Is The Voice fair?

[lvstephanie]

I just started watching the new singing show "The Voice", mostly because I love the concept of having the contestants judged solely on their voice. However watching the first episode last week, I found that I was confounded by their apparent rules for these blind auditions. Basically it would seem very improbable that each judge / trainer would get exactly 8 contestants / singers on their team while still being able to remain fair to all singers by voting yes / no just on the singer's voice and having the singer choose the correct judge to work with.

For example, it may be easier to understand what I mean if I broke it down strictly to percentages (I know "Ugh! Math!"...):

Let's assume that the voting for the singers is strictly random. In this case, each judge can make one of two choices, either "Yes, I Want You" or "Nope, sorry", meaning that from each judge, the contestant has a 1/2 or 50% chance of getting on a team. Since their are four judges, in order for the singer not to make any team, each judge would have to vote "no"... So 1/2 a chance that Judge 1 says no AND 1/2 Judge 2 says no AND 1/2 J3 says no AND 1/2 J4 says no... In probability, whenever you need two things to happen together (when you say A happens AND B happens), you multiply their chance of happening to get the total probability of the situation. This would mean in order for a singer to not get selected for a team (in a completely random setting) is 1/2*1/2*1/2*1/2 = 1/16. And therefore the chance of them getting on a team is 15/16 = 93.75%.

Now this is fine for the first contestant trying to get on a team. But what if 31 slots are already filled and the singer is trying to get in the last slot... Now not only is their the problem of the singer just getting voted for a team, but also selecting the correct judge that has the remaining open spot. For example, if all of the judges vote yes (even though 3 of the 4 judges have a full roster on their team), the singer then has a 1/4 chance of selecting the correct judge to get that last slot. If this were the case, then the last contestant has 15/16 chance of getting a yes vote AND 1/4 chance of getting the correct judge or 15/16*1/4=15/64=23.4% chance of getting into that last slot correctly. And that is just the probability that the last singer hits their slot correctly. How about factoring in all 32 contestants getting a slot perfectly giving each judge exactly 8 members on their team? The probability continues to get even smaller that this would happen...

To increase the probability that each judge gets exactly 8 on their team, they may need to institute other rules, such as once a judge gets a full team, they are no longer able to vote yes. Although this guarantees that no judge would get over 8 members, it also decrease the chance that each singer would get onto a team. The last singer would get 3 definite no votes (because by rule, these judges have to vote no), and so their probability of getting on a team relies solely on that final judge or a 50% chance of being picked for that last slot. So although 50% is better than the 23.4% chance for getting the correct last slot, it is also worse than the 93.75% chance that the first guy had in getting on a team.

Some may argue that the above example is unrealistic. That we aren't talking about flipping coins, but rather talking about some really awesome singers trying to get on the team. In this case, the judges are more than likely to vote yes. However, even if you weighted the singers so that they're more likely than not to get on a team (eg it isn't a true 50:50 chance that a judge would vote yes, but perhaps closer to 80:20) it would still mean that the first contestant has close to 99% chance of getting on a team, but only 80% that the last singer makes that last slot. And if you are taking into consideration of "human emotion" as to how much weight to add to each singer's chance of getting selected, perhaps we'd need to consider an opposite weight that the judge would add: if a judge knows they only have one slot left, they may hold-out on who they'd consider to be a good singer in hopes that a great singer comes along next. Thus at the beginning when a judge's team is wide open, that singer may have an 80% chance of getting selected by the judge, but when the judge has only 1 slot left, the judge may have a counterweight such that the singer now only has a 60% chance of getting selected by that judge.

The only thing I could think of that would make everything completely fair would be if the judges were not told how many singers to select for their team. The competition would keep sending out singers until all judges had at least 8 members on their team. And as chance would have it, their would likely be some judges that would have more than just 8 contestants, and would have to make their first cut down to a team of eight. Because the TV audience doesn't see this, it'd have to be done behind the scenes, and the contestants would probably need to sign a non-disclosure agreement to keep that part of the contest hidden from the viewing public.

The other option would be to pre-rank the singers before the blind auditions. The competition would then send the best singers out first and have the lesser singers go for those slots that have a lesser chance of being selected for the correct final slots. Although this doesn't make it completely fair in terms of having each contestant equal chance before the judges eyes (or rather "ears" as the case may be), it would still ensure that the best singers get on a team and are competing for that top prize.

What do you think? Firstly is my math correct, or are their other distinctions that might change the probabilities? And if you think my math is fair, then what scenario do you think is occurring? Is it just pure blind luck that each judge gets exactly 8 members on their team? Or is their a preliminary cut once each judge gets at least 8 members to pear down each team to exactly 8 singers? Or is their some type of ranking system in place? Perhaps as the show progresses, they'll explain better what the actual rules are...

[scollontrade]

I am impressed with how much thought you put into your presentation. I watched one episode. I don't know if it was the first or second one. I am also not sure of the rules regarding filling the 8 spots. Perhaps when one star gets their 8 they are out of the competition for more singers. But that does not seem fair to those who sing last. I will be watching a future episode to see how they handle it.

[mh874892]

A show I love and math all in 1 post > I'm sold!

I believe your probability statistics are correct. It is my understanding that once a judge has filled their 8 spots (which they know of beforehand), they can no longer vote. That is part of their challenge of getting a strong team by being picky and then by selling themselves when multiple judges pick a contestant. Was there only 32 contestant to begin with? If so, then it makes sense that everyone has a valid chance because there will be some no's (most likely) and leave spots available. It is definitely a benefit to go towards the front and middle. However, I think there are more contestants than that because the preview for next time say they are bringing some of the no's back (I think?). If there were only 32 then everyone would be guaranteed a position and that won't make a successful show.

As for cutting down the teams, I believe the judges start with 8 and it progresses from there. I do think it'll be better explained as the show continues. I am confused as to how exactly the cuts will be made, but I'll find out tonight I hope!. And I wish they would have explained how the contestants were picked in the beginning.

But to answer your main question, it is definitely a skewed competition like all judged events are. That's what makes it fun to watch though IMO. We get to see the judges reactions to their voice, then their appearance, and it will be fun to watch the coaching and competition aspect of it all. I am excited to watch every week. And I already enjoy it more than American Idol, which I haven't watched since about Season 3.

[lvstephanie]

I got to see the 2nd episode last night, and it was skewed as I thought... The judges did know exactly how many spots they had (which was only 8, and no additional ones behind the scenes). As the judges filled their slots up, they got to watch the entire performance, so the contestant's chance did dwindle as the competition went along. However it looked like they had just over 32 singers, because they did turn away some, but the judges also did run out of contestants before they filled their team, so some singers did get to try again if they didn't make a team the first time. The judges were put under a lot of pressure knowing how many slots they had left, and I think towards the end, they tended to be more conservative in their choices. I think Christina actually made a comment to that affect... She even said she thought she may have made a mistake by not choosing one girl, but I think that having only one slot left weighed heavily for her; at least for Christina it didn't matter as much since the singer she made that comment about was able to get a 2nd chance to sing again, and this time Christina voted for her.

I am also really enjoying this show, even if statistically it doesn't seem really fair. I think they really are trying their best to be as fair as possible and to really make the show be about the person's voice. From the previews, I like how they've structured the next part of the competition where each coach has to narrow their team from 8 down to 4 members... They will be pairing up the singers and having each pair do the exact same song at the same time. So once again the voting will be based mostly on the person with the better singing ability, and not on song choice, presentation, audience, etc.

I'm still somewhat concerned with how they'll handle the final 16 when the viewing public gets a chance to vote. Perhaps they'll not show the person singing so that the audience will also be voting purely on sound quality, but I doubt that will happen. Then again by this time, the final 16 will have already passed those initial tests and got to where they are based on voice alone, so when the audience gets to vote, all 16 will have really great voices.

[mh874892]

I am very excited for the upcoming battle rounds. It is going to be extremely difficult for the judges to narrow down their own team after spending time training and getting to know them. I think by the time America gets to vote, the best contestants will be remaining. So, even though it is no longer based solely on voice, it will almost guarantee that the best ones are left to choose from. That is what I like best about this show's concept: fan base and public appeal are far less important than the raw talent.. FINALLY!

[ElleRich]

I watched it last night because my husband if the true television lover.  I like the concept so far.  It will be interesting to feel if the judging is fair as it gets to the final round.

[kangagirl1321]

yes it is fair coz u have to have a good voice or at least have one of the judges like ur voice for u to more on. it's not like american idol.