2. These MPs will now choose a leader from amongst themselves. The ones with the ten most votes (designated the Prime Ministerial candidates) will enter something like the Big Brother House in which they will stay until they elect the Prime Minister of Britain. Every Prime Ministerial candidate will spend a day in discussion with each of the other candidates until he/she has spent a day with them all. This will take 9 days and the cameras will be broadcasting everything as it happens.
3. There will be a Diary Room where the candidates can take refuge and share their thoughts with the world at large. I think it would be fascinating if they were given a challenge or two to keep them occupied. I'm not sure exactly what but given that all politicians are expert at dissembling, intrigue and deception, something that plays to these attributes would be appropriate. Cluedo, perhaps?
4. On the tenth day, each of the candidates will vote for the candidate they think is most suitable for leadership, apart from themselves. The one with the highest number of votes becomes Prime Minister and the ritual smoke signal is sent out to the world.
This idea needs further development but it has got to be an improvement on the present system, hasn't it?