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Will Theresa May resign? Here are five possible replacements

060917 Rogan MAY
Let's say a leadership election is triggered. Who would run and who might win? (Stefan Rousseau/PA Wire)

British Prime Minister Theresa May is under pressure.

For losing her Parliamentary majority in yesterday's election, May has attracted the ire of senior Conservative politicians. They believe she is too arrogant, too inflexible, and too uncharismatic to lead the party to a better future. Many want a leadership election that would depose her.

In the U.K., the leader of the governing party automatically becomes prime minister. This means that a new Prime Minister would only need to be elected by Conservative Party members. He or she would not need a mandate from the broader electorate. That gives Conservative MPs an opportunity.

May says she is staying put. Britain, she says, needs her stability in leadership.

But ultimately it's up to the Conservative backbenchers (parliamentarians who do not hold ministerial posts in government). And if they want, they could force May out.

Time is of the essence. With Brexit negotiations due to begin in just over a week's time, the country needs clarity. That leaves the backbenchers with three choices.

First, they could bury their anger and accept May's continued premiership. Second, they could accept May's premiership for a few months so that the Brexit negotiations get off to a stable start. Third, they could push for an immediate leadership election.

Let's say a leadership election is triggered. Who would run and who might win?

I think five names stand out.

First up, Boris Johnson. The current foreign secretary (equivalent of the U.S. secretary of state), Johnson is charismatic and intelligent, but also eccentric. In Johnson's favor? He's popular with the public, and with Conservative politicians and party members. A proponent of leaving the European Union prior to the Brexit vote, Johnson is seen as a leader who would see Brexit through, whatever the costs. Johnson's problem? He's seen as unpredictable. Conservative MPs worry that as much as they like him, Johnson would mess up the Brexit negotiations with the EU. Or become a joke (for an example, click here).

Second, Amber Rudd. The current home secretary (responsible for domestic security), Rudd is close to Theresa May and respected across the party. She also has campaign leadership experience as May's chief surrogate. That said, Rudd is seen as perhaps too much of a May-type politician. Her style is direct and confident, but not terribly charismatic.

Third, David Davis. The current Brexit minister, Davis is a cool customer. He's also a political plotter who has long sought the Conservative leadership. Davis also benefits from his reputation with the public. Educated at public rather than private school (many Conservative MPs attended private school), and a former Special Forces reservist, Davis is seen as a politician who can win support from constituencies that lean towards Labour.

Fourth, Liam Fox. An avowedly pro-Brexit politician, Fox is currently Britain's international trade minister. But he's also an experienced minister who previously served as Britain's defense secretary. That experience gives Fox a platform to campaign and unbeatable Brexit credentials (an important factor for many Conservative backbenchers). Also in Fox's favor? The fact that he's Scottish. The Conservatives performed exceptionally well — to the surprise of many — in Scotland yesterday. They want to build on that success in the coming years. Fox's vulnerability? He may not be able to appeal to voters skeptical of a hard Brexit. He is also portrayed by the media as too right wing.

Fifth, Jacob Rees-Mogg. The epitome of an old-school upper class "Tory", Rees-Mogg is nevertheless popular with the public. An eloquent expert on Parliamentary procedure, he is also well-regarded by Conservative colleagues. And though he is the antithesis of David Davis, Rees-Mogg wears his upper class background on his sleeve but matches it to a self-deprecating sense of humor. This attracts voters who like his carefree attitude.

It is entirely possible, of course, that none of the above may ever live at 10 Downing Street. Perhaps May will quiet her critics and stay on for the next five years. Perhaps she will even win again in 2022! But if a leadership election does come, May has a big problem. And one of the above will likely become Britain's next prime minister.