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.

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.

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.)

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.

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.

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


Majority-choice approval satisfies the monotonicity criterion and the independence of clones criterion. It would satisfy the majority criterion were it not for the fact that voters are allowed to mark more than one candidate as Favored.

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 an acceptable compromise candidate.

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.

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.


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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.)

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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.

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.

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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.

MCA does not satisfy the Independence of irrelevant alternatives criterion.

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.'

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.

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
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