With all this talk of "unelected Prime Ministers", I think it would be very dangerous to insist that when the Prime Minister changes there is an election within 6 months. In my lifetime Anthony Eden, Harold Macmillan and Harold Wilson resigned due to ill health, I think it may have been more difficult for them to resign if an election would have followed. I don't want an unwell man or woman to feel under pressure to continue as Prime Minister. It is also interesting that in The USA when both the Vice President and President left office an "Unelected President" served the remainder of the term, Spiro Agnew, Richard Nixon and Gerald Ford respectively.