Voting II – Can Ranked Choice Voting Save Democracies Around the World?

We tend to think of polarization and divisiveness as symptoms of the current administration in the U.S. and maybe they will just disappear with future elections; well that’s not going to happen.  This has been trending for over forty years and getting rid of Trump will not change this.  Putin’s efforts to undermine the institutions of democracies around the world exploits this vulnerability, but this only highlights how bad it can get. With or without Putin’s help polarization will bring an end to many democratic regimesMaybe you want to blame it on the Republicans or on the Democrats, but fortunately our people are not entirely to blame.  The origins of the problem are more systemic than that.  Our own two-party system is particularly vulnerable where platforms are built at the extremes with merit based on how fanatically it opposes the other side’s position.

A major part of the systemic solution is in understanding the role of the voting method we choose.

In my last article Voting I: Ranked choice voting is the real thing we discussed the popular algorithm called the “instant run-off” which simply reads;

“The candidate or choice with the fewest top place ranking is eliminated.  This is repeated in rounds (instantaneously) until someone gets a majority.”

I can recap the advantages of ranked choice voting as follows.

  1. You can put your preferred (but lesser-known) candidate at the top of your ballot without worrying that your vote will be wasted. (Let’s call it honest voting)
  2. Two similar candidates won’t have to worry about splitting a majority of voters who may like them both. (Let’s call it running together in the same lane without tripping)
  3. The instant run-off vote has been adopted for both primary and general elections across the country, but barring an exact tie, this method will always find a majority winner in a single election regardless of the number of candidates.  (let’s call it easier for voters and election officials alike)
  4. Perhaps the most important benefit is how it can prevent the extreme polarization we have seen in recent years.

Can we really counter polarization by changing the way we vote?  The answer is “yes” but we can do a lot better than this.  We may only have one chance to “get this right.”  And while we’re at it, we can do a better job of electing the candidates the people really want and I can prove it.  We are entering the “name-calling” phase where Democrats and Republicans label each other as Socialists and Fascists.  Most of us don’t want to be branded with either one of these labels.  Already 44% of us identify as Independents with moderates of both parties joining these ranks every day leaving the power to select our candidates in the hands of fewer and fewer extremists.  Clearly the best candidates are getting lost in the primaries.  Let’s take a closer look at the algorithm.

The ranked choice ballot allows you to give a lot more information about what kind of candidate you want.  On a standard ballot with 15 candidates there are only 15 ways to complete the ballot.  The same ranked choice ballot can be completed over a billion different ways.  How can we make the most of all that information?  Is there a better way to do this?   Well, let’s try changing the algorithm to read;

“The candidate or choice with the fewest top place ranking is eliminated.  This is repeated in rounds (instantaneously) until someone becomes a Condorset winner.”

What the heck is that?  Let me start by saying a Condorset winner (also known as pairwise selection) is the gold standard.  Our two-party system exists because it helped reduce the field to two candidates, thus assuring that someone gets a majority.  But we certainly made a mess of “how we select the final two.”  Instead of reducing the field, pairwise selection compares every possible head to head matchup declaring a winner in each pair.  Where C is the number of candidates and M is the number of matchups

M = (C*(C+1))/2    e.g. if C = 10 then M = (10*11)/2 = 55 matchup elections

If one of these ten candidates wins matchups against all nine of his opponents, he will obviously win in the final round.  We can see this in the example below.  After seven elimination rounds no one has yet gathered a majority but there is a Condorset winner.  The pairwise chart on the right shows that M, the Condorset winner beats both R and D in head-to-head matchups making him the indisputable winner.  We are left with R, a right-wing Republican, M, a moderate Republican and D, a Democrat.  40% of ballots rank in order RMD, 31% rank them MRD while 29% rank them DMR.  R with the most (40%) first place votes would be a plurality winner.  But in an instant run-off D with the fewest (29%) first place votes is eliminated.  M inherits these votes making him a 60% majority winner in the final round.  In a competitive race pairwise selection favors moderate candidates or compromise choices which is exactly what we want to counter polarization.




But there is a problem.  Say the D picks up few votes from M in a last minute “get out the vote” drive.  Now the M with 29% has the fewest first place votes and is eliminated.  R inherits all of M’s votes making him a 69% winner in the final round.  That’s not cool!  Democratic voters get punished for the extra effort.

Anomalies like this give its critics ammunition to defeat ranked choice voting legislation.  That’s why we must get it right and the pairwise solution is always right.  If there’s a Condorset winner the election is over.  With ten candidates there could certainly be a Condorset winner, but as long as ballots are completed by humans who are by nature “conflicted” there is a high probability that there will be no immediate winner.  We must therefore resort to an imperfect method to reduce the field until a winner is found.  The problem with the “instant run-off” not only could it eliminate an identified Condorset winner if allowed to proceed, but it can eliminate would-be Condorset winners before they are identified.  There are other algorithms such as Coombs Rule (The candidate or choice with the most last place ranking is eliminated) which are far less likely to eliminate a “would-be winner.”  My preference is what let’s call “balanced elimination.”

balanced elimination;  half of your vote (+1/2) is credited to your top choice and half of your vote (-1/2) is debited from your last choice.  The candidate(s) with the lowest balanced elimination score is eliminated.

Since every ballot records a total of zero points 1/2 + (-1/2) = 0 the average score is zero.  Now say a candidate was ranked second on every ballot, he could still be a Condorset winner despite having the lowest possible instant run-off score of zero and the highest rating by Coombs Rule.  Balanced elimination gives him an average score of zero guaranteeing he will live to see another round.  That would make the algorithm;

“The candidate or choice with the lowest balanced elimination score is eliminated.  This is repeated in rounds (instantaneously) until someone becomes a Condorset winner.”

Maybe I’ve convinced you that balanced elimination is a much better solution, but convincing you is just half the job.  We must bring politicians on board with this idea and for this I will need your help.  Politicians can’t be moved by logical arguments, so we must show them a political argument.  Please stay tuned for my next post, “Politicians, If You Can’t Beat ‘um, Join ‘um.”