How could we fix our broken democracy?

I was listening to Start the Week this morning (BBC Radio 4 9am Start the Week) and someone said that our democracy worked in the 19th century because the electorate was relatively small and everyone spoke / understood the same political / cultural language, but that now the electorate is so heterogeneous it is no longer possible for politicians to say anything very sophisticated because most of the different demographics will simply not understand or relate to what the politician is saying. So we are reduced to soundbites and tweets, and constant repetition of simple messages (e.g. that the deficit is all Labour's fault, or that the Conservatives are cruel and heartless and want to privatise the NHS).

And the biggest problem is that the professionalised political class are only interested in the very small minority of the electorate that occupies the mysterious and mythical centre ground and will decide the result of a general election in a small number of marginal seats. So, unsurprisingly, the great majority of the electorate are simply bored and uninterested in what the politicians (and the political media) are saying.

So what's the answer?