Sen. Sherrod Brown, a Democrat from Ohio, speaks to members of the media about the Trans-Pacific Partnership (TPP) in the Senate Press Gallery at the Capitol in Washington, D.C., on Thursday, April 23, 2015. (Andrew Harrer/Bloomberg)

The House has just voted down an item of legislation that was critical to Obama’s hopes to get authority to negotiate TPP, a trade deal with countries in the Pacific region. It’s nearly certain that Congress will return to this legislation in the coming weeks or months. Nonetheless, some people believe that this cripples America’s ability to bargain hard with its allies. For example, Timothy Lee at Vox argues that the vote will “weaken the president’s bargaining position overseas as he wraps up negotiation over the TPP” because:

The leaders of other TPP countries such as Japan, Australia, and Chile will have to make politically costly concessions in order to conclude the TPP negotiations. They’re only going to be willing to do that if they think there’s a good chance the deal will actually be ratified.

Lee may be right, but there’s a body of work making just the opposite argument, stretching back to the Nobel Prize winning game theorist Thomas Schelling who conjectured that weakness back home may translate into negotiating strength abroad.

What is the Schelling conjecture?

Back in 1960, Thomas Schelling argued that U.S. negotiators would be best able to bargain with other countries when they were weak rather than strong. As he describes it:

when the United States Government negotiates with other governments on, say, the uses to which foreign assistance will be put, or tariff reduction … [i]f the executive branch is free to negotiate the best arrangement it can, it may be unable to make any position stick and may end by conceding controversial points because its partners know, or believe obstinately, that the United States would rather concede than terminate the negotiations. But, if the executive branch negotiates under legislative authority, with its position constrained by law… then the executive branch has a firm position that is visible to its negotiating partners.

Princeton political scientist Helen Milner has dubbed this claim the “Schelling conjecture.” It has given rise to a significant research literature in international relations, which looks at the complicated two level relationship between domestic politics and international negotiators. The logic is pretty straightforward. If the U.S. negotiator is ‘strong’ — that is, the negotiator has a lot of authority to do what is necessary to reach a deal — then other governments will be more likely to press for concessions, because they know that the U.S. negotiator can grant these concessions and may prefer to make concessions than to have the talks collapse. However, if they know that they are dealing with a weak negotiator, who doesn’t have the ability to make big concessions, they may be more prepared to accept U.S. demands. When this logic applies, it makes sense for the United States to ‘tie the hands’ of its negotiators in order to extract the strongest concessions possible. Schelling argues that the U.S. system — where the presidency is bound by the wishes of Congress — strengthens the hand of U.S. negotiators, exactly to the extent that it makes them weaker. Because the negotiators have to do what Congress has told them to do, they have little freedom to make concessions to foreign negotiators.

What has just happened could turn out to be an example of the Schelling conjecture in action. Congress has just voted down legislation, in part because Democrats worry about how a free trade deal will hurt labor. This could serve as a credible signal to the negotiators of other countries that the United States is serious in its demands for labor reform, by demonstrating that a deal that is weak on labor issues will have difficulty passing Congress. For the same reasons, it may oblige the administration to alter its negotiating position on sensitive labor issues to try to get legislation through in the future.

But mightn’t negotiations just collapse?

Possibly. Robert Putnam’s classic article on two level games provides a simple way to think about this. Imagine that there is a universe of possible agreements that the United States could find acceptable. Imagine that there is also a universe of possible agreements that the United States’s negotiating parties in the Pacific region could find acceptable. Putnam calls these universes of possible agreements ‘win sets.’ When countries win-sets intersect so that there are some possible agreements that are acceptable to all countries, then it is possible to do a deal. If there are no agreements that all countries can accept, then no deal is possible.

This helps us think about the consequences of today’s vote. What it does is to shrink the U.S. ‘win set.’ There are some possible agreements that the United States will not now sign up to, because they would cause too much domestic opposition. This has two consequences. First, it strengthens the U.S. bargaining position if a deal is possible, since it shows that politicians back home are simply unprepared to accept some deals, forcing other countries to move closer to U.S. preferences. Second, however, it makes a deal less likely. It may be that the United States win set has shrunk so much that there are no deals that are likely to be acceptable to the United States that would also be acceptable to all other negotiating parties.

What this logic of negotiating suggests is that there is a fundamental tradeoff between bargaining strength and the likelihood that a deal is reached. The tougher your negotiating stance, the easier it will be to extract concessions from your partners as long as there is an attractive deal for them on the table. If you are so tough that there’s no attractive deal for them (your win set is so small that it doesn’t intersect theirs), then both you and your negotiating partners are going to go home empty handed. Hence, the political science logic behind Lee’s argument would be that if other countries think that the U.S. win set is too small for there to be a deal, they won’t make concessions.

Is this way of thinking about the world right?

Not in all circumstances, but often enough to be useful. On the one hand, there isn’t much direct evidence for the Schelling conjecture, and indeed one prominent set of studies concludes that there is “little support for the proposition” that negotiators do better when their hands are tied. Furthermore, this way of thinking about the world leaves out important aspects of real life bargaining. Actual real life negotiators have some sense of the positions of their home country legislators and foreign opposite numbers, but there may also be a lot of uncertainty. On the other, it may be that it’s hard to prove or disprove these arguments because they are about what happens in people’s heads, which we obviously cannot observe directly. The Schelling conjecture and the idea of win sets (and later, more mathematically sophisticated game theoretic studies of this topic) do capture plausible and important aspects of the logic of international negotiations. They suggest that Obama’s loss may benefit U.S. negotiators rather than hurting them — but only as long as other countries still think that there is an attractive deal on the table.