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Encyclopedia > Majority Choice Approval

Majority-choice approval (MCA) is a voting system devised by Forest Simmons in April 2002 for use with three-slot ballots. That is, the voter has three possible choices for rating each candidate: ‘favored’, ‘accepted’, or ‘disapproved’. A rating of either ‘favored’ or ‘accepted’ signifies approval of the candidate. The Democracy Series Liberal democracy History of democracy Representative democracy Representation Voting Voting systems Elections Elections by country Elections by calender Politics Politics by country Political campaigns Political science Political philosophy Political parties Parties by country Parties by name Parties by ideology Voting systems are methods (algorithms) for groups of...

If at least one candidate is marked ‘favored’ by more than 50% of the voters, then the candidate marked ‘favored’ on the most ballots is elected. Otherwise, the winner is the candidate with the highest approval (i.e., the sum of ‘favored’ and ‘accepted’ marks). Ties can be broken based on the number of ‘favored’ marks.

Thus, MCA is equivalent to Bucklin voting with the voter only able to classify in two slots, but able to vote any number of candidates in those slots. Bucklin is a voting system that can be used for single-member districts and also multi-member districts. ...

Under an optional rule, when no candidate receives approval from a majority of the voters, all candidates are considered to be rejected by the voters. (See also None of the Above.) None of the Above (NOTA) is a ballot choice in some jurisdictions or organizations, placed so as to allow the voter to indicate his disapproval with all of the candidates in any voting system. ...

Another commonly suggested election method using three-slot ballots is to assign a number of points for each rating, and to elect the candidate with the greatest number of points. This results in the three-slot version of range voting, and would possess the particular properties of that method. Range voting, or average voting, or cardinal ratings is a voting system used for single or multiple-seat elections. ...

Voters may mark any candidate independently of other candidates: there is no limit on the number of candidates that may be marked into any one of the three categories. This independence of marking choice avoids the problem of overvoting. Such independence is lacking in forced-ranking methods such IRV and Borda count, and in some other constrained methods such as usual plurality voting. As a result, all these noted methods allow clone and spoilage problems in addition to overvoting. When the single transferable vote voting system is applied to a single-winner election it is sometimes called instant-runoff voting (IRV), as it is much like holding a series of runoff elections in which the lowest polling candidate is eliminated in each round until someone receives majority vote. ... The Borda count is a voting system used for single-winner elections in which each voter rank-orders the candidates. ... The first-past-the-post electoral system is a voting system for single-member districts, variously called first-past-the-post (FPTP or FPP), winner-take-all, plurality voting, or relative majority. ...

The name "Majority-Choice Approval" was suggested by Joe Weinstein.



Majority-choice approval satisfies the Majority criterion, the monotonicity criterion, the Independence of Clones criterion, and the summability criterion. The majority criterion is a voting system criterion, used to objectively compare voting systems. ... A voting system is monotonic if it satisfies the monotonicity criterion, given below. ... Strategic nomination is the manipulation of an election through its candidate set (compare this to tactical voting, where the manipulation comes from the voters). ... The summability criterion is a voting system criterion, used to objectively compare voting systems. ...

Plurality voting turns distinct but legitimate voter objectives into mutual spoilers: voters cannot both effectively support more than one favored, or support both a favored and a acceptable compromise candidate. The first-past-the-post electoral system is a voting system for single-member districts, variously called first-past-the-post (FPTP or FPP), winner-take-all, plurality voting, or relative majority. ...

The three levels in MCA is just enough for Favored, Compromise, and Disapproved, the minimum required for solving the spoiler problem without erasing the distinction between Favored and Compromise. This turns out to be an important distinction and is the main reason most IRV supporters believe that IRV solves the spoiler problem better than Approval does. This article or section should include material from Majority Choice Approval 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. ...

Majority-Choice Approval not only truly solves the spoilage problem in a way that incorporates the three-level distinction, but it also solves the quite different ‘majority-rule’ problem in a way that IRV cannot - you can't determine if the winner of an IRV vote won because of spoilage, genuine majority approval or one of many other procedural paradoxes that flaws IRV.

MCA is one of the voting methods used and advocated by the Florida affiliate of the American Patriot Party. See here and here. State nickname: Sunshine State Other U.S. States Capital Tallahassee Largest city Jacksonville Governor Jeb Bush (R) Official languages English Area 170,451 km² (22nd)  - Land 137,374 km²  - Water 30,486 km² (17. ... The United States Patriot Party, which is also known as the American Patriot Party, was founded on March 1, 2003 by several U.S. citizens who want to return the United States back to the original intent of the Founding Fathers and within the framework of the original U.S...


Imagine an election for the capital of Tennessee, a state in the United States that is over 500 miles (800 km) east-to-west, and only 110 miles (180 km) north-to-south. In this vote, the candidates for the capital are Memphis, Nashville, Chattanooga, and Knoxville. The population breakdown by metro area is as follows: State nickname: Volunteer State Other U.S. States Capital Nashville Largest city Memphis (largest metropolitan area is Nashville) Governor Phil Bredesen Official languages English Area 109,247 km² (36th)  - Land 106,846 km²  - Water 2,400 km² (2. ...

  • Memphis: 826,330
  • Nashville: 510,784
  • Chattanooga: 285,536
  • Knoxville: 335,749

If the voters cast their ballot based strictly on geographic proximity, the voters' sincere preferences might be as follows: Census. ...

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

26% of voters (close to Nashville)

  1. Nashville
  2. Chattanooga
  3. Knoxville
  4. Memphis

15% of voters (close to Chattanooga)

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

This shows that Nashville wins, and that everyone would accept Chattanooga as an alternative. (The majority of voters did not disapprove of Chattanooga.)

The results would be as follows: (Assume the voters favor the first city, accept the next 2 cities, and reject the last city.)

City Favor Accept Dislike
Memphis 42 0 58
Nashville 26 74 0
Chattanooga 15 85 0
Knoxville 17 41 42

No city is favored by a majority, so the city with most approval votes (favored + accepted) wins. Nashville and Chattanooga are tied at 100% approval since nobody voted against either. However, Nashville has more favored votes than the other, so it wins. The higher number of favored votes is what breaks the tie.


In its procedure for deciding a winner, in general, fails the Consistency criterion. It works one way under one condition and another way under another condition. As for almost all such hybrids, the method is inconsistent, in the sense that a candidate A may win all precincts but not the entire electorate. Here this inconsistency can occur if A wins some precincts on account of being majority favorite; but wins other precincts, which lack majority favorites, on account of being most approved. 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 alternative being selected, an election of the entire electorate also selects that alternative. ...

For instance, consider an electorate of two five-voter precincts, and a contest among five candidates A-E. Each marked ballot favors exactly one candidate X and accepts exactly one other candidate Y - symbolized below by the format XY.

Ballots in precinct #1 AB AB AB CB DB
Ballots in precinct #2 AB BA BA CA DE

A wins precinct #1 as the majority choice and precinct #2 as the most approved; but B wins the entire electorate as the most approved.

For Majority-Choice Approval (unlike some other methods) such inconsistency is easy to accept. The reason is simple: we prefer a majority favorite, which we may in fact happen to get in some precincts but do not necessarily expect to get overall.

MCA is not a Condorcet method, thus does not satisfy the Condorcet criterion. Any election method conforming to the Condorcet criterion is known as a Condorcet method. ... The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared in turn with each of the other candidates, is preferred over the other candidate. ...

MCA does not satisfy the Independence of irrelevant alternatives criterion. Independence of irrelevant alternatives is an axiom often adopted by social scientists as a basic condition of rationality. ...

MCA also shares a potential drawback with Approval voting: Voters may disapprove of all other candidates except their favorites. If a large majority of electors vote exclusively for their different favorites, the outcome of an election using MCA would resemble Plurality voting. There is, however, less incentive for voters to not vote for additional candidates under MCA than under Approval voting, as candidates rated 'favored' have an opportunity to win before being counted equivalently to those candidates rated 'accepted.' 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. ... The first-past-the-post electoral system is a voting system for single-member districts, variously called first-past-the-post (FPTP or FPP), winner-take-all, plurality voting, or relative majority. ...

Participation criterion failure example

The Participation criterion requires that a voter must not be able to obtain a preferable result from the election by not voting. Statement of Criterion Adding one or more ballots that vote X over Y should never change the winner from X to Y. Complying Methods Plurality voting, Approval voting, Cardinal Ratings, Borda count, and Woodalls DAC method all pass the Participation Criterion. ...

MCA does not satisfy this criterion. Example:

Assume that there are 100 voters and 3 candidates: A, B, and C.

51 A(favored), C(accepted), B(disapproved)
49 C(favored), B(accepted), A(disapproved)

Candidate A is elected, as A was 'favored' by more than half of the voters.

Now, suppose that three more voters are added:

51 A(favored), C(accepted), B(disapproved)
49 C(favored), B(accepted), A(disapproved)
3 B(favored), A(accepted), C(disapproved)

Now no candidate is 'favored' by more than half of the voters. Candidate C wins due to having the highest approval.

This is a failure of the Participation criterion, because by showing up to vote, the three additional voters caused their least favorite candidate to be elected.

External resources

  1. Forest Simmons' initial proposal of MCA
  2. Joe Weinstein coins the name "Majority-Choice Approval" and summarizes the method

  Results from FactBites:
Approval voting - Wikipedia, the free encyclopedia (1648 words)
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.
Historically, something resembling Approval voting for candidates was used in the Republic of Venice during the 13th century and for elections in 19th century England.
Approval voting passes the monotonicity criterion, in that voting for a candidate never lowers that candidate's chance of winning.
Choice (13725 words)
Our choices are foreseen and yet if we had made different choices, a different result would have occurred, which is why we have made the choices which we have made.
The choice that we have is to accept a God of wrath, and a prediction of wrath or to accept a God of love and the prediction of love.
A choice which will not be reversed despite occasional appearance to the contrary, a choice which was foreseen, a choice which was destined to be made, and the result of our choice is a destiny which has been foreseen and will be fulfilled, a love based environment.
  More results at FactBites »



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