Ranking Agendas for Negotiations

Consider a negotiation in which agents will make costly concessions to benefit others—e.g., by implementing tariff reductions, environmental regulations, or disarmament policies. An agenda specifies which issue or dimension each agent will make concessions on; after an agenda is chosen, the negotiation comes down to the magnitudes of agents’ contributions. We seek a ranking of agendas based on the marginal costs and benefits generated at the status quo, which are captured in a Jacobian matrix for each agenda. In a transferable utility (TU) setting, there is a simple ranking based on the best available social return per unit of cost (measured in the numeraire). Without transferable utility, the problem of ranking agendas is more difficult, and we take an axiomatic approach. First, we require the ranking to depend only on trade-offs between costs and benefits that an issue induces, not on choices of units. Second, we require that the ranking be consistent with the TU ranking on problems that are equivalent to TU problems in a suitable sense. The unique ranking satisfying these axioms is represented by the spectral radius (Frobenius root) of a normalized Jacobian—a statistic we interpret in terms of a network whose links represent agents’ abilities to help each other.