IRV advocates fire back at math prof.

Instant runoff voting advocates in Minnesota and nationally reacted strongly to a brief item published yesterday on The headline: “Mathematics expert: IRV not the answer.”

The piece was about mathematician Donald Saari, who gave a lecture Tuesday night at the U of M explaining why both traditional voting and instant runoffs can result in one candidate winning an election, even though most voters prefer someone else.


“What was the question posed to which Professor Saari responded that IRV is not the answer?” FairVote Minnesota Executive Director Jeanne Massey wrote in an e-mail not long after the story was posted.

FairVote successfully pushed for IRV in Minneapolis, which begins using the system in this November’s municipal elections. St. Paul voters will decide this year whether to switch to the system, too.

IRV allows voters to rank the candidates for a given office in order of preference. Winners are determined in a series of simulated runoff elections. This video explains it in just 90 seconds:

IRV supporters say it’s a better reflection of public opinion than so-called “plurality” elections. That’s the traditional system we’re all used to, where whoever gets the most votes wins.

But Saari, a mathematics professor at the University of California Irvine, says IRV suffers from many of the same problems as traditional plurality elections.

“We haven’t gotten rid of the cancer,” Saari said. “The plurality vote determines who’s going to go to the runoff. So, if we have a system that’s distorted and gets us the wrong two people for the runoff, we’re in trouble. The instant runoff does not solve any of the difficulties.”

In his U of M lecture, Prof. Saari used a simple example to make his point. Imagine you and 15 friends are trying to decide what beverage to serve at a party. There are three choices: wine, beer and milk.

This chart shows how everyone’s preferences break down:

beer wine milk.jpg

With a traditional plurality election, milk wins with 6 votes, even though 9 people consider it the least appealing choice. That’s why Saari calls it “one of the worst” voting systems.

With instant runoff voting, ballots are counted in rounds. To begin, you count the first choice votes: milk 6, beer 5, wine 4. Since no one has more than 50 percent of the vote, you eliminate the candidate in last place. That would be wine. The wine-lovers prefer beer to milk, and so beer wins the instant runoff against milk 9 to 6.

But Saari points out there’s a problem with that. While 9 of the voters prefer beer to milk, 10 of them actually like wine better than they like beer. Remember, 6 voters made beer their third choice. But instant runoff voting can’t see that, because it only counts the second choices of voters whose first choice is eliminated. Saari calls that “lost information.”

Saari says the best system of voting was the one developed by the French Mathematician Jean Charles de Borda in 1770. It starts out exactly like IRV: Voters rank the candidates from most to least favorite. And the vote counting is actually a lot simpler. Each rank is given a weight. With three candidates, it’s two points for a first-place ranking, one point for a second place ranking.

Using the Borda count, wine would come in first with 19 points, beer second with 14 points, and milk takes last place with 12 points — an outcome that will please the largest number of voters.

“The Borda count we now know is probably the strongest by far of any of the voting systems,” Saari said.

“Borda is a voting method that is mathematically neat, but utterly fails to be democratic in high-stakes elections because it is so easily and obviously manipulated through strategic voting,” responded Rob Richie, who works for the national arm of FairVote.

Richie argues Saari’s preferred system is too easily gamed by cunning voters, who would throw their second choice votes away on weak candidates, rather than casting them sincerely.

As for Saari’s critique of IRV, Richie says “there is no ‘perfect’ voting system that will satisfy everyone. That’s simply a fact, so you then try to do something that is better than what one has and fits in with voters’ expectations of what’s fair.”

For his part, Saari has another theory about why IRV advocates reject his analysis.

“They’ve spent a considerable amount of energy, time and money in putting forth a certain procedure,” Saari said. “It’s because of what they’ve invested that they’re not into it.”

  • Chuck Repke

    What is missed in these discussions is that we aren’t talking about choosing milk or beer with dinner. We are voting for Mayor and that is what is lost in the discussion.

    If you can name four of the candidates running for Mayor in Minneapolis, you spend to much time following politics and need a life. Yet, average voters are going to be asked to rank those candidates who they have never heard of until they walk in the booth.

    Because of IRV the voters in Minneapolis have lost any chance of actually having the Mayor debate a serrious opponent.

    And I’ll have a Coke

  • Colin

    Chuck, having seen plenty of boring local races, I’ll take a race with three candidates debating over a two horse race any day of the week. Typically, if there are only two candidates, the debate can devolve into either mudslinging or “I agree, I disagree”. You don’t leave much room for new ideas when the candidates are simply there to stand in the place of their political ideology. I expect to see issues raised in the Minneapolis mayor’s race which are rarely given the attention that they deserve.

  • chuck repke

    Well, Collin its September 25, and you haven’t herd anything yet. I wouldn’t hold my breath waiting for this IRV race to actually get interesting.

    And there isn’t three, there are eleven candidates and it will never get down to three and that is why you nor anyone else is ever going to actually see them debate anything. No media is ever going to cover the guys with the tin foil hats and their issues that “never get the attention they deserve.”

    IRV kills debate