On the other hand, in smaller districts the electorate will be more likely to share opinions and interests so maybe that counteracts the problem?
IIRC Spain has a system along these lines.
First past the post needs to go.
Approval voting is best for executive positions, like governor, mayor, sheriff.
https://en.wikipedia.org/wiki/Approval_voting
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FPTP is terrible. Among other reasons, per Duverger's Law, it begats a two party system.
https://en.wikipedia.org/wiki/Duverger%27s_law
People railing against duopolies (Democrats & Republicans) haven't yet learned it's the result of the form of elections, not a natural law.
Anyone that wants to be on a ballot for a particular position should have to do the same thing as anyone else (probably collecting a modest number of signatures on a petition, maybe with some rules to limit the number of candidates).
I guess parties might be allowed to place an endorsement on a ballot, but if not they could still release a list of endorsements.
In that arrangement, contesting the national delegate convention to get the endorsement of the party might still happen, but it would not be so inordinately important.
A party organization would still be hugely useful in getting wide ballot presence, but an incumbent organization would not have the huge advantages that they enjoy today.
The idea is to not solve every problem with democracy, but to remove the corrupting influence of needing to raise money from vested interests to spend on advertising so you can get elected. This is the major problem.
Unlike every other modern democracy, the US has opt-in voting. To the best of my knowledge, universal voting registration does not increase participation. But it does prevent disenfranchisement. Only compulsory voting would (otherwise) increase participation.
Some of our jurisdictions have switched to all postal balloting. This permits ballot chasing. In general, these campaigns no longer attempt to persuade. (Clinton vs Sanders is a notable exception, because most contests are face to face.) They spend most of the money on GOTV (get out the vote), turning out your base (supporters). Which has led to alienating voters. No one likes to be contacted 30 times per election (4 times a year) to be reminded to mail their ballot.
Postal balloting has also harmed the culture of voting. This intangible is very hard to measure. But some studies show that "I voted" style markers, visible to your friends and family, boost voter participation.
The second benefit, for election integrity activists, is preventing the "under vote", where down ballot races which are left blank, and potentially filled in by helpful administrators.
Note that in the US, ballots in metro areas can easily have dozens of races. Sheriff, judges, schools, water district, city, county, state, national, referendums, levies, etc.
I do agree that it is a very good idea, but compulsory voting doesn't solve the corrupting effect of large districts.
Mexico doesn't do too well, but apparently mandatory voting isn't enforced.
Radicals like me believe no taxation without representation. I support enfranchising pretty much everyone, especially for local issues.
It is an interesting question if the vote should be extended to non-citizens. I can see good and bad aspects to doing so and I am not sure which is more important.
For reasons of equality among the states, the US capital is not located in any of them. The District of Columbia, not being a state, doesn't have the privileges of a state either, such as being represented in the US government. This is not easy to fix; giving DC state privileges would be a severe blow to the idea that the federal government doesn't favor any one state over another.
It still gets taxed, though. People are sore enough about this that when someone submitted the suggestion of "no taxation without representation" for the slogan on DC license plates, it was vetoed by DC government for being "too controversial".
I would actually be OK with saying that DC doesn't get taxed, since they're legally prohibited from participating in the government. But I don't think that's a widespread viewpoint. Do you have an opinion?