> Ditching first past the poles and mitigating gerrymandering would also obviously help.
Mitigating gerrymandering is a lost cause with first past the post because someone has to draw the lines and whoever is in the majority at the time is going to find a way to benefit themselves. It's especially hard because in a state which is e.g. 60% for one party, drawing the lines in a "normal" way can pretty easily result in a bunch of districts that are each 60% for that party (i.e. they get 100% of the seats with 60% of the votes), and getting it to not do that is the thing that could require a bunch of strange looking lines.
Whereas if you switch from first past the post to score voting, gerrymandering is basically irrelevant.
First past the post de facto disenfranchises the majority of the district including members of both parties whenever the split isn't almost exactly 50:50, because then the outcome is effectively a certainty even if significant numbers of voters change their minds. Everyone who supports the losing major party or any third party fails to benefit them, and everyone who supports the victorious major party in excess of what they needed to secure the district is also not moving the needle even a hair.
Whereas with score voting, you can have more than two viable candidates, and then hyper-partisans can't win in a district where 40% of the voters hate them because they'd lose to a member of their own party, or a now-viable third party candidate, who can appeal to voters on both sides. Changing the composition of the district changes which candidate wins even when the change doesn't put a different party in the majority, and with more than two viable parties there may not even be a "majority" party anymore.
The problem is someone got the Democrats to start promoting IRV, which is barely better than first past the post in many cases and actually worse (i.e. more partisan) in some pretty common ones. Which in turn got a lot of Republicans to start opposing all voting system reforms because they didn't like the results. Meanwhile they would both benefit from using score voting instead of FPTP or IRV. I mean seriously, does either party actually like this partisan hellscape?
with FPTP, strategic voting means NOT voting for your favorite. so at the very least, you'd "vote for the person you'd normally support under FPTP, _plus_ everyone you like better".
but in real life, a lot of people will use intermediate scores.
No, to begin with the people who want to play stupid games would give the highest score to every candidate they approve of and the lowest score to everyone else, and then it devolves to approval voting, which is significantly better than FPTP -- and IRV.
And even doing that is people being too clever by half.
Imagine there are three candidates. The one you prefer is polling at a score of 6/10, another that you like almost as much is also polling at 6/10 and a third that you very much don't like is polling at 4/10. If you were voting honestly you'd give the first candidate 10/10, the second 8/10 and the third 1/10. So what should you do if you're voting strategically?
If you do the one that devolves to approval voting you give the first two candidates 10/10. But that's pretty dumb, the third candidate was just barely in the race and all you're doing then is screwing yourself by giving your second choice a better chance against your first choice.
If you do the one that devolves to FPTP you're really screwing yourself, because then you're putting the third candidate, which you hate, back in the running by tanking the chances of the second candidate that you were pretty okay with. You're making it so if your first choice doesn't win you get your third choice, which is bad for you, because the amount you wanted the first to win over the second is much smaller than the amount you wanted the second to win over the third but then you foolishly failed to express that even though the voting system allowed you to.
You can find some "proofs" that giving every candidate either a 1/10 or 10/10 is the optimal strategy, but the thing those proofs take as an assumption is that you know exactly how everyone else is going to vote, i.e. you have perfectly 100% accurate infallible polls. Which, of course, you don't.
And then think about what you have to do with that second candidate you'd like to give 8/10: Under that logic you're "required" to either give them 10/10 or 1/10. But you can't be sure if giving the second candidate a 1/10 will cause the first candidate to win or the third. Without knowing that, you can't know which one is actually better for you.
At which point the optimal strategy is to hedge by picking a number in the middle, and choose which one in proportion to how strongly you feel about each risk. But that's the same as voting according to your actual preferences! You end up giving the second candidate 8/10 because that's the measure of how much more you prefer that they defeat the third candidate than that they don't defeat the first.
The only real strategic choice here is to put some consideration of the polling into the weighting. If Hitler is on the ballot then you're definitely giving him the lowest score, but if he's only polling at 2/10 and you're pretty sure he's not going to win, you might want to give someone else you only moderately disfavor a 3/10 rather than 5/10 because you're not that worried about the probability of Hitler defeating them even if you're very worried about the consequences if it happened. But you still don't want to give them the same score as you give Hitler because you still want to hedge at least a little bit against even a small chance of something that bad.
There are several problems with IRV, but the most obvious one is that it can often knock the moderate candidate out of the final round.
Suppose you have a district that goes 60% for one party. That party runs two candidates and the other party runs one. With IRV, one of the first party's candidates is the most likely to get knocked out, because they'll each average ~30% of the vote (half of 60%) while the other candidate gets the other 40%. But if the majority party then has a preference for their own extremist, it's their moderate that gets knocked out, and then in a district that goes 60% for that party, the extremist has a decent chance of getting in.
The same dynamic can also cause the minority party candidate to win. 51% of the majority party (i.e. 30.5% of the district's voters) prefer an extremist, but enough of the majority party is afraid of them that in combination with the 40% of the vote from the minority party, the minority party wins the run off. Even though the "winner" would have lost to the majority party's moderate using score voting regardless of whether the extremist was on the ballot and even in a two-candidate election using FPTP.
Mitigating gerrymandering is a lost cause with first past the post because someone has to draw the lines and whoever is in the majority at the time is going to find a way to benefit themselves. It's especially hard because in a state which is e.g. 60% for one party, drawing the lines in a "normal" way can pretty easily result in a bunch of districts that are each 60% for that party (i.e. they get 100% of the seats with 60% of the votes), and getting it to not do that is the thing that could require a bunch of strange looking lines.
Whereas if you switch from first past the post to score voting, gerrymandering is basically irrelevant.
First past the post de facto disenfranchises the majority of the district including members of both parties whenever the split isn't almost exactly 50:50, because then the outcome is effectively a certainty even if significant numbers of voters change their minds. Everyone who supports the losing major party or any third party fails to benefit them, and everyone who supports the victorious major party in excess of what they needed to secure the district is also not moving the needle even a hair.
Whereas with score voting, you can have more than two viable candidates, and then hyper-partisans can't win in a district where 40% of the voters hate them because they'd lose to a member of their own party, or a now-viable third party candidate, who can appeal to voters on both sides. Changing the composition of the district changes which candidate wins even when the change doesn't put a different party in the majority, and with more than two viable parties there may not even be a "majority" party anymore.
The problem is someone got the Democrats to start promoting IRV, which is barely better than first past the post in many cases and actually worse (i.e. more partisan) in some pretty common ones. Which in turn got a lot of Republicans to start opposing all voting system reforms because they didn't like the results. Meanwhile they would both benefit from using score voting instead of FPTP or IRV. I mean seriously, does either party actually like this partisan hellscape?