Forthcoming research by Ravideep Sethi illustrates how democracies can structure treaty negotiations, how groups of plaintiffs can bargain with defendants, and how shareholders might haggle with corporate raiders.

Two countries bargain with each other over a new treaty. Any resulting deal must go through a ratification process within each nation. How should the nations bargain? What ratification rules make sense?

This question is fundamental to the design of national institutions. The United States Constitition, for example, requires the Senate to ratify any treaty by a 2/3 supermajority. Further, the Senate has in practice delegated much of the final negotiation of treaties to the Senate Foreign Relations Committee. Do these two practices — supermajority requirements and delegation — lead to better negotiated outcomes?

Using the mathematical tools of noncooperative game theory, Professor Ravideep Sethi and co-author WonSeok Yoo examine these questions. Their paper, which is now forthcoming in the journal Games and Economic Behavior, shows that while supermajority rules can help a nation strike a good deal, delegation is not a smart negotiating tactic.

“Our key insight is that institutional structures can impact how intensely group members compete against each other to extract the gains from a deal. The winners and losers can be played against each other,” Sethi said. “This fact then feeds back to influence the deals that are proposed by each side in the negotiation.”

Sethi explained that a treaty under consideration in the US Senate might be good for Utah, but bad for Idaho. If only a simple majority of Senators is needed for passage, then the other party to the treaty — Canada, for example — can exploit this by proposing a deal that is good for just 26 of the 50 States. If, in contrast, a 2/3 supermajority of Senators is required, then Canada must propose a deal that will attract yes votes from 34 States. The US supermajority rule limits Canada’s ability to play the States off against each other, and increases the overall value captured by the US in the negotiation.

Delegation can also feed into the Sethi-Yoo winners-and-losers effect, but in an opposite way. “When negotiations are delegated to a chosen subgroup, the group members who are not in the subgroup realize they will be unable to craft a deal that benefits them,” Sethi explained. “This means they are more willing to accept a not-so-great deal, which weakens the group’s overall ability to bargain effectively.”

As an concrete example of these effects, Sethi and Yoo highlight the 1944 US/Mexico Water Treaty, in which the two nations reached an agreement on how water in the Rio Grande and Colorado Rivers would be allocated. Interestingly, this deal created stark winners and losers among the US States. In exchange for a larger share of Rio Grande water (which was usable only by Texas), the US agreed to give Mexico a larger alottment of Colorado River water (which would have been used mostly by California).

The elements of delegation and supermajority were both present in this setting. Important elements of the negotiation were delegated to the Senate Foreign Relations Committee, chaired at the time by Tom Connally of — you guessed it — Texas. While this delegation may have allowed Mexico to make proposals benefitting Texas but against California’s interests, this effect was somewhat curtailed by the Senate’s requirement of a 2/3 majority to approve the treaty. Any agreement would require the approval of 64 of the 96 (at the time) Senators, thus limiting Mexico’s ability to pit the states against each other in ratification.

Sethi emphasized that international treaty negotiations are not the only application of his analysis. “Bargaining on a behalf of a group is common in business settings as well,” he said. “Labor unions negotiate with employers, but the gains from any union contract might be spread unevenly across union members. And this means the delegation and supermajority choices made by the unions could have a big effect on outcomes.”

Ravideep Sethi and WonSeok Yoo, 2024, “Group Bargaining: A Model of International Treaty Ratification,” Games and Economic Behavior, forthcoming.