"A majority of British voters cast votes for Gordon Brown under the expectation that he would manage the economy, and that's all. Instead he used his role to grab power, at the expense of the people"
Is this a fair paraphrasing?
I can then rephrase your original sentence:
"Democracy is when elected officials act in a way that voters approve of. Politics is when elected officials act in their own self interest, in a way contrary to what voters want"
Is that it? Or let me try a second, different, way of paraphrasing:
"Democracy is when elected officials act in a way that benefits the public good ( whether the public realizes it or not). Politics is when an elected official acts in a way the benefits himself, regardless of the public good"
Is one of these summaries fair? I'm not trying to be difficult, I'm just trying to nail down precisely what you are trying to say.