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
make a decision only on the basis of this information?
choose an alternative which is Pareto-undominated (i.e., which cannot be improved upon for one of the parties at no cost to the other)?
not force upon the parties an agreement which leaves one worse off than if no agreement had been reached?
choose symmetrically when the original problem is symmetric?
not change his mind if he learns that an agreement which he was not going to choose anyway was in fact not feasible?
If so, then the arbitrator must always choose the agreement that maximizes the product of the parties' utility gains (see this).
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.
If a social choice procedure is monotonic (i.e., if raising an alternative in some individual's ranking never lowers its social ranking),
if the individuals as a group can put any alternative “on top”, and
if the social ranking of any two alternatives depends only on the individual rankings of those two,
... then one of the individuals must be a dictator.