I haven't really been following American Idol this season, but everyone who talks about the show consistently mentions that Sanjaya Malakar sucks almost as bad as his hair. Comedians have begun to make his suckiness yet sustained ability to stay on the show into joke fodder.

American Idol has two problems with its vote system. The first is capacity. Season 2 saw a severe capacity problem in the final round, and I think that had the phone lines been available, Clay Aiken would have won hands down. Anyone I know who tried to vote in that last round couldn't get through the entire night. Maybe they've solved the problem and maybe they haven't, but it bears inspection.

The second problem is, Sanjaya is basically what mathematicians would call a local minimum. In designing neural networks, or in various mathematical formulas designed to give an optimum solution, sometimes the algorithm encounters a spot where the answer appears to be the best it will get; it hones in on that and then terminates. But a local minima is not necessarily a global one, meaning the real solution was nowhere close to what the system found.

In programming, one kind of data structure used for sorting is a heap. A heap works by finding the maximum or minimum values, and constructing a tree based on that. Heaps are a very effective method for sorting. But, if you ever need to search the heap in the opposite order, it can't help you much.

Sanjaya has stayed in the competition because he has a core group of dedicated fans who can overlook his relative vocal problems compared to the rest of the field, or his hair compared to the standard by which all human beings are judged. For shorthand, I'll call this core group "morons", although I'm pretty sure 9-to-12-year-old girls would be a far better description. The morons have voted consistently every week to keep him on the show, and their votes, although a significant percentage, are in the minority. When the field narrows enough, that minority will not be enough to protect Sanjaya from the positive votes garnered by the contestants who have earned the right to stay. But until that happens, that fixed percentage of votes every week is distorting the outcome significantly; as badly as most of America wants him to go, X% want him to stay.

The point is, American Idol is using a heap, but they're using it backwards. It's based on positive outcome, votes for a performer to stay, yet it does not select the top of the heap but rather one of the ones that didn't make it. The bottom tier in a heap tends to be badly sorted and doesn't give you any useful information--specifically it doesn't tell you the least positive result, or even guarantee it will be down there. What Idol really needs is a deap, a double-ended heap, that takes into account not just how badly America wants to keep a performer in the running, but how badly it wants them to go. American Idol needs a two-tiered vote: One positive, one negative. To work at its best, the "winner" of the negative vote every week should be ejected, unless they also won the positive vote, in which case the runner-up of the losers should be thrown off.

Under this system, someone like Sanjaya would gravitate to top of the negative heap. On the positive heap, he never had a prayer of reaching the top. So if he's getting, say, 20% of the vote to stay every week, which might ordinarily bump off an 11% contestant right below him, but the negative vote puts him at a solid 55%, he gets the boot.

Another option of course is simple subtraction. Positive vote means +1, negative means -1. The Brunching Shuttlecocks used to work that way, with an occasional feature called "good or bad" where people would vote for things, and their comparitive rankings went from very positive to very negative. Bash.org works the same way with quotes.

To boil it down, there's more than one way to set up a voting scheme. Americal Idol is run like a runoff election; it ditches the candidates with the fewest votes and runs again. But, as its widespread adoption all over Europe and elsewhere has proven, it's a pretty stupid way to run an election. It selects neither the best candidate nor the least unpalatable. The only way to properly handle a runoff is to run off only the ones who earn the most relative ire. I doubt this would work in simple majority elections, but it does work well for a ranking scheme.

Food for thought if you ever implement a voting system of any kind in your game. In the meantime, remember: Friends don't let friends vote for Sanjaya.