1. Mandatory voting. I'm talking a small fine if you don't show up to a polling place and get your name checked off;
2. Preferential voting. Vote for the candidates in the order you want. The one with the least primary votes gets eliminated and those votes get distributed to the second preferences. This continues until one candidate has 50.1% of the vote. This way you can vote for a third-party candidate without wasting your vote.
3. Voting over a two day period, probably Saturday and Sunday. This will allow you to use a whole host of government buildings as polling places such as schools that are almost by definition widely geographically distributed;
4. Zero electronic voting. None. Nada. Zilch. More, the standards need to be tightened to have high accuracy voting methods. Optically read ballots where you fill in a circle work wondrously well. Punch cards do not. See the Florida recount of 2000 if you want to see what happens with that;
5. An end to politicizing the election process. It's incredibly dangerous. No more elections for a supervisor of elections or the like. Other countries seem to manage with an electoral commission. The US can too;
6. An end to state governments controlling redistricting. The same electoral commission(s) should handle this.
Of course, none of this will actually happen.
EDIT: several commenters raised three points in particular.
1. Mandatory voting. I come from Australia where we have mandatory voting. By "mandatory" it means you just have to show up to a polling place and get your name ruled out of a large file. It's slightly more tedious if you vote out of your registered district but only slightly.
There's nothing stopping you putting an empty ballot in the box or drawing a picture or just voting invalid. There is no free speech issue here.
I used to be against it until I came to the US to see what havoc voluntary voting wreaks.
The US has a long history of voter suppression because voting isn't mandatory. Getting out the vote is one thing. But the US in parts goes much further than this including:
- Removing your vote if you're convicted of a felony. Why exactly?
- Removing you from the electoral rolls if your name matches that of a felon on the other side of the country;
- Sending mail to your registered address. If it's returned undeliverable, strike you off the rolls;
- Making you wait hours to vote to discourage you from voting, particularly in areas heavily populated with those that might otherwise vote against you (in Australia it never took me more than about 5-10 minutes to vote).
People argue about the evils of having the uninformed vote but if Trump has taught us nothing it's that choosing to vote isn't exactly a recipe for informed voting either.
All of the above are a direct consequence of a politicized electioneering process made possible by non-mandatory voting.
2. Electronic voting. This is a recipe for a foreign power or just a hacker to steal your election by modifying the results in a database rather than interfering with paper ballots that can be audited and recounted.
Sure you can ballot stuff with fake ballots but that's something that requires physical proximity and is far harder to do on the scale that large scale tampering with a database might mean.
Electronic voting is a wholly terrible idea with literally no upside.
3. Mail in ballots. All in favour of it if it's like Oregon where you have the month before the election to send it in. It needs to be easy and flexible.