Friday, October 20, 2017

Guest Post: Free Voting Method and Bad Apple Sorts

This is a guest post from Mike Sawyer who runs a blog at Dare to Ask! and who collaborates with Prof. Brian Zurowski of Davidson College.  Mike has some great ideas to promote ranked-choice voting and also how to allow voters to express more information about their preferences.

When Brian Zurowski and I started a project on voting theory, we needed a mission statement to keep us on track and avoid duplicating the good work of so many others.  Our mission statement is:

To familiarize the public with and build trust in Ranked Choice Voting 
thus paving the way to better group decision making at every level.

The vast majority of group decisions that most of us encounter are small, often casual in nature.  Small elections pose some unique problems.  Jeff O’Neill talked about a few of these in his blog article Elections with a Small Number of Voters.  But exposing the public to small less consequential elections is the best way to build trust so we needed to solve these problems.  The first question we must ask is, “How can we build trust in any voting method when seemingly all methods can disagree about how to find the one right choice?”  A voter doesn’t have to be familiar with Arrow’s Impossibility Theorem to see the problem.  Actually mathematicians created this problem by framing the objective too loosely saying the perfect voting method must reflect the “will of the people.” In our view this phenomenon is as my grandmother would say is, “a blessing in disguise.”  Simply put, “the will of the people” can have an entirely different meaning for a close-knit cooperative group of friends than it would in say a hotly contested political election.  The challenge is this, “Can we tailor the voting algorithm to the ‘mood’ of the election?”

To demonstrate, let’s compare the instant runoff voting method to the Coombs method.  With the IRV method we successively eliminate the choice with “the fewest first place rankings” while with Coombs we successively eliminate the choice with “the most last place rankings.”  Run these two algorithms on a series of randomly generated ballots and you will likely have a close election in which the two methods agree as to the best choice.  In the real world ballots are not randomly generated; that’s the whole point of elections.

We often expect individual voters will have a “positive focus” (focus on their top or top few choices) but a decision among friends is more likely to have a “negative focus” (focus on their bottom few choices).  Let’s say a group of friends are deciding which movie to see.  Depending on genre you’re probably happy to see most of the new movies as long as you haven’t already seen it.  You have a negative focus because your first criterion is that it be one you haven’t yet seen.  It is likely that everyone in your group has not only a similar negative focus but also prefer to select a movie no one in the group has seen.  This calls for the more “inclusive” Coombs algorithm, because it’s more likely to eliminate everyone’s last choice(s) than the more “competitive” IRV.  I prefer to call Coombs voting a BAS (bad apple sort) because it’s like successively throwing out the worst apple in the basket until only the prize apple remains.

While in the case of selecting a movie or a meeting time, we can make an educated guess that most voters will have a negative focus best served by a more inclusive algorithm; this is not always the case.  In the 2016 Republican primary some voters were for Trump and some wanted “anyone but Trump.” The primary was determined by a plurality vote, which by definition the most “competitive” voting method.  Focus is a personal matter, so it was manifestly unfair for all voters to be stuck with a competitive method.  So the next question is, “Can we allow individual voters control the focus of their own vote?”  This turns out to be easier than I would have expected.

There is a hybrid between IRV and BAS, where each choice is scored (number of first place votes less number of last place votes) and the choice with the lowest score is successively eliminated until only the winner remains.  For tidiness we would design it so half of your vote is “credited” toward your first choice and half is “debited” against your last choice.  If you credit 100% of your vote to a positive focus this duplicates IRV results, while if you debit 100% to a negative focus you have placed a BAS vote.  But since “focus” is a personal in nature, why not let each voter decide how much of his single vote to credit or debit by clicking on a slide bar (avoiding even fractions)?  Rather than guessing whether a “competitive” or “inclusive” algorithm best serves the group, we just let the voters set these parameters.  As a bonus the resulting odd fractions almost guarantee no ties in any elimination round thus solving another common problem with small elections.

Another common form of voting approval voting offers its own unique advantages.  Here you can place one vote for each acceptable choice, as many as you want.  Think of these acceptable choices as “peas in a pod” and your vote says, “I’ll take any one of these.”  By being more flexible you increase the odds that one of these will win but lose control of picking between the peas in the pod.  Would it make sense to allow voters to insert a “pod” instead of a single choice on their ranked choice ballot?

To see the logic of using pods you need only imagine you are voting (say instant runoff) on a list of restaurants for your groups luncheon tomorrow. Your preference is Mexican cuisine and you see three Mexican restaurants on the list, but you’ve been to none of them, so you group them in a pod and rank the pod first on your ballot. It’s not that just any one will do, but your best bet is the one others rank highest. This is tallied by counting one first place vote for each choice in the pod reducing the chance that any of the three will be eliminated. This is in effect an approval vote followed by individual rankings.

You might have ranked this pod in second place in which case the pod (with its surviving members) becomes an “approval pod” only when your first choice is eliminated. In fact a ballot could have multiple pods by simply stringing together consecutive choices that have only trivial differences. An RCV ballot with five choices would have not just 120 voter profiles but 520 (if I did that right). “Approval Pods” (or perhaps Coombs disapproval pods) should be possible with most single winner RCV algorithms. Effective use of approval pods may gain a small strategic advantage for more flexible voters, but for the most part the choice is a trade-off sacrificing “selection” (the ability to choose between “peas” or pod members) in exchange for “protection” (greater assurance that at least one pod member will survive).

The voters will handle pods by giving all its peas the same numerical ranking while the algorithm will treat all omitted choices as a last place pod (the field pod).  All this may not make the process of voting any easier for the average voter.  In fact we know he will have a lot more to consider as well as a lot more to say with his vote.  If he wants he can still cast a simple plurality vote, a regular approval vote, a standard IRV or BAS.  He can also mix any blend of these he wants.  It may seem challenging, but I can tell you after years of coffee drinking I still haven’t found the perfect blend and I’m still trying.

Brian and I agree this method which we might call “free voting” will serve voters well in small elections but have dissenting opinions on how well this might be accepted in larger political elections.  My opinion is, “It doesn’t matter” as long as it works for the small casual electorate.  It serves the objective of building trust in RCV.  The way voters use it will tell us something about their preferred voting method we can use as a guide in larger elections.  And after all it may just work.

The critical size threshold is where scientific polls and professional campaigns come into play, not to mention the influence of foreign powers.  Today’s average voter is clueless about the relationship between competitive voting and the polarized political atmosphere.  A political campaign where the objective is for your candidate is “be liked by the most voters” is quite different from one where the objective is “be disliked by the fewest voters.”  Highlighting the difference are strategies such as belittling your opponent which swells the ranks of both these groups.  If we can develop a voting app that brings the differences to light and empowers voters to react to the threats it would be a great service.

After thoughts:

  • I’m going to throw this out.  It occurred to me a two-stage elimination algorithm might give us purer results (just a hunch).  By purer I mean a greater success rate against the tests in Arrows Impossibility Theorem.  Stage-one would be to remove the choice with the highest score to a “safe zone” and then successively repeat this process on the remaining choices until the last choice not moved to the safe zone is eliminated. Stage-two is to do it again and again eliminating one choice per round.
  • I am an advocate of BAS voting because it strongly counters polarizing campaigns.  Everybody claims to hate mudslinging ads, but we all know the work and they work by creating divisiveness. I’m not sure how this argument carries with the public.  But divisiveness is the very same tool the Russians have used to disrupt the democratic process.  Developing the argument around foreign interference just might be much more powerful.