Why not just pop everyones name in to a hat and pick out MP's at random. Make it a little more interesting choose (randomly) an MP for every county and every City. That way there should be more of a real sample of the populase. What we have by voting is 'in general', male, white, middle aged with a law degree and mostly (mediocre conceited sicophants*). Unless you believe Mrs. Smith of Arcacia Ave, Sheffield is a lesser person than say D. Cameron.

*Personal opinion.