Wednesday, November 17, 2010

What "The People" "Want", Part One: It Depends

Now that the election is fading from your memories—and I assure you it is—I thought I’d kick off what I hope will be a series of semi-regular posts on how elections really work. 

When you read that, some of you thought, “Nathan is going to tell us how the corporations are in control,” or, “Nathan is going to tell us about how Harris personally designed those butterfly ballots to confuse people and steal the election.” 
Nope. Not that there aren’t some legitimate concerns about the manner in which elections are run, but what I want to talk about are the fundamental challenges that stand in the way of the people getting what they want.
“What they want,” in fact, is today’s topic. We’ll get started, anyway—there’s a lot to cover. You might think that deciding what a group of people wants is straightforward. In a democratic society, people vote, right? Sure, if you’ve only got two options, everything’s fine. Everybody prefers one or the other or doesn’t care, and if more people prefer option A to option B, then the group chooses option A. Simple.
The reality: there are always more than two options.
Let me first dissuade my U.S. readers of the silly notion that there are only two options. Commentators and indeed many political scientists describe the U.S. as a “two-party” system. Well, it’s not. In the last 30 years in the U.S., there have been, depending on how you count, five times when a third-party candidate was a factor in the election—John Anderson in 1980, Ross Perot in 1992 and 1996, and Ralph Nader in 2000 and 2004. We can quibble about Anderson and Nader, but Perot is clear: he got nearly 20% of the vote in 1992 and nearly one in ten votes in 1996. In those 30 years, there have been eight elections. So: between one-quarter and five-eighths of the presidential elections in the last 30 years have had a significant “third-party” candidate. So much for the two party system.
Third party candidates have an impact, too. Forget about Nader and Perot and Anderson. Chilean president Salvador Allende won office in 1970 in a three-way race, and if you know your history, you know that did not end well. If you don’t know your history, I hear Patricio Guzmán’s The Battle of Chile, about the 1973 coup that brought Augusto Pinochet to power, is good. (I owe this example to the very readable first chapter of Don Saari’s Basic Geometry of Voting.)
You can’t always get what you want, but if you try sometimes, you get...uh...?
Now that you understand even the U.S. has more than two options, let’s ask: what did citizens in the U.S. in 1992 want? Forget the Electoral college, the problems of voter turnout, the fact that people don’t know what they want (oh boy, that’s a topic for another time). What did the people want? Did they want to Clinton to win?
Well what does that even mean? Presumably, it means that the people want what the people vote for, but that’s tricky, because there are different ways to vote. A lot of people—not just Americans, incidentally—are used to plurality rule: if you get the most votes, you win. But there are other methods. The single transferable vote and instant runoff voting seem to be increasingly popular in local elections. I’ll focus on the Borda count. It’s not so common, but it is simple and instructive. The Borda count works like this: each person ranks the candidates, and each candidate gets points corresponding to these rankings—one point for the first ranked candidate, two for the second candidate, and so on. Then, you add the points, and whoever gets the least points wins, just like golf, except without sand traps.
So: 1992. Let’s say, for the sake of argument, that everybody voted sincerely, i.e., each person voted for his or her first choice, and let’s say that 38% of people preferred Bush to Perot to Clinton (rank Bush first, Perot second, Clinton third) 43% preferred Clinton to Bush to Perot, and 19% preferred Perot to Bush to Clinton, corresponding approximately to the popular vote in 1992 and my hunches about everybody’s second choices. Under plurality rule, Clinton wins, since he gets more votes than the other two.
Let’s work it out under the Borda count. For simplicity, assume there are 100 voters.
First, 38 voters give Bush one point, Perot two, and Clinton three. The tally is then 38 points for Bush, 114 for Clinton, and 76 for Perot. 
Second, 43 voters give Bush two points, Clinton one, and Perot three. The tally is now 124 points for Bush, 157 for Clinton, and 205 for Perot. 
Finally, 18 voters give Perot one point, Bush two, and Clinton three. The final tally is 160 points for Bush, 211 for Clinton, and 223 for Perot. Bush wins.
Clinton wins under plurality rule. Bush wins under the Borda count. So what did “the people” want? It depends. Was one voting method the “right” method? No. It comes down to this: do you favor the Borda count or plurality rule?
The lesson you should take away is that you can’t necessarily define what the people want. Maybe if everybody prefers one thing over all the other options, the people can get what they want, but the fact is, this example is only the beginning. Things get much, much worse. You might hope that there is at least a way to vote that has some basic, desirable properties—you know, not being a dictatorship; if everybody favors one thing to another, society does as well; allowing all types of preferences; the choice between two options doesn’t depend on how people feel about a third. Things that seem obvious.  
Sorry. There isn’t. Stay tuned.