IRV – Does the Math Work?

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I debated writing this post separately or including it in the open thread which already has some IRV comments here http://greenmountaindaily.com/…

I find IRV to be a confusing and debatable issue with adamant people on both sides of the issue. No matter what questions I’ve asked no one has clearly articulated exactly how it works, that is until I read Sunday’s Burlington Free Press My Turn by Burlington High School math teacher Andrew Mack.

I am not a candidate nor an office holder. I am simply your neighbor. One of the subjects I teach covers various nonweighted (each votes counts the same) voting methods: plurality, plurality with elimination (aka instant runoff, or IRV), Borda Count (used for the Heisman Trophy, among other applications), Condorcet (aka pairwise) and variations on these. The overall conclusion of this examination is represented by Arrow’s Impossibility Theorem, which states that no voting system satisfies all fairness criteria. For fun and by way of demonstration, our textbook has a sample election with preferential ballots formulated so that each of these methods produces a different winner.

Andrew has a well-written explanation that walks the reader through the election process step-by-step.  Read it here.  After a lengthy description, which one should read, Andrew says

…detailed study finds IRV to be the more fair method. The candidate with a majority of voter approval wins. More civil and intelligent debate informs the campaign. The “instant” feature ensures that the highest number of voters will decide the election. So why do some hold IRV in disfavor? Because IRV favors that ideological position which is in the majority. Those who object generally hold the less favorable view.

Today WDEV radio host Mark Johnson and Seven Days Columnist Shay Totten had an interesting discussion regarding IRV on Mark’s morning show.  You may want to listen to the podcast as a follow-up to insight regarding Burlington politics.  It will be interesting to see how today’s votes split.

More from Andrew – read his whole My Turn here.


So it is left to decide which system works best for the election being held. For elections to office, the two main contenders are plurality (most votes wins) and plurality with elimination (IRV). Our text states, “In spite of its frequent usage, the plurality method has several flaws and is generally considered a very poor method of choosing the winner of an election among several candidates.”

One thought on “IRV – Does the Math Work?”

  1. Your post is timely and it also reminds me of a post on the subject from 2006 as Burlington was adopting IRV:


    In any event, it seems clear to me that the buzz in Vermont is entirely too binary; either the current system or IRV – and that the debate over IRV is too binary as well; you’re either for it (and for more representational democracy) or against it. For my part, I support IRV (as I’ve said many times), but I also support a healthy, honest debate on the matter and recognize the unfortunate truth handed down by Arrow’s theorem. From Science News:

       Is there a best voting procedure? In 1952, Kenneth Arrow, a professor emeritus of economics at Stanford University in Palo Alto, Calif., proved that no voting system is completely free from counter-intuitive outcomes. Arrow looked at voting systems that satisfy two harmless-sounding properties. First, if everyone prefers candidate A to candidate B, then A should be ranked higher than B. Second, voters’ opinions about candidate C shouldn’t affect whether A beats B-after all, if you prefer coffee to tea, finding out that hot chocolate is available shouldn’t suddenly make you prefer tea to coffee. These sound like reasonable restrictions, yet Arrow proved that the only voting system that always satisfies them is a dictatorship, where a single person’s preferences determine the outcome. . . .  

    Or perhaps we’re just faced with another social manifestation of Heisenberg’s Uncertainty Principal. Perhaps if you look too closely at any human institution, process or component, the results get a little… fuzzy.

    All the more reason to move forward with deliberation and without dogmatic preconceptions or preconceived outcomes – but as always, to keep moving forward nonetheless.

    For more (and there is much more), check out the Proportional Representation Library and by all means come back and post on your favorite.

    Regardless of pros/cons (legitimate or imaginary), Burlington has shown that we can have a range of candidates who would either (1) not be in the mix without IRV, or (2) candidates who would not be taken seriously (e.g., Kurt Wright) without the benefit of IRV allowing them to campaign as legitimate candidates.

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