On last night's News Night, Shami Chakrabarti said police chiefs shouldn't be elected by referendum. She didn't elaborate why, except to paint a picture of an elected BNP police chief, which is perhaps a bit unlikely considering that BNP members are banned from the police. I imagine one worry is the "tyranny of the majority" argument. Perhaps another concern is that senior police should be focused on policing, not electioneering, but, given that the police's role isn't just to fight crime, but to reduce the fear of crime, aren't they already in the game of public perception?
Page 57 of the 2010 Conservative Manifesto says that they will enable a "directly elected individual" power over local police budgets and strategy.
Page 72 of the 2010 Liberal Democrat Manifesto proposes "direct election of police authorities", but concedes that they can involve other members to improve diversity.
Behind the idea of Interactive Democracy is that all of politics should be opened to public votes, with the exception of issues of national security that require secrecy. Worries about the tyranny of the majority are worries about democracy its self!