[nightwing]

With e-voting can keep mostly the same system we have now, but augment that with two small changes. 1) you can change your representative at any time, which changes the weight of his vote, 2) you can overrule your representatives vote on issues you care about.

In this way there won't be a situation like Brexit because after initial open ended vote people can participate in subsequent votes too, and can eventually decide that they don't want Brexit or want it even without any trade agreements.

Fake news, (or rather people not smart enough to distinguish fake news), will remain a problem, but democracy uses assumption that most people are smart enough, if this assumption is not true then oligarchs buying politicians is actually useful to the society, but i don't think this is very likely.