In brief, Conservative MPs whittle the candidates down to two and then the party members choose between those two.
The whittling down is by a crude, and rather cumbersome, variation of Alternative Vote (AV) known as the “Exhaustive Ballot”. Yes, curious isn’t it? The Conservative Party campaigned against AV in the 2011 referendum!
The MPs start with a ballot paper that lists all the candidates – five this time – and they can each vote for one candidate.
The candidate with the fewest votes will be eliminated.
Then the MPs vote again on the four remaining candidates. Again, the candidate with the fewest votes will be eliminated, to leave three this time.
Finally, the MPs vote all over again on the three remaining candidates. Yet again, the candidate with the fewest votes will be eliminated, to leave the final two this time.
So, unless any candidates withdraw, MPs vote three times. It’s a good job there are only five candidates!
The system is described more fully at http://www.conservativeelectoralreform.org/conservative-leadership-election-explained/#comments.
The good news is that the party uses a system that is much better than the First Past The Post (Winner Takes all) system) it supports for electing MPs. The bad news is that the system it uses is so slow and inefficient.
If the Conservative Party used a preferential voting system like proper AV, there would still be up to three stages of counting but only one stage of balloting and the result would have been known today. All they would have to do would be to number the candidates in order of preference.