The “Battle of Brexit” has left British politics in chaos. After Boris Johnson became leader of the governing Conservative Party on July 23, he promised to take the United Kingdom out of the European Union by Oct. 31, “do or die.” To achieve this, he prorogued (suspended) Parliament and wants to hold a general election.

Opposition politicians, assisted by Conservative rebel MPs and Speaker John Bercow, have thwarted Johnson’s efforts, promising to not let the United Kingdom leave the E.U. without a deal. They maintain they will allow an election only after the Oct. 31 deadline has passed. Some time in November seems likely.

If there is an election, what are the parties’ chances? What strategies might they pursue to maximize their support?

We used data on voting in the last general election in June 2017 and 350 polls conducted since then to determine how many seats British parties would probably win. Our prediction is a “hung Parliament” with no clear majority. The Conservatives win the most seats (323 of 650). Among the opposition parties, Labour gets 223 seats, the Liberal Democrats 32, and the Scottish Nationalists (SNP), 48. Nigel Farage’s new Brexit Party is shut out.

Tactical voting and cross-party appeals might have big consequences

Here’s how the parties might boost their chances. Labour and Liberal Democrat supporters might try tactical voting, opting for the other party in competitive (marginal) constituencies where that party has a good chance of winning. By combining their votes Labour and the Liberal Democrats would boost their chances of defeating the Conservative candidates.

Figure 1 shows that this strategy would produce a large increase in Labour seats (from 223 to 271), with the Conservatives reduced to 277. The Liberal Democrats would win 30 seats and the SNP would get 48. The Brexit Party would win one seat. This outcome would enable Labour to form a minority government supported by the Liberal Democrats and SNP.

The second strategy involves the Conservatives winning back followers of Farage’s Brexit Party. In the May E.U. Parliament election, the Brexit Party came in first with an impressive 30.5 percent vote share. The Conservatives were reduced to 8.8 percent, their worst showing in history.

Figure 2 shows the Conservatives would benefit handsomely by getting these voters back. Our survey data show nearly two-thirds of Brexit Party voters identify with the Conservative Party — they strongly favor leaving the European Union, and many prefer to go with “no deal.” Our analysis assumes there is Labour-Liberal Democrat tactical voting, but also assumes half of Brexit Party supporters (7 percent of all voters) return to the Conservatives.

Under this scenario, the Conservatives win a comfortable majority with 362 seats; Labour is reduced to 196, and the Liberal Democrats and the SNP capture 27 and 41 seats, respectively.

Analysts see getting Farage’s “Brexiteers” back on board as a priority for the Conservatives. Nearly two-thirds of the 632 British constituencies had “Leave” majorities in the 2016 E.U. referendum. With the help of erstwhile Brexit voters, Conservative candidates would do well in many of these places.

It may be tough for Conservatives to win Brexit Party voters over

But can the Conservatives attract Brexit Party voters? Many of them are very unhappy with former prime minister Theresa May and her Conservative government, who failed to deliver the promised Brexit.

There’s a further trust issue — pro-Remain advocates note the Conservative Party sacked Johnson earlier in his career for lying. On Friday, the U.K. Supreme Court ruled that Johnson lied to the Queen when he sought her formal approval to prorogue Parliament, making his suspension of Parliament unlawful.

The fear among some U.K. voters is that Johnson would use Brexit Party supporters to win an election and then double-cross them by negotiating a “soft Brexit” with the E.U., not materially different from what May attempted to do.

There are also rumors that Farage and chief Conservative strategist Dominic Cummings dislike each other intensely — making Farage less likely to ask his voters to support the Conservatives. Their enmity originates in the 2016 E.U. referendum, when they competed bitterly to lead the “Leave” campaign. According to a recent news report, “senior Conservatives” have emphasized that Farage and his major financial backer, Arron Banks, are not “fit people” to be anywhere near government.

Liberal Democrats and Labour have decisions to make

The Liberal Democrats also face strategic trade-offs about helping Labour with tactical voting. Invigorated by articulating a clear pro-Remain position and a strong showing in the E.U. Parliament elections, many Liberal Democrats may believe they are poised to replace Labour as the major left-of-center alternative in British politics.

Labour is having its own troubles. Party leader Jeremy Corbyn remains massively unpopular, with approval ratings under 20 percent. Also, many Labour supporters are unhappy that Corbyn is unwilling to advocate a clear pro-Remain position. Major disputes at Labour’s annual conference over the weekend show that the party is deeply divided on the issue.

Recognizing these difficulties, Liberal Democrat leader Jo Swinson may decide not to cooperate with Labour. If Labour loses badly, post-election recriminations could quickly split the party — leaving the Liberal Democrats to “hoover up” Labour moderates fed up with their party’s actions.

Swinson recently said she will not do a coalition deal with any rival party, including Labour. Making a strong pitch for the Remain vote, she promised a Liberal Democrat government would prevent Brexit by revoking Article 50 without holding a second referendum.

Nothing is simple in U.K. politics at the moment. The decisions the parties make will be consequential. Johnson needs to attract Brexit Party supporters if he is going pull off a majority government. If he fails, he very likely will be one of the shortest-tenured prime ministers in British history.

Harold Clarke is Ashbel Smith professor at the School of Economic Political and Policy Sciences of the University of Texas at Dallas.

Matthew Goodwin (@GoodwinMJ) is professor of politics and international relations at the School of Politics and International Relations, University of Kent.

Marianne Stewart is a professor at the School of Economic, Political and Policy Sciences of the University of Texas at Dallas.

Paul Whiteley is professor in the Department of Government at the University of Essex.