Thank you for highlighting the need for electoral reform, and pointing towards the "winner takes all" nature of most US elections as being the poisonous tree from which these fruits keep falling.
A proportional voting system would both allow new parties to emerge and prevent extremist or divisive candidates from leading those parties. That in turn would give people more options and make them more likely to vote (and less likely to excuse bad actors within their own party).
I would be careful about directing the blame at "single member districts", though. In the US, the most popular type of reform seems to be Instant Run-off Voting, which has its flaws, but avoids the potential criticism that multi-member districts face, namely that a voter's elected representative may end up living much further away from them. (Personally I'd rather a representative who is closer to my political viewpoint than to my physical residence, but I think that much of the criticism for multi-member districts are in bad faith anyway, and thus not amenable to reasoned debate).
I'd say the problem with Instant Run-off is that it feels good and tangible but doesn't accomplish anything.
A prime example is the Australian parliament, where the lower chamber is essentially IRV while the upper chamber has some variation of multi member districts.
The lower chamber has 4.5% of the seats being outside the two major blocks, the senate has 18.5%. I.e., the people want more choice but the system does not allow for it.
IRV doesn't solve the problem of gerrymandering either.
I'm completely with you on the distance vs. political opinions. There is something extremely powerful in electing one, who has personally convinced you, from your town to go and represent us all, but the world doesn't operate on that scale anymore.
That's an interesting analysis, thank you, but I'm not sure how much of the problem is due to the deficiency of IRV and how much is due to other idiosyncratic features of the Australian political scene (such as the influence of Murdoch media, or even the policy of mandatory voting).
In any case, fortunately there are better options out there than IRV, even with the requirement that districts don't change size. One popular (and simple) option is Approval Voting, although it is slightly harder to count than plurality (at least by hand, since you need to separate ballots into potentially 2^n piles, for n candidates).
The alternative I'd recommend is Asset Voting, where the ballots, districts, and counting remain the same, but after the count is complete, the losing candidates (from least popular to most) get to reassign their votes to other candidates until one of them has over 50%.
Months ago someone posted a research paper on here that came to the conclusion that the only reliable way to avoid two dominant parties is approval voting.
I can't find that paper using this site's search feature, and I'd be very surprised if it didn't have a questionable definition of "reliable" or considered only a limited set of possible reforms.
There may be some clever game-theoretic argument that could be made about spherical voters in a vacuum, but I think that "political science" results are likely to depend too much on data with too small a sample size (for example, the set of countries that use Approval Voting for national elections).
A proportional voting system would both allow new parties to emerge and prevent extremist or divisive candidates from leading those parties. That in turn would give people more options and make them more likely to vote (and less likely to excuse bad actors within their own party).
I would be careful about directing the blame at "single member districts", though. In the US, the most popular type of reform seems to be Instant Run-off Voting, which has its flaws, but avoids the potential criticism that multi-member districts face, namely that a voter's elected representative may end up living much further away from them. (Personally I'd rather a representative who is closer to my political viewpoint than to my physical residence, but I think that much of the criticism for multi-member districts are in bad faith anyway, and thus not amenable to reasoned debate).