daughterofbonniebelle
One of the many depressing aspects of this whole pantomime is that the new prime minister is not appointed democratically, but voted in by some smug Daily Mail readers, and the population accepts this whole sorry process as reasonable and normal.
He/she is appointed democratically. When you vote, you vote for YOUR MP, not the PM or the leader of the Party. The party with the most MP's (all fairly elected under the current rules) then puts its leader in the top role. You could equally argue that we don't vote for the Chancellor of the Exchequer, the Foreign Secretary, etc, etc.
If you want to vote for a Prime Minister, join the Party so you are entitled to vote. If you did, you could also legitimately campaign for a change in the rules of how the Tory Leader is chosen.