LONDON — Things were simpler for Britain’s governing Conservatives in 1963, when a group of bigwigs called the party’s “magic circle” simply got together and chose the new party leader, and hence prime minister, themselves.

The question facing the Conservative Party today is whether the current system is really much of an improvement.

This month, either the former foreign secretary Boris Johnson, or his successor in the post, Jeremy Hunt, will replace Theresa May after ballots among Conservative lawmakers in Parliament, six hectic weeks of campaigning and a vote among the 160,000 members of the party — about 0.3 percent of voters — who are the only ones with a voice in this contest.

While the vote by that tiny minority has rankled many, it is hardly the only thing that critics say is wrong with the process. In fact, some say it may be the only thing right about it.