Sympathy for May? How Game Theory Explains Her Brexit Strategy

By Xiaodon L. Liang

Theresa May is on her way out, finally. This week, Conservative detractors rallied enough support to credibly threaten another leadership challenge, forcing her hand. Never mind the process or the method—neither is important when her rivals have been demanding she step down since December, when her Brexit withdrawal agreement was first introduced to parliament. The charge: the Brexit “mess” created by her lack of a clear strategy.

As a social scientist, it’s always humbling to recognize that some models and methods may be good for explanation, but not necessarily prediction. After all, what’s the point of a theory that can’t tell us anything about the future? In the case of Theresa May’s Brexit, however, applying a few basic concepts from game theory to merely explain her strategy since December does have value. First, it demonstrates that such a strategy existed. Second, it exposes just how ignorant—perhaps willfully—her critics have been in mischaracterizing this past winter of parliamentary politics as a rudderless exercise in time wasting.

Between late November, when the withdrawal agreement was agreed, and the original Brexit deadline of March 29, 2019, two years after the United Kingdom first notified the European Union that it was leaving, the problem confronting May could be described as an extensive game with incomplete information. “Extensive,” in game theory vocabulary, simply means that key decisions must be taken one after the other, rather than all at the same time. First, members of parliament (MPs) had to decide whether to endorse the deal. Second, if the deal failed, they had to decide whether to crash out of the EU without a deal. With complete information, an extensive game can be solved by working backwards from the final possible outcomes, figuring out which end-states are acceptable to which players in the game. With incomplete information, however, that becomes difficult.

The critical incomplete information for May was not how parliament would vote on her deal—she knew by December that the numbers were not there. Rather, the critical hidden information was what the order of preferences across the possible end-states was for the key voting blocs. That is, what were the second- and third-most preferred outcomes for each group when they knew that their first choice was taken off the table? Without knowing these preferences over outcomes, we cannot work backwards to solve the game. Clearly, May believed that second and third choices would generate a majority for her deal. To that end, her strategy focused on controlling perceptions of what outcomes existed and slowly forcing MPs to reveal their second- and third-choice preferences.

For May’s strategy to work, she first had to define which outcomes were possible. She attempted to do this by claiming that without endorsement of her deal, Britain risked a no-deal Brexit or no Brexit at all. Thus, in May’s framing of the game, there were three—and only three—outcomes: her deal, a hard Brexit on March 29, or a soft Brexit/second referendum (which I’ll refer to in this blogpost as SBSR, recognizing that these are not the same and that there are many divisions within the Remain camp).

The major blocs in parliament, organized in terms of their first preferences among these outcomes, were fairly easy to identify. To generalize, there were three groups: “hard Brexiters,” “Remainers,” and “May loyalists.” For the hard Brexiters, a no-deal Brexit was the only acceptable outcome. For the Remainers, forcing a second referendum or a permanent customs union was the goal. And for most of May’s loyalists in the Tory party, her deal could be a middle path toward a managed Brexit. The problem of incomplete information arose because it was unclear whether hard Brexiters would prefer Theresa May’s Brexit deal or SBSR if a no-deal Brexit was taken off the table by the clear majority against no deal. This was, in effect, a choice between accepting half a policy loaf or receiving nothing while standing up for ideological purity. Similarly, it was not clear how many of the Remainers would see Theresa May’s Brexit deal as a second-best choice if the other option was a no-deal Brexit that would hurt the economy and cement UK estrangement from the EU.

The second part of May’s strategy was to slowly reveal second preferences by convincing both hard Brexiters—primarily in her own party—and Remainers—both on her party’s centrist flank and in the Labour party—that their most-favored outcome was becoming less likely over time. Essentially, she was engaged in two games of “chicken” at once. In the chicken game, two players are on a path of mutual destruction unless one—or both—decide to swerve. May sought to convince hard Brexiters to swerve toward her deal by creating the fear that her loyalists’ second preferences would lead them to endorse SBSR as the March 29 cliff’s edge approached. At the time, she sought to convince Remainers to swerve toward her deal by creating the simultaneous fear that she would allow the Conservative party to jump off the same cliff’s edge.

May bet that enough hard Brexiters would be exposed as preferring her version of Brexit over the possibility of no Brexit at all. Indeed, this strategy almost worked. After her deal was defeated in January by 230 votes—a record government defeat in modern times—it improved its support in early March when it was defeated by only 149 votes. As whips—both in government and the press—attempted to count the number of hard Brexiters who would switch to supporting the deal as March 29 approached, the likely margin improved over time. She had less luck with opposition Remainers, picking off only a few of the relatively scarce Labour hard Brexiters.

This strategy may have been duplicitous, and it may have generated inconsistent headlines and actions, but it was still a coherent and valid strategy. That the British press described it as otherwise was a failure of explanatory journalism, laced with open hostility toward a universally disliked prime minister.

If the strategy was coherent, why did it fail? The key condition for success, control of parliamentarians’ options, escaped May’s hands. With parliament threatening credibly to take control of the agenda and to force an extension, May could no longer insist on a choice between the outcomes she had constructed. Extension and the possibility of a general election both emerged as alternatives.

While I’ve argued that May deserves more sympathy than the British press has given her, there is a limit to this charity. Her approach was narrowly focused on extracting the minimum number of votes from parliament through a strategy of brinksmanship, rather than working across the aisle early on to forge a compromise that could win a maximum number of votes. Her strategy risked divisiveness and failure in a bid to preserve the autonomy and electoral support of the Conservative party. In the end, she delivered the worst of both worlds, dividing the country and splitting her party despite her best efforts. Whether that failure deserves punishment through dismissal or not, her critics must at least recognize and appreciate the strategy that produced the defeat. May deserves at least some sympathy, independent of how much condemnation should go along with it.