Citizendia
Your Ad Here

On an approval ballot, the voter can vote for any number of candidates.
On an approval ballot, the voter can vote for any number of candidates.
Electoral methods
This series is part of the
Politics and the Election series. A voting system allows voters to choose between options often in an Election where candidates are selected for public office. Politics Politics is the process by which groups of people make decisions An election is a Decision-making process by which a population chooses an individual to hold formal office
Politics Portal  view • talk • edit 

Approval voting is a single-winner voting system used for elections. 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 The two-round system (also known as the second ballot or runoff voting) is a Voting system used to elect a single winner The exhaustive ballot is a Voting system used to elect a single winner This article is about voting systems that use ranked ballots For alternative meanings see Preferential voting (disambiguation. The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters A Condorcet method is any single-winner election method that meets the Condorcet criterion, that is which always selects the Condorcet winner, the candidate Copeland's method is a Condorcet method in which the winner is determined by finding the candidate with the most pairwise victories The Kemeny-Young method is a Voting system that uses Preferential ballots Pairwise comparison counts and sequence scores to identify the Minimax is often considered to be the simplest of the Condorcet methods It is also known as the Simpson-Kramer method, and the successive reversal method The Borda count can be combined with an Instant Runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method. Ranked Pairs (RP or Tideman (named after its developer Nicolaus Tideman) is a Voting method that selects a single winner using votes that express The Schulze method is a Voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. Bucklin voting is the name of a Voting system that can be used for single-member and multi-member districts. The Coombs' method, also called the Coombs rule is a Voting system created by Clyde Coombs used for single-winner Elections in which Instant-runoff voting ( IRV) is a Voting system used for single-winner elections in which voters have one vote and rank Candidates in order of The Borda count is a single-winner election method in which voters rank candidates in order of preference Range voting (also called ratings summation, average voting, cardinal ratings, score voting, 0–99 voting, or the score A voting system allows voters to choose between options often in an Election where candidates are selected for public office. Proportional representation (sometimes referred to as full representation or PR is a category of electoral formula aiming at a close match between the percentage of votes Cumulative voting (also accumulation voting or weighted voting) is a multiple-winner Voting system intended to promote Proportional representation Mixed member proportional representation, also termed mixed-member proportional voting and commonly abbreviated to MMP, is an ' additional member ' Party-list proportional representation systems are a family of Voting systems used in multiple-winner Elections (e Open list describes any variant of Party-list proportional representation where voters have at least some influence on the order in which a party's candidates are elected Closed list describes the variant of Party-list proportional representation where voters can (effectively only vote for political parties as a whole and thus The D'Hondt method (mathematically but not operationally equivalent to Jefferson's method, and Bader-Ofer method) is a Highest averages method for The highest averages method is one way of allocating seats proportionally for representative assemblies with party list Voting systems. The largest remainder method is one way of allocating seats proportionally for representative assemblies with party list Voting systems. The Sainte-Laguë method of the highest average (equivalent to Webster's method or divisor method with standard rounding is one way of allocating seats proportionally for Single transferable vote (STV is a preferential Voting system designed to minimize Wasted votes and provide Proportional representation The Quota Borda System or Quota Preference Score is a Voting system that was devised by the British philosopher Michael Dummett and first published in 1984 in his The matrix vote can be used when one group of people wishes to elect a smaller number of persons each of whom is to have a different assignment The Additional Member System (AMS is a branch of Voting systems in which some representatives are elected from geographic constituencies and others are elected under Parallel voting describes a mixed Voting system where voters in effect participate in two separate elections using different systems and where the results in one election have Cumulative voting (also accumulation voting or weighted voting) is a multiple-winner Voting system intended to promote Proportional representation The single non-transferable vote or SNTV is an Electoral system used in multi-member constituency elections Limited voting is a Voting system in which electors have fewer votes than there are positions available Sortition, also known as allotment, is an equal-chance method of selection by some form of lottery such as drawing coloured pebbles from a bag A voting system allows voters to choose between options often in an Election where candidates are selected for public office. An election is a Decision-making process by which a population chooses an individual to hold formal office Each voter may vote for (approve of) as many of the candidates as they wish. 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. [1]

Approval voting is a form of range voting with the range restricted to two values, 0 and 1. Range voting (also called ratings summation, average voting, cardinal ratings, score voting, 0–99 voting, or the score Approval voting can be compared to plurality voting without the rule that discards ballots which vote for more than one candidate. 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

The system was described in 1976 by Guy Ottewell and also by Robert J. Weber, who coined the term "approval voting. Robert J Weber (born 1947 is the Frederic E Nemmers Distinguished Professor of Decision Sciences at the J " It was more fully published in 1978 by political scientist Steven Brams and mathematician Peter Fishburn. Steven J Brams (born November 28, 1940) is a game theorist and Political scientist at the New York University department of politics Peter C Fishburn (born 1936 is known as a pioneer in the field of decision making processes [2] Approval voting is used by some professional societies. Voting systems which incorporated aspects of approval voting have been used historically.

Contents

Uses

Approval voting has been adopted by the Mathematical Association of America (1986)[3] The Institute of Management Sciences (1987) (now the Institute for Operations Research and the Management Sciences),[4] the American Statistical Association (1987),[5] and Institute of Electrical and Electronics Engineers (1987). The Mathematical Association of America ( MAA) is a professional society that focuses on Mathematics accessible at the undergraduate level The Institute for Operations Research and the Management Sciences (INFORMS is an international society for practitioners in the fields of Operations research and Management The Institute for Operations Research and the Management Sciences (INFORMS is an international society for practitioners in the fields of Operations research and Management The American Statistical Association (ASA, a scientific and educational society founded in Boston Massachusetts on November 27, 1839, is the second The Institute of Electrical and Electronics Engineers or IEEE (read eye-triple-e) is an international Non-profit, professional organization According to Steven J. Brams and Peter C. Fishburn, only the IEEE has rescinded the decision. They report the IEEE Executive Director, Daniel J. Senese, as stating that approval voting was abandoned in 2002 because "few of our members were using it and it was felt that it was no longer needed. " Unlike the situation with MAA and ASA, Approval Voting was implemented by the IEEE board and rescinded by the board. [6]

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

Example

Tennessee's four cities are spread throughout the state

Imagine that Tennessee is having an election on the location of its capital. Tennessee ( is a state located in the Southern United States. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire electorate lives in these four cities, and that everyone wants to live as near the capital as possible. A constituency is any cohesive corporate unit or body bound by shared structures goals or loyalty

The candidates for the capital are:

The preferences of the voters would be divided like this:

42% of voters
(close to Memphis)		 26% of voters
(close to Nashville)		 15% of voters
(close to Chattanooga)		 17% of voters
(close to Knoxville)
  1. Memphis
  2. Nashville
  3. Chattanooga
  4. Knoxville
  1. Nashville
  2. Chattanooga
  3. Knoxville
  4. Memphis
  1. Chattanooga
  2. Knoxville
  3. Nashville
  4. Memphis
  1. Knoxville
  2. Chattanooga
  3. Nashville
  4. Memphis

Supposing that voters voted for their two favorite candidates and that Tennessee has 100 residents, the results would be as follows (a more sophisticated approach to voting is discussed below):

Effect on elections

The effect of this system as an electoral reform measure is not without critics. Memphis is a City in the southwest corner of Tennessee, and the County seat of Shelby County. Tennessee ( is a state located in the Southern United States. Electoral reform is change in Electoral systems to improve how public desires are expressed in election results Instant-runoff voting advocates like the Center for Voting and Democracy argue that approval voting would lead to the election of "lowest common denominator" candidates disliked by few, and liked by few, but this could also be seen as an inherent strength against demagoguery in favor of a discreet popularity. Instant-runoff voting ( IRV) is a Voting system used for single-winner elections in which voters have one vote and rank Candidates in order of FairVote is a Non-profit organization based in Takoma Park Maryland, whose mission is to achieve universal access to participation a full spectrum of meaningful In an editorial, approval voting advocates Steven Brams and Dudley R. Herschbach predict that approval voting should increase voter participation, prevent minor-party candidates from being spoilers, and reduce negative campaigning. Steven J Brams (born November 28, 1940) is a game theorist and Political scientist at the New York University department of politics Dudley Robert Herschbach (born June 18, 1932) is an American Chemist at Harvard University. [11]

One study [12] 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 (first round) - it instead would have chosen Chirac and Jospin. The 2002 French presidential election consisted of a first round election on 21 April 2002 and a runoff election between the top two candidates ( Jacques Chirac and This seems a more reasonable result since Le Pen was a radical who lost to Chirac by an enormous margin in the second round.

A generalized version of the Burr dilemma applies to approval voting when two candidates are appealing to the same subset of voters. 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 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. [13][14]

According to Brams, Approval voting usually elects Condorcet winners in practice. The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters [15]

Strategic voting

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. ' " [16] They also give a specific definition of a sincere approval vote in terms of the voter's ordinal preferences as being any vote that, if it votes for one candidate, it also votes for any more preferred candidate. Preference (also called " taste " or "penchant" is a concept used in the Social sciences particularly Economics. 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

Strategy with ordinal preferences

A sincere voter with multiple options for voting sincerely still has to choose which sincere vote to use. Voting strategy is a way to make that choice, in which case strategic approval voting includes sincere voting, rather than being an alternative to it. [17] 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. The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters In single-winner Voting system theory the Condorcet loser criterion is a measure for differentiating voting systems 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. [18] In one sense, conditions where this can happen are robust and are not isolated cases. [19] 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. [20]

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). [21] 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. [22] However, having dichotomous preferences when there are three or more candidates would not be typical. It would be an unlikely situation for all voters to have dichotomous preferences when there are more than a few voters. [17]

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. [23] 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. [16]

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. [17]

With threshold voting, it is still possible to not elect the Condorcet winner and instead elect the Condorcet loser when they both exist. The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters In single-winner Voting system theory the Condorcet loser criterion is a measure for differentiating voting systems However, according to Steven Brams, this represents a strength rather than a weakness of approval voting. Without providing specifics, he advocates that the pragmatic judgements of voters about which candidates are acceptable should take precedence over the Condorcet criterion and other social choice criteria. The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters [24]

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, so voting for a candidate can cause that candidate to win instead of a more preferred candidate. The later-no-harm criterion is a Voting system criterion formulated by Douglas Woodall On the other hand, approval voting satisfies the monotonicity criterion, so not voting for a candidate can never help that candidate win, but can cause that candidate to lose to a less preferred candidate. This article is about a voting system criterion See Monotonic function for a mathematical notion 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 von Nuemann-Morgenstern utilities, and the probabilities of how others will vote.

A rational voter model described by Myerson and Weber specifies an approval voting strategy that votes for those candidates that have a positive prospective rating. In Voting systems tactical voting (or strategic voting or sophisticated voting) occurs when a voter supports a candidate other than his or her Roger Bruce Myerson (born March 29 1951) is an American Economist and Nobel laureate recognised with Leonid Hurwicz [25] 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. In Economics, utility is a measure of the relative satisfaction from or desirability of Consumption of various Goods and services.

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.

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

Another strategy is to vote for the top half of the candidates, the candidates that have an above-median utility. When the voter has no knowledge of how other voters will vote, 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. [27]

Optimal strategic approval voting fails to satisfy the Condorcet criterion and can elect a Condorcet loser. The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters In single-winner Voting system theory the Condorcet loser criterion is a measure for differentiating voting systems Strategic approval voting can guarantee electing the Condorcet winner in some special circumstances. A Condorcet method is any single-winner election method that meets the Condorcet criterion, that is which always selects the Condorcet winner, the candidate 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. [28]

Strategy examples

In the example election described earlier, 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  
Faction 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 probababilities 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 without any knowledge of, or at least without any regard for, how other voters might vote. 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 this scenario, the winner is also the Condorcet winner.

Other issues and comparisons

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 whom 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:

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 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 and is subject to the Burr dilemma, among other problems. Proportional representation (sometimes referred to as full representation or PR is a category of electoral formula aiming at a close match between the percentage of votes 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

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 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 include spaces for 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.

See also

References

  1. ^ Brams, Steven and Fishburn, Peter (1983). The Borda count is a single-winner election method in which voters rank candidates in order of preference Bucklin voting is the name of a Voting system that can be used for single-member and multi-member districts. 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 A Condorcet method is any single-winner election method that meets the Condorcet criterion, that is which always selects the Condorcet winner, the candidate The Schulze method is a Voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. Instant-runoff voting ( IRV) is a Voting system used for single-winner elections in which voters have one vote and rank Candidates in order of Range voting (also called ratings summation, average voting, cardinal ratings, score voting, 0–99 voting, or the score A voting system allows voters to choose between options often in an Election where candidates are selected for public office. Approval Voting, Boston: Birkhäuser, p. 3
  2. ^ Brams, Steven and Fishburn, Peter (1978). "Approval Voting". American Political Science Review 72(3): 831-847
  3. ^ ,MAA Bylaws
  4. ^ INFORMS bylaws p. 7
  5. ^ ASA Bylaws
  6. ^ Going from Theory to Practice: The Mixed Success of Approval Voting
  7. ^ Lines, Marji (1986) "Approval Voting and Strategy Analysis: A Venetian Example" Theory and Decision 59: 155-172
  8. ^ Analysis of voting method for election of Doges in Venice
  9. ^ The Normative Turn in Public Choice, p. 4
  10. ^ http://www.unsgselection.org/files/WisnumurtiGuidelinesSelectingCandidateSecretary-General.pdf
  11. ^ Brams and Herschbach "The Science of Elections" (2001). Science 292 (5521): 1449. doi:10.1126/science.292.5521.1449. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.  
  12. ^ Results of experimental vote in France, 2002 (PDF, French)
  13. ^ Nagel, J. French ( français,) is a Romance language spoken around the world by 118 million people as a native language and by about 180 to 260 million people H. (2007) "The Burr Dilemma in Approval Voting" The Journal of Politics 69(1): 43-58 [1]
  14. ^ Nagel, J. H. (2006) "A Strategic Problem in Approval Voting," Mathematics and Democracy pp. 133-150. Studies in Choice and Welfare series (Springer)
  15. ^ Steven J. Brams, Mathematics and Democracy, Princeton University Press, 2008, p. 16, See also S. Brams and P. Fishburn, Going from Theory to Practice: The Mixed Success of Approval Voting (PDF)
  16. ^ a b Brams, Steven and Fishburn, Peter (1983). Approval Voting, Boston: Birkhäuser, p. 29
  17. ^ a b c Niemi, R. G. (1984) "The Problem of Strategic Behavior under Approval Voting" American Political Science Review 78(4) pp. 952-958
  18. ^ Yilmaz, M. R. (1999) "Can we improve upon approval voting?," European Journal of Political Economy 15(1) pp. 89-100
  19. ^ Saari, D. G. and Van Newenhizen, J. (2004) "The problem of indeterminancy in approval, multiple, and truncated voting systems", Public Choice 59(2) pp. 101-120
  20. ^ Saari, D. G. and Van Newenhizen, J. (2004) "Is approval voting an ‘unmitigated evil?’ A response to Brams, Fishburn, and Merrill" Public Choice 59(2) pp. 133-147
  21. ^ Brams, Steven and Fishburn, Peter (1983). Approval Voting, Boston: Birkhäuser, p. 31
  22. ^ Brams, Steven and Fishburn, Peter (1983). Approval Voting, Boston: Birkhäuser, p. 38
  23. ^ Brams, Steven and Fishburn, Peter (1983). Approval Voting, Boston: Birkhäuser, pp. 16-17
  24. ^ Brams, S. J. and Remzi Sanver, M. (2005) "Critical strategies under approval voting: Who gets ruled in and ruled out," Electoral Studies 25(2) pp. 287-305
  25. ^ Myerson, R. and Weber, R. J. (1993) "A theory of Voting Equilibria", American Political Science Review 87(1) pp. 102-114.
  26. ^ Brams, Steven and Fishburn, Peter (1983). Approval Voting, Boston: Birkhäuser, p. 85
  27. ^ Brams, Steven and Fishburn, Peter (1983). Approval Voting, Boston: Birkhäuser, p. 74, 81
  28. ^ Laslier, J. -F. (2006) "Strategic approval voting in a large electorate," IDEP Working Papers No. 405 (Marseille, France: Institut D'Economie Publique)

External links

Dictionary

approval voting

-noun

  1. A voting system in which each voter approves as many candidates as he wishes, and the candidate most approved of wins.
© 2009 citizendia.org; parts available under the terms of GNU Free Documentation License, from http://en.wikipedia.org
 Dapyx Software network: MP3 Explorer | Ebook Manager | Zenithic