Kenneth Arrow, now a professor emeritus at Stanford University, identified what he perceived as a fundamental flaw in our democracy: Put simply, he argued that devising a perfectly fair voting system is mathematically impossible.

For decades, there was almost a kind of despair among voting theorists of getting any better system than we had. What’s interesting, though, is that the impossibility theorem doesn’t apply to systems where you score the candidates rather than rank them. With scoring, you’re essentially filling out a report card—if you think there are two candidates who deserve four stars you can give them both four stars—whereas with ranking you have to artificially give one a number one and one a number two. That turns out to be crucial.

What does the Constitution say about how we elect people?
It’s kind of funny. When we first wrote the Constitution there’d been a lot of thought in revolutionary France about what’s the best way to vote, and they basically discovered the spoiler effect and a lot of these problems Arrow was addressing. And because of that, the founders really didn’t guarantee anyone the right to vote for president or Congress or anything in the Constitution. The democracy we have now is kind of a retrofit

Briefly summarizing the pros and cons of the various voting methods, let’s start with our current system.

Plurality voting is the simplest system possible because each person casts one vote for one candidate, so it’s very easy to count votes and so forth. The con, the one thing on which all the experts basically agree, is that plurality is the least fair of all the systems.

Briefly summarizing the pros and cons of the various voting methods, let’s start with our current system.

Plurality voting is the simplest system possible because each person casts one vote for one candidate, so it’s very easy to count votes and so forth. The con, the one thing on which all the experts basically agree, is that plurality is the least fair of all the systems.

How about Borda?
The first modern system invented to try and better plurality voting was the Borda count, invented in 18th-century France by a guy named Jean-Charles de Borda. Unfortunately, it’s very easily manipulated.Borda basically said, “My system is intended for honest men,” and people weren’t entirely honest.

Condorcet?
Condorcet was Borda’s great rival. He had a system where you rank the candidates, but the idea is that whichever candidate can beat all the other candidates in two-way races should be the winner. The main problem is sometimes you don’t have a candidate who beats everyone else. You can actually have a very weird situation where candidate A beats B, B beats C, and C beats A. It is also possible to manipulate.

approval voting a good way to go?
It’s very simple. It basically uses the same ballot we have now except, if you want, you can vote for more than one candidate, and whichever one gets the most votes tends to win. I’m not sure there’s any real known disadvantage.

What about instant runoff?
The voters rank the candidates based on how much they like them. It works quite well as long as you have what we might call a typical American election, where there’s a Republican and a Democrat and you’re sure one of those two is going to win. The problem is when you have three or more strong candidates as you would in the race for a party’s nomination, then it’s subject to some of the same vote-splitting effects as the plurality vote.

The emerging system of range voting.
Range voting is the newest in the sense of people being aware of it and promoting it: If you’re rating a video on YouTube you give it one to five stars, and they take that information and show you the average score of all the people who bother to rate it. We use it with a report card. The valedictorian of a school is the winner of a range vote by the teachers for each of their classes. In the Olympics, they hold up those cards to rate someone’s performance—that’s another example. People are pretty familiar with the idea. Nobody has given a convincing argument that there’s anything seriously wrong with it—the one thing you sometimes hear is it’s complicated, but that’s about it.

In 2000, mathematician Warren Smith published a study where he ran simulations to determine which of the common voting methods gave the most satisfactory, or least regrettable, outcome for the greatest number of voters. He found that range voting was the most fair.
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That one paper has convinced a lot of people that we ought to be taking range voting pretty seriously.

How did the other methods rank?
The second best was approval voting, which is the short-form version of range voting. Instead of rating someone on one to five stars, or one to ten, you basically have two ratings—thumbs down and thumbs up—and it’s almost as good. Next is the Borda count, although this particular simulation doesn’t factor in that there’s an incentive to manipulate the vote, so I wouldn’t rate that as too great an endorsement—Condorcet voting is a little better. Then you get into instant runoff and then plurality voting, which is the worst of all these systems.

Which method most benefits the small parties?
Anything that addresses the spoiler effect. The Greens and Libertarians would probably get many more first-place votes or high scores than they do now. I think that would have the effect of legitimizing them and making it a little easier for them to raise money. Once you legitimize them, there would start to be elections in some areas of the country where they would be able to win a few races.

We’re still in a situation where the people in politics really don’t understand the various systems—it would almost have to be that the public would start having an outcry saying we want this, that, or the other thing.

But I didn’t quite understand what you meant by the ranking talk near the end. What did you mean?

And just a quick nitpick — the president/vice president votes are majority votes, not plurality ones. In the case of no majority, the top three are voted on in the House.