The Nash Arbitration Scheme

Given complete information about (1) the available alternatives, (2) the preferences of the two parties, and (3) both parties' best alternatives to agreement, should an arbitrator

If so, then the arbitrator must always choose the agreement that maximizes the product of the parties' utility gains (see this).

Arrow's Impossibility Theorem

A social choice procedure associates a preference ordering (for society) with each collection of individual preference orderings.

Assume there are at least three alternatives, and at least two individuals.

... then one of the individuals must be a dictator.