Ranked choice or similar would only give you an occasional third party win here and there, in some small number of electoral districts. It will not give you serious and viable third parties with long living organizations.
What you'd need is, proportional voting for the House. Electoral districts the size of at least 10 House representatives. This would give you third parties that consistently get House representatives in many electoral districts, and thus have a viable and serious party organization, with routine and experience to to run campaigns from elections to elections. This is how European countries work, except UK and France.
If you want out of the two-party system, I don't think anything else works.
Here's a more technical explanation by Warren Smith, a Princeton math PhD whose work was the centerpiece of the book "Gaming the Vote".
Finally, see real world data from a century of IRV in Australia.
Australia has single-representative voting districts with instant-runoff voting, and they seem to have something that looks to me being close to a two-party system in practice. I admit, I didn't browse though all possible countries, so perhaps you know a better example?
There are much better single-winner systems available: see approval voting, score voting, and Condorcet voting. But if you want a legislature with proportional representation, you really need a system with multi-representative districts.
Third parties would greatly benefit from range-voting. I used to favor Condorcet voting methods as an improvement over plurality, but now I favor range-voting. Mostly for how much more straightforward the vote outcomes are, and the simplicity of explaining it. The no-show paradox inherent in Condorcet systems also bothers me.
There is a good summary of the properties of different voting systems on wikipedia.
That is a myth. Instant Runoff Voting does not eliminate the lesser evil (spoiler) problem. See this explained by a math PhD.
* Small parties sometimes have disproportionate power in coalitions.
* Coalitions tend to not be real stable, leading to unstable governments that can't get much done (ok, for some this is a
feature, but for some things, I think it isn't).
* People matter, but with a proportional system, the party picks the candidates, and you vote for the party. In some cases, I think this leads to worse people being elected.
Ranked choice means you give your #1, #2, #3 pick etc. Then if your #1 loses, your vote goes to your #2. It prevents these "A vote for [minority candidate] is a vote for [enemy candidate]" situations.
Proportional means each party can elect a number of representatives proportional to the number of votes the party got.
They both empower third party candidates, but in a different way.
I don't know, Italy might be chaotic under any system. What do you think of e.g. Germany, Denmark?
I don't know the details of politics in Germany or Denmark well enough to know whether there were elections, parties, issues or areas where things didn't work out very well and a different electoral system might have been an improvement. There are a lot of "what if's" to consider even in places I know well.
* IRV or approval voting in the Presidency/executive
* Multi-member districts in the House.
MMD in the House, by State, would effectively end gerrymandering - there is no way state borders will change radically enough to affect electoral results. Combine that with breaking the two party duopoly and it's a huge win.
Side note: I know you don't (nor probably anyone in this thread; HN has fewer trolls) have any intention of subverting the idea, but when people online are supporting electoral reform of ANY kind, the first response should be "I agree".
I agree with electoral reform, and my ideas are X, Y, and Z.
If people squabble too early, it kills momentum. Furthermore, perhaps 1% of the population gives a damn about voting systems and its impact on the country. The rest don't know about it, or are part of the private powerhouse organizations known as the Republican National Committee and Democratic National Committee.
Support electoral reform first, then discuss options.
Problem: Most states don't have 10 House representatives. And in general it allows candidates to bifurcate voters in the same way that gerrymandering does. If you have a group of aligned people who should by population have their own representative, splitting them between two or three districts means they get no representation at all.
The better solution is range voting:
Then you can use the existing districts without changing anything else, but it immediately makes third parties viable. And it boots out anyone who doesn't represent their entire district when there is anyone running against them who does, which puts a damper on all this line drawing nonsense as well.