This is very helpful but I wonder that faculty are as prone to cognitive dissonance? Thinking about what could have been had there “preferred” candidate joined?
How much does it matter that you are a school's #1 choice? Anyone face the tradeoff of being one school's first choice and another school's later choice?It matters exactly 0. Choose the school that you actually want to work at - Don't choose something that's worse for you out of some weird spite. Once you're there, you're there, it won't matter whether you were their second choice.
Sometimes the second choice is just as preferred (or indifferent) but for some "circumstances" the offer is given to someone else. Remember, if you flew out, you went through 2 screening processes and unless you committed some serious gaffe most of them liked you.