Majority Choice Approval

Majority-choice approval (MCA) is a voting system in which the voter has three possible choices for rating each candidate: as ‘favored’, as an ‘accepted’ compromise, or as ‘disapproved’. An ‘affirmative’ mark (either ‘favored’ or ‘accepted’), signifies ‘approved’. An altenative designation can be: 'Support', 'uncertain or indifferent', and 'oppose', where 'support' only signifies approval, reducing the possibility of insincere voting that can occur with some other voting methods. MCA in its original form was devised by Forest Simmons in 2003.

In majority-choice approval, if at least one candidate is marked ‘favored’ by more than 50% of all voters, then the winner is a candidate with the highest number of favored marks. Otherwise, the winner is a candidate with the highest number of approved (i.e., favored or accepted) marks. This system elects a candidate who is favored by a majority, and rejects all candidates in case none gains majority approval (favored or accepted status).

This method allows multiple candidates to receive majority approval.

A numerical method of implementing majority-choice approval is to assign points for each option, and then sum the points. If 2 points are assigned for favored candidates, 1 point for accepted candidates, and 0 for disapproved candidates, the Majority-Choice Approval becomes a variation of range voting. The winner is the candidate with the highest number of points. If two or more candidates are tied for most points (or within the margin of error), the candidate with the most favored (2 point) votes wins.

An analogous method for support, indifferent, oppose would assign points of 1 for support, 0 for indifferent, and -1 for oppose. A positive tally would indicate the degree of support and a negative tally would indicate the degree of opposition.

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.

Commentary

Majority-choice approval satisfies the monotonicity criterion, the favorite betrayal criterion, the summability criterion, the independence of irrelevant alternatives criterion, the independence of clones criterion, the Strong Defensive Strategy criterion, and the Weak defensive strategy criterion. The participation criterion is satisfied for the point-value MCA method. The Consistency criterion is only satisfied when unitary value voting vectors are employed, such as (1,0,0) and (1,1,0).

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 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.

Example

Imagine an election for the capital of Tennessee, a state in the United States that is over 500 miles east-to-west, and only 110 miles 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:

• 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:

Suppose that voters were told to grant 2 points to any city they preferred, 1 point to any city they could accept, and 0 points to any city they do not want as the capitol. And then suppose they prefer only their first choice, but the next two are acceptable alternatives, and the last one is not acceptable.

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

If the voters granted 2 points to their top two choices, 1 point to their third choice, and no points to their last choice, the outcome would be:

Again, Nashville wins.

If the point-counting implementation was not used, but instead the original implementation was used, the results would be as follows: (Assume the voters favor the first city, accept the next 2 cities, and reject the last city.)

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.

Drawbacks

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.

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 does not satisfy the Majority criterion. A candidate with majority favored standing can still lose to a candidate with mixed favored and accepted votes. For example, at a committee meeting with ten members, using the (2,1,0) voting vector, candidate A gets 6 favored votes (12 points) and candidate B gets 4 favored votes (8 points). If every member who votes for A as favored (6) votes for B as accepted, then B gets 6 additional points. If every member who votes for B as favored (4) disapproves of A, then B wins with 14 points. B would also be the Approval winner, but by a different ratio. In this case, A is the Condorcet winner, the Borda winner and the Plurality winner.

It also follows from the above example that MCA does not satisfy the Condorcet criterion.

Comments on participation criterion

If we apply the "non-point" implementation of MCA to the example provided above, then MCA does not satisfy the Participation criterion. However if we apply the point system for counting MCA votes, then it becomes a variation of Range Voting, and hence it does satisfy the criterion. Here is an example:

Using the non-point-counting implementation:

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)

Here, the MCA winner is candidate A since A got a majority of the favored votes.

However, when 3 more voters add 3 B(favored), A(accepted), C(disapproved), then the MCA winner is candidate C. Candidate A no longer has a majority of the favored votes, but more voters approve of C than any other.

Using the point-counting implementation:

Candidate C wins with the most points – and candidate A's chances are hurt by the high disapproval.

By adding in 3 more votes, the result is:

Candidate C still wins even though the additional votes supported A and B over C.