When you get the choice of going first or second, do you get to look at your opponents set? Or is it a blind choice? The list in my opinion is open information, and objectives considered as part of the list.
Example
I win initiative, I think I want to go first, but then I look at the 3 objectives my opponent presents, and realize all 3 of them will just be bad for me. So I choose to go second and let him/her choose obj's from my set.