How do hiring/promotion/grant committees assess individual applicants who've authored papers with huge teams While reading this slightly-too-snarky question, I was reminded of a slightly more serious question I’ve wondered about from time to time: how does being one of the 1000+ authors on a paper like the LIGO discovery or one of the CERN collaborations influence your career?  I’m used being in a field (mathematics) where most papers have between one and three authors (I’ve written with three separate four-person teams, and people have often considered this a bit exotic), so when reading a CV, one can reasonably ascribe most of the “credit” for a paper to any of the authors.  

If you’re in a situation where you have to judge the research output of a scientist (like a hiring or tenure committee), how does seeing a paper from an enormous collaboration change your thinking?  What do you if you have make a decision between candidates whose publication lists are identical (due them being in the same collaboration)?
There's generally a way of assessing your contribution to the project even if it's enormous. So even if you're 29th author, if you were the senior manager of say particle detection and analysis, that's knowable. And they'll have a letter of recommendation from the project supervisor detailing your role.

And people on the committee (especially the person's department head) if they think you're great will advocate for you, the importance of your role, and the importance of your contribution to it.