A pedestrian shelters from the rain beneath a Union Jack umbrella near the Big Ben clock face and the Elizabeth Tower at the Houses of Parliament in central London on June 25, following the pro-Brexit result of the U.K.’s EU referendum vote. (Justin Tallis/Agence France-Presse via Getty Images)

Boris Johnson, the former mayor of London and likely future candidate for leader of the Conservative Party and prime minister, insists that Britain could strike an attractive deal with the European Union even if they’re not part of it. Johnson argues that Britain could still have free access to E.U. markets, while restricting immigration, avoiding E.U. rules and not paying into the E.U.’s budget. Will this actually play out?

Political scientists have done a lot of research  on countries’ bargaining strength in international organizations (IOs), as well as how well those organizations work when their members are more or less willing to go it alone outside of the organization. Here’s what that research shows.

Britain was already in a weak negotiating position

You might think (unless you have already read otherwise) that with the will of the people on its side, the Brits will be able to set favorable terms for any negotiations. Our research suggests the opposite.

Sometimes threatening to leave an organization like the E.U. can provide a government with bargaining leverage. More often, however, it leaves the government in a weak negotiating position. The key factor determining whether your threat makes you seem strong or weak is your exit options. If your exit options are attractive — that is, you are likely to do pretty well if you walk out the door — then your threat to leave is credible and you are in a good position to extract concessions. If, alternatively, it’s clear that you’ll have a hard time on your own, your negotiating partners have little incentive to be generous toward you or to cave to your demands.

This explains why British Prime Minister David Cameron’s talks with the E.U. in the run-up to the referendum didn’t provide a very attractive deal. However, if Britain now comes crawling back after a second referendum (or after failing to invoke the E.U. treaty article that would start the exit process), it will be in an even weaker position. It will have essentially jettisoned its exit options and its voice within the organization along with it.

Britain will have a tough time getting an attractive exit deal from the E.U.

If (as is likely) Britain leaves, it will then have to approach the E.U. as a non-member seeking an association agreement to regain access to E.U. markets. It is not going to be in a position to demand a good deal.

First of all, it will face the E.U.’s unanimity requirements. All the E.U. member states will have to agree to any deal before it goes forward. This means that just one member state can block the agreement. Before the referendum, Britain could count on the help of other governments that were sympathetic to it. Now, any deal will effectively be shaped by the single government most unsympathetic to Britain’s case, and most eager to punish it, since all other member states will need that state’s assent. If one or several remaining member states want to make the establishment of an association agreement very costly for Britain, the British will find themselves in a very weak bargaining position.

The E.U. will be very different without Britain

Furthermore, the E.U. that Britain is negotiating with will look very different than the E.U. that it left. With the U.K. gone, the balance of power within the institutions of E.U. decision-making will shift.  For example, the European Parliament will no longer have British MEPs. This means that it will shift somewhat to the left and toward more pro-integration positions.

Right now, 44 of the 73 British members of the European Parliament belong to right-wing, Euroskeptic parties. Patterns of conflict in the European Council could also change. While the precise nature of change will likely depend on the issues under consideration, it is plausible that the large states at the core of Europe — Germany and France — will gain even more influence.

The losers from all of this are likely to be the governments that are ideologically closest to the British. This may lead to new pressures on those governments that feel left out of the current system. We’ve argued that when one member wants a special deal with less integration, as the U.K. does, it can lead to a cascade of like-minded countries clamoring for the same.

This has implications for other international cooperation

The world, of course, is full of international organizations. None is quite so strong or binding as the E.U., but there are plenty of others — such as NAFTA and the Trans-Pacific Partnership and the United Nations.

Our research shows that generally, international cooperation works better in organizations where any one member would face significant costs — in trading opportunities, influence and overall prosperity —  if it were to exit. That is, international cooperation succeeds bests when there’s not much of a chance of any one member leaving.

Part of the reason why the E.U. has been so successful was that it was a club that everyone wanted to join. But when even one member starts edging toward the exit, the future starts looking uncertain. German Chancellor Angela Merkel already noted that since the referendum, markets seem to think that the E.U. looks ungovernable.

Any organization seeking to promote deeper cooperation would be wise to make the high cost of leaving very clear to all members.

Julia Gray is assistant professor of international relations at the London School of Economics and Political Science whose book “The Company States Keep: International Organizations and Investor Perceptions” will be available in paperback in July.

Christian Jensen is assistant professor of political science at the University of Nevada at Las Vegas. 

Jonathan Slapin is professor of politics and director of the Essex Summer School in Social Science Data Analysis at the University of Essex. His most recent book is “The Politics of Parliamentary Debate(co-authored with Sven-Oliver Proksch) and is the recipient of the 2016 Richard Fenno Prize and the 2016 Leon Epstein Outstanding Book Award.