Let's say we could fix our voting-machine problems for good. Every person would have their one vote counted, and the most popular candidate would win. Everything would be perfect - right? For an answer, we'll turn to Nobel Prizewinning economist Kenneth Arrow. In 1951, Arrow famously asked what would make a voting system perfect. Here's a hint: his idea is called the "Impossibility Theorem."

Arrow's mathematical proof first assumed that people were voting honestly, not strategically. He also assumed that people were voting using a ranking system. (Our method of voting in the U.S. is essentially a ranking system where only our first choice matters.) Then he named four criteria for a perfect voting system. Here are those rules, as summarized by William Poundstone, author of Gaming the Vote:

1. Transitivity. If I prefer candidate A over B1 and B over C, then I should also prefer A over C (and the voting system should reflect that).

2. Unanimity. If every single voter prefers candidate A1 he should win.

3. Nondictatorship. Another obvious one: Everyone's vote should count equally.

4. Independence of irrelevant alternatives. Let's say I like candidates A and C, but I don't like candidate B. If the race comes down to just candidates A and B1 then how I feel about candidate C should be irrelevant: I still prefer A to B. (More on this in a moment.)

Arrow did a lot of complicated math, and came to a grim conclusion: Satisfying these four simple requirements in a voting system is impossible. Our current system in the U.S., for example, has a big problem with those "irrelevant alternatives." When the 2000 election came down to an extremely tight race between George W Bush and Al Gore, Gore may have lost only because Green Party candidate Ralph Nader - or, candidate C - was also in the race. The people who voted for Nader probably would have preferred Gore to Bush, but their votes for Nader ended up hurting Gore.

Is it really hopeless? There may be no perfect voting system, but there are systems that are better. One possibility is called instant runoff voting. Voters rank all of the candidates, from their first choice through their last choice. If no candidate has a majority of first-choice votes, the candidate with the least first-choice votes (say, Ralph Nader) is eliminated. If I ranked Ralph Nader first, and Al Gore second, my vote now goes to Gore, and the votes are tallied again.

For the time being, if you want to use instant runoff voting to elect your president, you'll have to move to Ireland.

- E.P.

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