Monday, June 06, 2005

Idol Speculation

From this week’s Marilyn von Savant column (not yet available online):
I believe that the voting for American Idol is inherently flawed. The performer with the fewest votes must leave the show. But we vote for the one we like best! If we voted for the performer we think is worst, the person who leaves might be someone else.
– Vic Gregorini, Belle Vernon, Pa.

[Marilyn:] That’s true, but if you kept voting “against” a performer each week, I think you’d probably still end up with the same person as the winner – except the show would seem negative instead of positive.
Marilyn was wise to include that “probably,” because it gives her some wiggle room. But she’s making an empirical claim here without any basis. As a theoretical matter, it’s simple to find patterns of voter preferences that yield significantly different results depending on the voting rule.

Suppose we have three contestants denoted A, B, and C, and 100 voters with preferences like so:
A pref B pref C (40)
C pref B pref A (35)
B pref A pref C (15)
B pref C pref A (10)
With these preferences, contestant B is the Condorcet winner; that is, B would win in a one-on-one vote against either A or C. The very notion of a “general will” of the public is terribly problematic, but if anyone has a claim to it, it’s B. (One reason the “general will” is problematic is that a Condorcet winner does not always exist; for example, see here.)

Now, what will happen under a Vote-for-the-Best (VFB) rule versus a Vote-for-the-Worst (VFW) rule? Assume people vote their true preferences, rather than voting strategically based on knowledge of others’ preferences. Under VFB, contestant B will get eliminated in the first round of voting, as she has the fewest number of voters who consider her the best. Then A will face off against C, and A will win. Under VFW, on the other hand, contestant C is eliminated in the first round, and then B beats A in the face-off. So VFW awards the prize to the Condorcet winner, while VFB does not.

Thus, for some preferences, the existing rule (VFB) is inferior, as Marilyn’s reader claims. But with different preferences, the opposite is true. Suppose we keep the 100 voters above, and add two more voting groups:
A pref C pref B (10)
C pref A pref B (30)
(We now have 140 voters.) With these preferences, the Condorcet winner is C. Under VFB, contestant B is eliminated in the first round, and then C beats A in the face-off. Under VFW, contestant C is eliminated in the first round, and then A beats B in the face-off. So VFB gives the prize to the Condorect winner, while VFW does not.

The point, of course, is that every voting system is flawed for some voter preference distributions. To decide one system is superior (as Marilyn’s reader says) or that they are “probably” equivalent (as Marilyn herself says), we have to know a lot more about the structure of people’s preferences.

(Readers familiar with voting theory may note that VFW failed to select the Condorcet winner in the latter case only because we included non-single-peaked preferences. So if we assume single-peaked preferences, VFW might look superior. But why should we assume single-peaked preferences?)


Anonymous said...

I wish Bo Bice had won. He's cool!

Anonymous said...

Even if the final outcome is the same under both systems (which it will not necessarily be) it is very likely that the order in which contestants are knocked off would be different if viewers voted for the singer they disliked. In that respect, I think the current system is clearly superior.

If you vote for the person you want to stay, more unique and differentiated singers will stay in the competition longer. If you vote for the person you want to leave, more differentiated singers will be knocked out early. If you have three singers that are nearly identical, it's unlikely that all of them will attract enough votes to survive the early rounds, but it's very likely that none would attract enough votes to get knocked out early.

Also, more controversial singers are more likely to attract a lot of votes to stay or a lot of votes to leave. It probably makes the show more interesting if they try to retain the singers who inspire a strong reaction in viewers.

Anonymous said...

Well, the nice thing about American Idol versus your typical voting scenario is that it isn't winner take all. The top 4 or 5 performers in a given season almost always end up with *some* kind of music industry deal, often in proportion to the votes they got in the course of the show.

Bo Bice is releasing a record. He gets pretty much all the same perks as he would if he'd won. Even Constantine has some kind of deal going right now, and he was voted out in, what, the 6th round?

The nice thing about the VFB model on the show is that it really provides what the show's producers are after: a guess on the market size for that contestant releasing an album. Kelly Clarkson, Clay Aiken and Ruben Blades all released albums with very predictable (and enormous) sales numbers.

Anonymous said...

Ruben Blades is a 50-something Panamanian actor/singer/politician who's a Harvard Law School graduate and, I believe, the current minister of tourism in Panama. Pretty sure he doesn't have anything to do with Clay Aiken or Kelly Clarkson. But I've been wrong before.

Anonymous said...

yes, it's ruben studdard. i haven't watched 'idol' since clay aiken was on, but i'd say that only clarkson made it far. clay aiken has his appeal too for young girls and gay men. =)
actually, i think he's a great singer and his old school crooner style is a refreshing change from the typical contemporary music style (not that i have anything against that).


Anonymous said...

Sort of reminds me of a post I did a few months ago...

I'm a firm believer in the anti-vote.


Anonymous said...

on a funny note: i heard on the radio that dr. phil had a show once about young boys who were always beat up at school by bullies because they seemed wimpy or effeminate. anyway, dr. phil wanted to make a point of "kids who were bullied when they're young can grow up to be great people, so hang in there." so he invited a famous celebrity that was bullied as a boy. And guess who it was? CLAY AIKEN!

so the radio host was commenting that now that kid on the show is sure to get beat up at school because the role model they brought out was aiken. "you too can grow up to be an effeminate singer too." i was dying laughing it was so hillarious. the radio host kept saying how he should have brought out some CEO, ball player, or inventor.