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The problem as I see it is less how the people voted(/debated) either way, and more of the establishment's arrogant disdain for the people that disagree with them.

"Those pesky proles wouldn't actually vote Leave, and even if a few do there's no way it will be a majority, so we can stay the course with the EU because that's all we are offering and they are gonna have to take it either way." - my mental image of center-left politicians.

Exact same attitude annointed Clinton with the nomination.