Significance of specific votes in sample selection

[Bkkkk]

I was wondering is there any way to quantify how much "power" a given selection has on the final outcome of a voting. More specifically, say you have a sample 330,000 people and you need to pick one. However, before you get to make a choice a pre-selection is applied and the sample is narrowed to only 20 people, you then choose one person.

How significant is your choice compared to that of the pre-selection in determining who is finally chosen?

 

[HallsofIvy]

Assuming you are talking about an election in which every one gets a single vote, none at all.

 

[Bkkkk]

Specifically I was referring to an x-factor style selection. So there are 200,000 who initially attend auditions. In auditions the number of candidates is reduced to 12 from the original 200,000 by the x-factor producers and judges. The rest of the competition uses a combination of judges and public vote to actually select the final winner. I was wondering if there was any way to quantify how much choosing power or selection power the x-factor team have over the public vote.

My intuition suggests that since the x-factor team reduce the sample of possible participants by a huge amount they have the overwhelming decision power and the public vote as a whole is completely negligible.