This is part three of a series analyzing the 12 best voting-systems. See the introductory article for the series here. The five voting systems described here, although less well known, are an essential ingredient to this series of articles constituting my magnum opus on election methods. The five systems discussed below are:

• MMPOsc (MinMax Pairwise Opposition symmetric completion)
• IC,MMPO (Improved Condorcet, MinMax Pairwise-Opposition)
• MAM (Maximize Affirmed Majorities)
• MAPW2 – (Majority-Approval Pairwise)
• MAPW

(The numbering below is continued from previous article)

8. MMPOsc:

That stands for “MinMax Pairwise Opposition symmetric completion.” You vote a candidate-ranking. The winner is the candidate over whom fewest voters have ranked some same other candidate. To say it more wordily, but maybe more clearly:

For each candidate, find which other candidate is ranked over hir by the most voters. The number of voters ranking that candidate over hir is hir “max defeatedness”.

The winner is the candidate whose max defeatedness is the least.

An additional rule:

For any pair of candidates that you don’t rank, you’re counted as ranking each one over the other, with half of a vote.

9. IC,MMPO:

“IC,MMPO” stands for “Improved Condorcet, MinMax Pairwise-Opposition”. This is a 2-part method, making its definition a little longer:

1. First, find out who is unbeaten:

X beats Y if the number of people ranking X over Y is greater than the number of people ranking Y over X, plus the number of people ranking both X & Y at top.

In other words, the only thing different about this definition of “beats” is that ranking both candidates at top counts as a vote against either one beating the other.

The purpose of that unusual definition of “beats” is to avoid any possible incentive to rank a compromise over your favorite. Without it, a search for an unbeaten candidate would create such an incentive for some voters.

2. Choose among the unbeaten candidates by MMPO.

For the purposes of determining a candidate’s max defeatedness in this MMPO-count, use hir greatest defeatedness by any candidate, not just the unbeaten ones. (This second rule is likewise for the purpose of avoiding any incentive to vote a compromise over your favorite.)

Advantages:

Electing an unbeaten candidate is, of course, an advantage. Also, this method improves on MMPOsc’s protection between your upper & lower middle-ranked candidates. (Details in the Comparisons section.)

10. MAM:

MAM stands for “Maximize Affirmed Majorities”.

1. X “beats” Y if more people rank X over Y than vice-versa.

2. If X beats Y, then Y has a “defeat” by X.

3. The strength of a Y’s defeat by X is measured by the number of people who rank X over Y.

4. A “cycle” is a cyclic sequence of defeats, such as X beats Y beats Z beats X.

5. A defeat is “affirmed” if it isn’t the weakest defeat in a cycle whose other defeats are affirmed.

The part of this definition that distinguishes MAM from other Condorcet methods is that latter paragraph, paragraph #5.

Paragraph #5 is stated briefly, recursively. It defines the method, but it doesn’t tell a procedure.

So, here is a procedure to achieve what paragraph #5 calls for:

a) Arrange all of the pairwise defeats in a vertical list, ordered with the stronger defeats higher in the list.

b) Starting from the top, consider each defeat as follows:

Affirm it if it isn’t in a cycle with defeats that have already been affirmed.

Otherwise, skip it and consider the next defeat in the list.

c) When you’ve considered each defeat in the list, of course some of them will be affirmed.

That’s the procedure for determining which defeats are affirmed.

Now, resuming the rules:

6. A candidate wins if s/he has no affirmed defeats.

As you notice, MAM’s definition is wordy. But, once the definitions of “beats”, “defeat” “cycle”, & “defeat-strength” have been said, the recursive (non-procedural) version of paragraph #5 is all that’s needed, and that paragraph says it very briefly, with one sentence.

Advantages:

For a pairwise-count method, MAM gives the best protection from the kinds of offensive strategy that pairwise-count methods are subject to. That’s largely because, in addition to being fully truncation-proof (as are MDDA & IC,MMPO), MAM deters (instead of merely foiling) burial. Those 2 offensive strategies will be defined in the Comparison section.

Disadvantages:

Doesn’t have an easy, built-in way to avoid the chicken-dilemma. (IRV, Benham, MDDA, MDDAsc, MMPOsc, & IC,MMPO, MAPW, & MAPW2 do have that.)

Doesn’t meet FBC, meaning that, for some overcompromisers, there can be some strategic incentive to rank a compromise over their favorite. (Approval, Score, Bucklin, MDDA, MDDAsc, MMPOsc, & IC,MMPO, MAPW, & MAPW2 meet FBC.)

11. MAPW2:

“MAPW” stands for “Majority-Approval Pairwise. The “2” refers to the fact that it’s a 2nd version (the 1st version is defined next). Here is the definition of MAPW2:

Balloting:

You can rank, in order of preference, the candidates you most want to win. You’re counted as approving all of the candidates you rank, but you can individually un-approve any 1 or more candidates that you want to.

Count:

1. If no one is majority-approved (approved by a more than half of the voters), then just do MDDA, MDDAsc, MMPOsc, or IC,MMPO.

2. If 1 candidate is majority-approved, s/he wins.

3. If 2 or more candidates are majority-approved, then choose among them by MDDA, MDDAsc, MMPOsc, or IC,MMPO.

…but, for the purposes of that MDDA, MDDAsc, a candidate is majority-disqualified if any candidate (not just a majority-approved candidate) is ranked over hir by a majority. For the purpose of MMPOsc or IC,MMPO, a candidate’s greatest pairwise-opposition is hir greatest pairwise opposition among all of the candidates, not just the majority-approved ones.

(That provision in the paragraph before this one is for the purpose of avoiding any incentive to rank a compromise over your favorite.)

Meets FBC & provides an easy way to avoid chicken-dilemma (as do MDDA, MDDAsc, MMPOsc, IC,MMPO, & MAPW).

Advantages:

More Approval-like than MDDA or MDDAsc is.

Disadvantages:

Its greater Approval-likeness, and its lesser use of pairwise defeats, and the fact that it sometimes chooses entirely by Approval—Those things make less suitable to satisfy the needs &/or wants of people who need or want rankings. …and satisfying those needs &/or wants is one of the reasons to use rankings.

Because of that disadvantage, I wouldn’t propose MAMDDA to current electorates. But its greater Approval-like-ness, for a method without a chicken-dilemma problem, might be desirable for some future electorates.

12. MAPW:

MAPW stands for “Majority-Approval Pairwise”

Balloting:

You rank the candidates whom you most want to win. You’re counted as approving all the candidates you rank, but you can individually un-approve any 1 or more candidates you want to.

Count:

1. If no one is approved by more than half of the voters, then do MDDA, MDDAsc, MMPOsc, or IC,MMPO.

2. Otherwise, elect the most approved candidate.

Advantages:

Meets FBC, and provides a convenient, easy, reliable way to avoid chicken-dilemma.

Similar to MAPW2, with same advantages & disadvantage, but uses Approval more, and pairwise-count less.

It’s MAPW2, but moreso.