Voter participation and majority rule are often considered the heart of democracy. However, the most common form of single-winner voting in the United States — “one person, one vote” (technically known as Plurality or First Past the Post) — implicitly assumes there are only two candidates. When there are more than two candidates, not only is there a risk that no candidate will get an absolute majority (versus a plurality), but voters are faced with the dilemma between voting ‘strategically’ (for the lesser of two evils) vs. ‘sincerely’ (for whom they feel is the ‘best’ candidate). This dilemma tends to promote a two-party system, which despite its many merits is vulnerable to systemic bias (as evidenced by low voter turnout, due to a perception that neither party offers a meaningful choice). The end result is that candidates lack a true majoritarian mandate, due both to low voter turnout and the possibility of a split vote.
To address these problems, we recommend an alternate election system we call Maximum Majority Voting, or MMV [1]. Maximum Majority Voting is based on the latest research into election reform, but is still designed to be as simple as possible to use and understand. Each voter simply fills out a ranked ballot, listing the candidates in order of preference. The winner is the candidate with the largest majority voting for them over other candidates. By specifying a complete set of preferences, you never have to worry about “wasting your vote”; e.g., if your most-preferred candidate doesn’t win, your vote still helps your second choice to beat your third (or worse) choice. Thus, you can still vote your conscience without giving up the ability to influence the election.
While there are several forms of ranked voting[2], Maximum Majority Voting is one of the best at reducing the need for strategic voting[3]. The reason you generally don’t need to vote strategically under MMV is that each election is broken down into a series of one-on-one matchups, like a round-robin tournament. For each pairing of candidates A and B, MMV compares the number of voters who prefer A over B (often written “A > B”) to those who prefer B over A (“B > A”). Each voter’s list of preferences is interpreted in terms of these pairwise contests, so a vote of “A > B > C” implies A > B, A > C, and B > C. Even if the top two candidates are B and C, it still doesn’t hurt for me to vote for A first, since my vote for B > C counts just as much as my vote for A > B. Thus, all of each voter’s preferences are used to determine the final ranking, rather than treating higher or lower-preferences separately.
In addition to reducing the need for strategic voting, MMV provides a number of other benefits:
Thus, in contrast to traditional Plurality voting, MMV actually becomes more effective — rather than more polarized — with more candidates and greater citizen involvement. In the place of a splintered and disenfranchised electorate, it can actually help us find and elect candidates who reflect our underlying shared values.
The formal definition of Maximum Majority Voting involves six phases:
Each voter votes for all the candidates they like, indicating order of preference if any.
Consider an example in a five-candidate election, where a voter likes A most, B next, and C even less, but doesn’t care at all for D or E. In that case, their ballot would be “A > B > C > D = E”; this can be shortened to “A > B > C” since unranked candidates are considered to be at the bottom and equivalent. Similarly, if another voter liked E most, considered D and C tied for second, and ranked B over A, their ballot would be “E > D = C > B > A” (with the last “> A” being optional, since it is redundant).
Each ballot defines preferences based on one cycle of pairwise matchups between each of the candidates.
Thus, the ballot A > B > C would be interpreted as:
A > B, A > C, A > D, A > E B > C, B > D, B > E C > D, C > E
while “E > D = C > B > A” would be:
E > D, E > C, E > B, E > A D > B, D > A C > B, C > A B > A
When all the balots are counted, this gives a final score for each matchup. [4].
Say we have nine voters, who voted as follows
4: A > B > C 3: E > D = C > B 2: C > A > D
this gives:
6/3: A > B 4/5: A > C 6/3: A > D 6/3: A > E 4/5: B > C 4/5: B > D 4/3: B > E 6/0: C > D 6/3: C > E 2/3: D > E
Note how some matchups add up to less than 9, because some candidates were given equal preference by some voters. Also, the total number of matchups for N candidates is always N * (N-1)/2, or 10 for N = 5.
Next, the matchups are sorted from the largest win to the smallest. If two matchups have the same number of winning votes, the one with the largest margin (weakest loser) is listed first. It is also possible for two matchups to have the exact same score; while such “same-size majorities” are extremely unlikely in public elections, they could well occur in small committees.
The ballots above would thus be reordered to give:
6/0: C > D 6/3: A > B 6/3: A > D 6/3: A > E 6/3: C > E 5/4: C > A 5/4: C > B 5/4: D > B 5/4: E > B 3/2: E > D
This list of matchups is used to rank the candidates, starting from the largest win on down. The order is important, because in rare cases [5]a later matchup may conflict with an earlier one:
(i) If a matchup later in the list conflicts with the previously-determined order, the latter matchup is superseded (ignored).
(ii) In the even unlikelier case where several matchups with same-size majorities conflict with each other, all such conflicting matchups are ignored (though any non-conflicting matchups of that size are still included).
[6].
Stepping through the ordered list of matchups above, we find (using [X,Y] for unordered candidates):
1: C > D (C > D) 2: A > B, C > D (A > B) 3: A > B, [A,C] > D (A > D) 4: A > [B,E], [A,C] > D (A > E) 5: A > B, [A,C] > [D,E] (C > E) 6: C > A > [B,D,E] (C > A + A > B => C > B) 7: C > A > [B,D,E] (C > B already assumed) 8: C > A > [D > B, E] (D > B) 9: C > A > [D,E] > B (E > B) 10: C > A > E > D > B (E > D)
Based on the above, we see that MMV typically generates a strict ranking of candidates in the order they were preferred by the most voters (unless all the pairwise matchups for multiple candidate are precisely identical). The winner is thus the top candidate, i.e. the one with the Maximum Majority. In the extraordinary case there really is a complete tie among all the top candidates, then the winner would need to be chosen by some external mechanism.[7].
Since Maximum Majority Voting uses all the information available, and weights larger majorities over lesser ones (in case of conflict), it will always reflect the Maximum Majority of the electorate to the maximum extent possible – no matter how many candidates. This should allow for greater choice among candidates, and greater involvement from voters. While electoral reform may not solve all our political problems, by increasing competition it allows us to encouarge higher-quality candidates, thus opening the door to a more representative and accountable democracy.
Ernest N. Prabhakar, Ph.D.
Founder, RadicalCentrism.org
February, 2004
RadicalCentrism.org is an anti-partisan think tank based near
Sacramento, California, which is seeking to develop a new paradigm of
civil society encompassing politics, economics, psychology, and philosophy. We
are dedicated to developing and promoting the ideals of Reality,
Character, Community & Humility as expressed in our Radical Centrist Manifesto:
The Ground
Rules of Civil Society.
For example, given the following results from 9 voters:
4 votes of A > B > C (over D and E) 3 votes of D > C > B (over A and E) 2 votes of B > A (over C, D and E)
The pairwise matrix (sometimes called the Condorcet matrix) would be:
A B C D E A - 4 6 6 6 B 5 - 6 6 9 C 3 3 - 5 7 D 3 3 3 - 3 E 0 0 0 0 -
One Comment on “Maximum Majority Voting”
I think Andrew Yang is doing a credible job of introducing people to the idea: https://www.forwardparty.com/ranked_choice_voting
While I’m not a huge fan of the specific implementation of Instant-Runoff Voting, it’s still a big step forward, and opens the door for other refinements down the road.
Also, there is potential for introducing this idea to crypto communities, which are highly technical (and fully automated). Perhaps later in 2022, via the Datocracy movement...
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