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At this point, of course there's always a risk that something could go awry, but I'm willing to accept the risks inherent in a one-person-one-vote system -- essentially an elective republic.
Both parties gerrymander. Both parties engage in "principled" discussions supporting positions seeking only expedient means to their practical objectives. I may be convinced that you believe in purely democratic election of the president, I'm not convinced that the Democratic party as an organization truly does.
I'm not a Republican. But I do like the existing system, where one house in the legislature represents the states, the other represents the people, and the executive is selected by the states with impunity regarding the criteria of selecting him. I'm also very happy that every state has independently decided that their citizens should be the arbiter of that outcome. I would not be happy with that though being encoded in such a way that this was not optional for states, I prefer the status quo, where it is just the stable state of the system and emergent out of existing incentives.
I'd be happier if the electoral college was closer to the popular vote, but my preferred method for achieving that would be the ratification of the congressional apportionment amendment, because it empowers the people at the expense of the federal government and the parties, and also empowers them in the legislature as well as the executive branch, whereas just direct vote only empowers them in the executive branch, not the legislature, and does so at the expense of the states and not at all at the expense of the parties.
It's true that the Democrats gerrymander. I think it gives them an advantage in Illinois and Massachusetts. I'm personally willing to give that up, and let my party take its chances in an elective republic.
I agree that your preferred method makes sense. I can't think of another way.
I don't believe that the House represents the people. In my state, the House delegation, and the state legislature, are effectively chosen by the ruling party through gerrymandering. This could be found to be illegal, since the Constitution requires the states to have a republican form of government. But I'm not sure I'm willing to take my chances with letting the Supreme Court decide on this right now.
I think that eliminating gerrymandering might have an impact on policy, since both parties would have to change how they appeal to voters.
Requiring representatives to represent a maximum number of people wouldn't eliminate gerrymandering, but it would significantly reduce it's efficacy. I think, districting based on geography is the ultimate cause of the problem, the theory goes that people in close proximity share interests, but we see that that's not really optimal. It would be nice if something like, people can form groups together in a state that would function like districts, with a maximum number of members, and a maximum number of groups based on the number of representatives in the state (which is of course a function of the total population in the state), and elect theirs, basically let the people self organize and voluntarily associate so they can maximize their representation. I'm sure there are unforeseen consequences to that, like unions dominating many representative groups, or issues local to a small region going unaddressed, but it's interesting to think about and there is an optimal solution to the gerrymandering issue that requires us to change the way we think of a representative constituency.