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## Purple America – The Best Election Maps

For all the talk of red states and blue states, much of America is really purple.

That simple observation has inspired some great alternatives to the standard red and blue maps depicting electoral outcomes.

Princeton’s Robert Vanderbei, for example, has created an animation that makes three improvements on the standard red/blue map: he maps counties not just states; he uses shades of purple to reflect the mix of Democratic and Republican votes; and he uses green for third parties.

Here’s his animation for the 1960 to 2008 elections; keep an eye out for Ross Perot. (Vanderbei also has a static version of the 2012 results.)

Michigan’s Mark Newman also adopts the purple view, with another wrinkle. Traditional maps emphasize geographic area, not the location of electoral votes (or population). Using some fancy math, he resizes and reshapes states to reflect their relative electoral import. The result resembles a smooshed butterfly, with blue areas (mostly cities) amid a red web:

## Can a Candidate Win Any Number of Electoral Votes from 0 to 538?

Let’s take a break from the presidential campaign to consider a recreational math question posed by New York Times correspondent Binyamin Appelbaum. On Twitter, he wondered:

Is there any number of electoral votes between 0 and 538 that is impossible to amass, assuming electors are faithful?

Put another way, could a presidential candidate win any number of electoral votes from 0 to 538?

The answer is intuitive if you know a key piece of electoral college trivia. But there’s still a fun question of how best to actually prove that intuition.

My best attempt below. Stop reading now if you want to figure it on your own.

So many fascinating economic issues, so little time to blog.

Here are some of the fun items that I would have discussed in recent days if I had infinite time:

Have a wonderful Thanksgiving.

## The Feud over the 2009 Burlington Mayoral Election

In March 2009, Burlington Vermont used a non-traditional system of voting—Instant Runoff Voting—to select its mayor. The voters returned the incumbent, Progressive Bob Kiss, to the mayor’s office and, in so doing, set off a surprisingly fierce debate among advocates for voting reform. Some tout the Burlington results as a success for Instant Runoff Voting, while others cite them as evidence of its fundamental flaws.

In this post, I will try to settle one part of this debate: whether the Burlington results display a voting pathology known as non-monotonicity. That sounds geeky—ok, it is geeky—but it boils down to a simple question: could a candidate lose an election if voters showed more enthusiasm for him or, equally perversely, win an election if voters showed less enthusiasm?

Several readers asked me to weigh in on this debate after my previous post on alternative voting systems (check out the comments on that post if you want to get a flavor of the debate). I should state from the outset that I am not an expert on voting systems, but I am a card-carrying math and economics geek and enjoy mediating interesting debates, so I gave it my best shot. I reached three main conclusions:

• The Burlington results provide a fascinating case study in American voting for reasons that have nothing to do with non-monotonicity. In what was effectively a three-way race, Instant Runoff Voting (henceforth IRV) appears to have chosen a better winner than our usual system, plurality voting. That’s great news for IRV except for one thing: it failed to choose an even better winner. IRV thus appears to have elected the “wrong” candidate, but traditional voting would have elected an even “wronger” candidate. That weird result illustrates how challenging it can be to design a democratic voting system.
• The debate about non-monotonicity–which pales in importance next to the larger issues posed by the Burlington results–confuses technical semantics and electoral substance. The Burlington results do illustrate the possibility for non-monotonicity in real world voting data, as IRV critics claim. But, as IRV proponents emphasize, that potential had no effect on the election outcome.
• The debate among voting reformers would be more fruitful if they adopted some new lingo to distinguish between the potential for non-monotonicity and its actual impact. Inspired by the world of accounting, my suggestion is to distinguish between material non-monotonicity, in which it affected an election outcome, and immaterial non-monotonicity, in which it didn’t. The Burlington election results display the immaterial variety. (Suggestions welcome for better ways of saying this.)

For further details in a handy-if-lengthy Q&A format, keep on reading.

## What’s the Best Voting System?

Last February I highlighted a New Yorker piece about instant runoff voting (IRV) in awarding the Oscar for Best Picture. (Kudos to author Hendrik Hertzberg for correctly predicting the winner: The Hurt Locker.)

As I said at the time, I think elections to public office would benefit from IRV as well:

Why? Because it eliminates the downside of voting for a third-party candidate. In a race between D and R, you may worry that voting for third-party candidate I is “throwing your vote away.” That worry disappears with IRV. You can give I your number one vote and either D or R your number 2 vote. If I loses in the first round, you’ll be disappointed. But you won’t have wasted your vote since your second-place vote now becomes operative.

I think that would be a substantial improvement over the winner-take-all vote tallying that dominates the American political system today. But would it be the best of all possible voting systems?

In this week’s New Yorker, Anthony Gottlieb answers no, pointing to a potential flaw in IRV:

Such transferrable-vote elections can behave in topsy-turvy ways: they are what mathematicians call “non-monotonic,” which means that something can go up when it should go down, or vice versa. Whether a candidate who gets through the first round of counting will ultimately be elected may depend on which of his rivals he has to face in subsequent rounds, and some votes for a weaker challenger may do a candidate more good than a vote for that candidate himself. In short, a candidate may lose if certain voters back him, and would have won if they hadn’t.

The practical importance of this theoretical concern is a matter of heated debate, much of which has focused on a 2009 mayoral election in which Burlington, Vermont used IRV (as it had in 2006). According to IRV detractors Burlington ran right into the “non-mononicity” issue, with the “wrong” candidate winning (at least by some voting metrics). IRV supporters reject that view. (Sorry, I haven’t had time to sort this through; if you are interested, just Google “Burlington 2009 election” and have fun.)

As best I can tell, however, both sides agree that the current system is flawed. For example, many of the IRV detractors believe we should adopt a different system: range voting, which allows voters to express how much they like or dislike a candidate. Rather than just ranking Oscar movies, for example, voters would award scores: (e.g., Hurt Locker 10 points, Up in the Air 9 points, Avatar 2 points). The movie with the highest score would win.

That would also solve my primary concern about not discouraging votes for third-party candidates. But perhaps range voting has other hidden problems as well? As Gottlieb notes there is a limit to how far theorizing can take us in this debate:

Mathematics can suggest what approaches are worth trying, but it can’t reveal what will suit a particular place, and best deliver what we want from a democratic voting system: to create a government that feels legitimate to people—to reconcile people to being governed, and give them reason to feel that, win or lose (especially lose), the game is fair. The novelty of range and approval voting in modern politics is so great that we can’t know how they’ll work out without running experiments.

Let me second that recommendation: more experiments with IRV, range voting, approval voting, and other innovations would be well worth the effort.

But I think we can take a pass on the voting system of old Venice, which Gottlieb describes as follows:

Thirty electors were chosen by lot, and then a second lottery reduced them to nine, who nominated forty candidates in all, each of whom had to be approved by at least seven electors in order to pass to the next stage. The forty were pruned by lot to twelve, who nominated a total of twenty-five, who needed at least nine nominations each. The twenty-five were culled to nine, who picked an electoral college of forty-five, each with at least seven nominations. The forty-five became eleven, who chose a final college of forty-one. Each member proposed one candidate, all of whom were discussed and, if necessary, examined in person, whereupon each elector cast a vote for every candidate of whom he approved. The candidate with the most approvals was the winner, provided he had been endorsed by at least twenty-five of the forty-one.

## Instant Runoff Voting Awards the Oscar

As even the most casual film buff knows by now, the Academy of Motion Picture Arts and Sciences expanded the field of nominees for Best Picture. This year ten films have been nominated for the Oscar, up from five in recent years. Nominees include Avatar, The Hurt Locker, Up in the Air, the Blind Side, and Up.

What I didn’t realize until today is that to accommodate this expansion, the Academy also changed its voting process. Under the old system, members of the Academy voted for their favorite film, just like Americans vote for President (well, if you ignore that whole Electoral College thing). Each member got one vote, and the flick with the most votes won. Simple, but, if you think about it, problematic. In principle, a film that 21% of the members love and 79% despise could bring home the golden statuette. And with the expansion to 10 films, that minority could be as little as 11%.

As Hendrik Hertzberg describes in this week’s New Yorker, the new, improved system is instant run-off voting:

Members—there are around fifty-eight hundred of them—are being asked to rank their choices from one to ten. In the unlikely event that a picture gets an outright majority of first-choice votes, the counting’s over. If not, the last-place finisher is dropped and its voters’ second choices are distributed among the movies still in the running. If there’s still no majority, the second-to-last-place finisher gets eliminated, and its voters’ second (or third) choices are counted. And so on, until one of the nominees goes over fifty per cent.

This scheme, known as preference voting or instant-runoff voting, doesn’t necessarily get you the movie (or the candidate) with the most committed supporters, but it does get you a winner that a majority can at least countenance. It favors consensus.

I’ve long been a fan of instant runoff voting (IRV) in elections to public office. Why? Because it eliminates the downside of voting for a third-party candidate. In a race between D and R, you may worry that voting for third-party candidate I is “throwing your vote away.” That worry disappears with IRV. You can give I your number one vote and either D or R your number 2 vote. If I loses in the first round, you’ll be disappointed. But you won’t have wasted your vote since your second-place vote now becomes operative.

Hertzberg speculates that the switch to IRV may affect the  Oscar race:

[H]ere’s why it may also favor “The Hurt Locker.” A lot of people like “Avatar,” obviously, but a lot don’t—too cold, too formulaic, too computerized, too derivative. (Remember “Dances with Wolves”? “Jurassic Park”? Everything by Hayao Miyazaki?) “Avatar” is polarizing. So is James Cameron. He may have fattened the bank accounts of a sizable bloc of Academy members—some three thousand people drew “Avatar” paychecks—but that doesn’t mean that they all long to recrown him king of the world. (As he has admitted, his people skills aren’t the best.) These factors could push “Avatar” toward the bottom of many a ranked-choice ballot.

On the other hand, few people who have seen “The Hurt Locker”—a real Iraq War story, not a sci-fi allegory—actively dislike it, and many profoundly admire it. Its underlying ethos is that war is hell, but it does not demonize the soldiers it portrays, whose job is to defuse bombs, not drop them. Even Republicans (and there are a few in Hollywood) think it’s good. It will likely be the second or third preference of voters whose first choice is one of the other “small” films that have been nominated.

For a nice graphic illustrating how IRV may work in the Oscars, see this USA Today piece.

For a summary of recent IRV advances, see this Huffington Post piece.