Thinking and Deciding

NEGOTIATION 437
outcomes for one party on one axis of a two-dimensional graph and the possible
outcomes for the other party on the other axis. The axes can now represent utilities,
or amounts of money, or any other quantities. The diagram represents a hypothetical
case in which two brothers bargain over an inheritance that they must divide among
themselves and that is their main wealth. The axes are the utilities. Brother A lives
in a country that taxes inheritances above a certain amount.
An important set of outcomes is shown as a dark line. These are “best possible”
outcomes, in a certain sense: Each outcome cannot be improved upon for one party
without making the situation for the other party worse. Outcomes of this sort are
called Pareto optimal (after the economist Vilfredo Pareto). Pareto optimal outcomes
are said to dominate all other outcomes, because they are at better in some ways and
worse in no ways. The set of Pareto-optimal outcomes is called the “Pareto frontier.”
For any outcome not on the Pareto frontier, we can find another outcome that is better
for at least one of the two parties and worse for neither. Nonoptimal outcomes cannot
maximize utility, so we can say something about utility maximization, even when we
cannot compare precisely the utilities of the parties.
A body of theory has developed to help choose among Pareto-optimal outcomes
(see Elster, 1989b, and Luce and Raiffa, 1957, ch. 6). Although utilitarian theory
specifies that the outcome chosen must have the highest total utility, the parties cannot
find that outcome unless they trust each other and know enough about each other
to compare their utilities. (Married couples can sometimes approximate this situation,
but strangers or adversaries typically cannot.) Nash (1950) suggested maximizing
the product of the two utilities rather than their sum. This yields the same
solution, even if one of the axes is multiplied by a constant, and it has other neat
properties. It does not make the task of negotiation much easier, however.
A third representation of negotiation is possible when two or more dimensions
are at issue. For example, in the sale of a house, the parties often negotiate about both
the price and the time when the transfer will occur. If the seller needs the money in
a week to pay for a new house but the buyer is in no hurry, the speed of the sale can
mean much more to the seller. Unless she gets the money right away, she will have