate is preferred by a majority of voters, then that candidate must win"....

, because it is possible that the candidate most preferred by the majority of voters, for example, winning 60% in a plurality election, will lose, if 65% indicate another candidate is at least acceptable to them. If 40% strongly dislike candidate A but like candidate B, and 60% mildly prefer candidate A over candidate B, approval voting might elect candidate B, whereas plurality
Plurality voting system
The plurality voting system is a single-winner voting system often used to elect executive officers or to elect members of a legislative assembly which is based on single-member constituencies...

would elect candidate A in a two candidate race.
Approval voting without write-ins is easily reversed as disapproval voting
Disapproval voting
Disapproval voting is any voting system that allows many voters to express formal disapproval simultaneously, in a system where they all share some power. Unlike most voting systems, it requires that only negative measures or choices be presented to the voter or representative...

where a choice is disavowed, as is already required in other measures in politics (e.g. representative recall
Recall election
A recall election is a procedure by which voters can remove an elected official from office through a direct vote before his or her term has ended...

).
Approval voting makes it much easier for voters to vote against a candidate by voting for several others instead of just one other, increasing the probability that some other candidate will win and thus that the first will not.
In contentious elections with large groups of organized voters who prefer their favorite candidate vastly over all others, approval voting may revert to plurality voting. Some voters will support only their single favored candidate when they perceive the other candidates more as competitors to their preferred candidate than as compromise choices. Range voting
Range voting
Range voting is a voting system for one-seat elections under which voters score each candidate, the scores are added up, and the candidate with the highest score wins.A form of range voting was apparently used in...

and Majority Judgment
Majority Judgment
Majority Judgment is a single-winner voting system proposed by Michel Balinski and Rida Laraki. Voters freely grade each candidate in one of several named ranks, for instance from "excellent" to "bad", and the candidate with the highest median grade is the winner. If more than one candidate has the...

allow these voters to give intermediate approval ratings, but at the cost of added ballot complexity and longer ballot counts.

Multiple winners

Approval voting can be extended to multiple winner elections. The naive way to do so is as block approval voting, a simple variant on block voting

Plurality-at-large voting

Plurality-at-large voting is a non-proportional voting system for electing several representatives from a single multimember electoral district using a series of check boxes and tallying votes similar to a plurality election...

where each voter can select an unlimited number of candidates and the candidates with the most approval votes win. This does not provide proportional representation

Proportional representation

Proportional representation is a concept in voting systems used to elect an assembly or council. PR means that the number of seats won by a party or group of candidates is proportionate to the number of votes received. For example, under a PR voting system if 30% of voters support a particular...

and is subject to the Burr dilemma

Burr dilemma

, among other problems.

Other ways of extending Approval voting to multiple winner elections have been devised. Among these are proportional approval voting for determining a proportional assembly, and Minimax Approval for determining a consensus assembly where the least satisfied voter is satisfied the most.

Ballot types

Approval ballots can be of at least four semi-distinct forms. The simplest form is a blank ballot where the names of supported candidates are 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 include spaces for write-in candidates as well.)

All four ballots are theoretically equivalent. 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. The "single bubble" format is incapable of producing invalid ballots (which might otherwise be rejected in counting).

Fraudulently adding votes to an approval voting ballot will not invalidate the ballot, (that is, it will not make it appear inconsistent), thereby making secure "chain of custody" of ballots important.

External links

Citizens for Approval Voting
Americans for Approval Voting
Approval Voting Article by The Center for Election Science
Approval Voting Free Association Wiki
Approval Voting: A Better Way to Select a Winner Article by Steven J. Brams.
Approval Voting on Dichotomous Preferences Article by Marc Vorsatz.
Scoring Rules on Dichotomous Preferences Article by Marc Vorsatz.
Approval Voting: An Experiment during the French 2002 Presidential Election Article by Jean-François Laslier and Karine Vander Straeten.
The Arithmetic of Voting article by Guy Ottewell
Critical Strategies Under Approval Voting: Who Gets Ruled In And Ruled Out Article by Steven J. Brams and M. Remzi Sanver.
Going from Theory to Practice:The Mixed Success of Approval Voting Article by Steven J. Brams and Peter C. Fishburn.
Strategic approval voting in a large electorate Article by Jean-François Laslier.
Spatial approval voting Article by Jean-François Laslier, published in Political Analysis (2006).
Approval Voting with Endogenous Candidates An article by Arnaud Dellis and Mandor P. Oak.
Approval Voting and Parochialism Article by Jonathan Baron, Nicole Altman and Stephan Kroll.

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Theory

Uses

Effect on elections

Sincere voting

Examples

Strategy with ordinal preferences

Dichotomous preferences

Approval threshold

Strategy with cardinal utilities

Strategy examples

Compliance with voting system criteria

Other issues and comparisons

Multiple winners

Ballot types

See also

External links