Under Harsanyi's original axioms, you cannot say anything about the signs of the coefficients. My axioms are slightly stronger, but I think still not quite enough. However, if you make the even stronger (but still reasonable, I think) assumption that the agents' utility functions are linearly independent, then you can prove that all of the coefficients are non-negative. This is because the linear independence allows you create situations where each agent prefers A to B by arbitrarily specifiable relative amounts. As in, for all agents k, we can create choices A and B such that every agent prefers A to B, but the margin by which every agent other than k prefers A to B is arbitrarily small compared to the margin by which k prefers A to B, so since FAI prefers A to B, c_k must be nonnegative.