How should one choose a prime minister?

This blog post from Tim Bale looks at the selectorate of Conservative Party activists that will choose the next prime minister. Unsurprisingly, they are neither demographically or ideologically representative of the population as a whole. Party activists have been called a zealocracy: Party members who will elect prime minister

This has attracted plenty of objections, but how one would do it differently? One argument is that it should be left to MPs who at least know the strengths and weaknesses of the candidates. But does this give too much power to a much criticised political class?

Some would argue that the selection of a new prime minister should lead to a general election. But that is to treat the UK as a presidential system which it isn't. Some would say it is in effect. However, following such a rule would undermine cabinet government even further.

Of course, there may well be a general election within the next year anyway, either from a position of strength or weakness for the new prime minister.