Currently, the choice of who takes over if a Prime Minister steps down is left to the party he represents. 

'Party leaders are chosen by an internal process normally in advance of a general election, or in the case that a leader steps down or is forced out. To take part in the race, a Conservative member of parliament needs to be nominated by at least eight colleagues. Likely candidates to follow Johnson include former finance minister Rishi Sunak, former defense secretary Ben Wallace, and former health secretary Sajid Javid, among others. A winner is selected from the nominated individuals in a two-stage process.

First, MPs whittle the candidates down in a series of secret ballots, whereby the candidate with the fewest votes is eliminated at each round until two are remaining.

In the second stage, card-carrying grassroots party members vote on the final two candidates. (It’s possible that it never goes to a final run-off, as was the case in 2017, after May’s opponents were eliminated or eventually withdrew.) Anyone in the U.K. can become a member of a party, provided that they pay a membership fee—which is £25 ($30) for the Conservatives. The Conservative party has around 200,000 members. This means that the final decision to select Johnson’s successor will be made by roughly 0.29% of the British population. (Credit: Time.com)'

This is fundamentally unfair. The majority of the population voted for Boris Johnson, based on his campaign. Not for the party. Switching the representative of that party mid-term and not allowing that same populace a vote on who should replace him is nothing more than a bait and switch. 

Since this petition was created, we've had another Prime Minister who stepped down after less than 2 months in office, and yet again we have a new Prime Minister we did not vote for. This is untenable, and unconstitutional. 

Who replaces him and other Prime Minsters who step down mid-term should be the subject of a referendum.