The problem with FPTP is that as soon as you have more than two parties, the two most similar parties split the vote among their common constituency and give the win to the least similar party. As a result any candidate who wants a chance at winning has to run on the ticket of the major party they most agree with, or else they split the vote with them and lose. Hence two party system.
With a cardinal voting system, someone can run on a ticket which is similar to one of the major parties and should get approximately the same level of approval as that party's candidate. Which is to say, they can potentially win. Then more third party and independent candidates run, giving people more options.
It's not just about what voters do, it changes what candidates do.
That's not necessarily all that different from now. We have a two stage system. In the primary people with broadly similar platforms run against each other. The "third parties" are factions within the two major ones.
Those options exist, and it's a multi way election. Primaries receive far less attention but they are where the real work of democracy is done.
I believe people are hoping they can vote for a radical candidate and a mainstream candidate, on the off chance people will love the radical candidate if they just get on the general ballot. I'm not convinced that will ever happen, and such people will be not just disappointed, but continue to be convinced the system is rigged against them.
> In the primary people with broadly similar platforms run against each other. The "third parties" are factions within the two major ones.
No, you still have that problem of splitting the vote in the primaries.
Remember how Donald Trump used to be the most hated Republican candidates within the Republicans in around 2015 / 2016? As in the one that the most people actively disliked in polls; but he was different enough from the other candidates that he didn't suffer from the internal vote splitting that they did.
The primaries still use first-past-the-post in the US, don't they?
With a cardinal voting system, someone can run on a ticket which is similar to one of the major parties and should get approximately the same level of approval as that party's candidate. Which is to say, they can potentially win. Then more third party and independent candidates run, giving people more options.
It's not just about what voters do, it changes what candidates do.