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> Systems like approval voting or STV when used with single member districts do not reduce the two party duopoly.

What do you mean?

Suppose you have a single member district with four parties running: Democrats, Republicans, Greens and Libertarians. First past the post polling shows 48% Democrat, 48% Republican, 2% Green and 2% Libertarian. Your preferred candidate is polling at 2%.

You're then going to vote for one of the major parties because you know perfectly well that your preferred candidate is not going to win and you also know that you prefer one of the major party candidates over the other one.

By contrast, with approval voting, all four candidates get around 50% approval because there are no spoilers and no reason not to approve of the candidate you actually want, so one of the third parties can plausibly edge out both of the major parties for the highest approval and win the district. They also have a much better case that they could win which means they can get into the debates etc.

Also, approval voting makes it plausible for independents to win when they tailor their platform to the district, which just might destroy the political parties whatsoever -- and that would be most excellent.

> It can be argued now ~40% of people who vote for the loser in our current system don’t have a representative, and a more proportional system would clearly improve this.

No one disputes that the existing system is terrible. But approval voting still fixes that, because a candidate with 60% approval loses to one with 70% approval, so someone who can make more of the district happy wins. And there is no way to give full consideration to 100.0% of the voters short of direct democracy, which has its own set of problems.



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