The U.S. system is somewhat unique in that we have regularly scheduled elections with a regularly scheduled process for choosing candidates, mostly by means of elections open to most voters. Other countries do things differently. Many countries are parliamentary systems with the Prime Minister being a hybrid of the U.S. President (in terms of power), the U.S. Speaker of the House (in terms of being officially chosen by the whole House and removable by the whole House), and Majority Leader of the Senate (in terms of being removable by the majority of the majority party).
In recent weeks, the Trumpish Prime Minister of the United Kingdom, Boris Johnson, has been bogged down by scandals. Last week, the heat got too high for many members of the Conservative Party, and an open revolt forced Boris Johnson to agree to resign. Under the British system, this means that the Conservative Party has to choose a new leader who will then become Prime Minister.
There are no formal rules for this type of leadership election and, when this situation occurs, it falls to the Conservatives in Parliament to draft the rules that will apply to this election. This time, they have chosen a rather expedited process. The rules were announced just yesterday.
Under those rules, any person wanting to run for the leadership had to file by the end of the day today. To qualify, a candidate needed the support of at least 20 of the Conservatives in Parliament. As the Conservative Party only has 358 members, this instantly guaranteed a maximum of 15 contenders could file. By the end of the day today, a total of eight senior members of the Conservative Party had filed.
The first round of voting will be tomorrow in the early afternoon. Initially, the voting is limited to those 358 Conservative Members of Parliament. In the first round, a candidate needs at least thirty votes to advance. If all eight get to that threshold, the last placed candidate will be eliminated. There will then be successive rounds of voting scheduled with the last placed candidate being eliminated. Once the field is narrowed to two candidates, the voting will switch to all dues-paying members of the Conservative Party. The vote among all members of the party will be a party-run election conducted by postal vote. The exact timetable for this postal vote is unclear, but the expectation is that the winner will be announced no later than early September.