My thoughts:

1. You do always get a linear combination.

2. I can't tell what that combination is, which is odd. The non-smoothness is problematic. You run right up against the constraints - I don't remember how to deal with this. Can you?

3. If you have N units of resources which can be devoted to either task A or task B, the ratios of resource used will be the ratio of votes.

4. I think it depends on what kind of contract you sign. So if I sign a contract that says "we decide according to this utility function" you get something different then a contract that says "We vote yes in these circumstances and no in those circumstances". The second contract, you can renegotiate, and that can change the utility function.

ETA:

1. In the case where utility is linear in the set of decisions that go to each side, for any Pareto-optimal allocation that both parties prefer to the starting (random) alllocation, you can construct a set of prices that is consistent with that allocation. So you're reduced to bargaining, which I guess means Nash arbitration.