Reality shows eliminate contestants one at a time. Shows like American Idol do this by holding a vote. The audience is asked to vote for their favorite contestant and the one with the fewest votes is eliminated.

Last week on American Idol something very surprising happened. The two singers who were considered to have given the best performances the night before, and who were strong favorites to win the whole thing received among the fewest votes. Indeed a very strong favorite, Jessica Sanchez was “voted off” and only survived because the judges kept her alive by using their one intervention of the season.

The problem in a nutshell is that American Idol voters are deciding whom to eliminate but instead of directly voting for the one they want to eliminate, they are asked to vote for the person they don’t want eliminated.  This creates highly problematic strategic incentives which can easily lead to a strong favorite being eliminated.

For example suppose that a large number prefers contestant S to all others. But while they agree on S, they disagree about the ranking of the other contestants and they are interested in keeping their second and third favorites around too.

The supporters of S have a problem:  maintaining support for S is a public good which can be undermined by their private incentives.  In particular some of them might be worried that their second favorite contestant needs help. If so, and if they think that S has enough support from others, then they will switch their vote from S to help save that contestant. But if they fail to coordinate, and too many of the S supporters do this, then S is in danger of being eliminated.

This problem simply could not arise if American Idol instead asked audiences to vote out the contestant they want to see eliminated. Consider again the situation described above.  Yes there will still be incentives to vote strategically, indeed any voting system will give rise to some kind of manipulation.  But a strong favorite like S will be insulated from their effects. Here’s why.  An honest voter votes for the contestants she likes least.  A strategic voter might vote instead for her next-to-least favorite.  She might do this if she thinks that voting out her least-favorite is a wasted vote because not enough other people will vote similarly.  And she might do this if she thinks that one of her favorite contestants is a risk for elimination.

But no matter how she tries to manipulate the vote it will be shifting votes around for her lower-ranked contestants without undermining support for her favorite. Indeed it is a dominated strategy to vote against your favorite and so a heavily favored contestant like S could never be eliminated in a voting-out system as it can with the current voting-in system.