I was reading the original BGW paper. Great paper. I'm confused about Theorem 2, though.
The Theorem states, "There are functions for which there are no n/2-private protocols."
The proof is simply that two players cannot compute an OR without one of them leaking information.
But the way I see it, that isn't an MPC problem, that's a problem with the function being evaluated. Normally, the security of MPC is evaluated on the basis of whether it accurately simulates a trusted third party who receives inputs, evaluates the function and distributes outputs. Even with a trusted third party, evaluating an OR would always leak information about one of the inputs to the other party.
Similarly, couldn't you just argue by the same logic that if you evaluate the function $f(x_1, ... x_n)=x_1$ for arbitrarily high number of players $n$, then this leaks information about player 1's input?
So you could argue, by the same argument that "There are functions for which there are no 1-private protocols."
Or am I misunderstanding their proof?