So make at least one of them a party with reasonable policies
Give them a voting base that they can do that with. You can disagree with policy all you want, but if the votes aren't there then it's hard for politicians to justify voting against their constituents. You'll just get the present situation where a smattering of politicians support more left policies, but most Democrats are center-left.
Of course people care. That’s the lock-in.
Okay, but the problem is that those third parties have no chance of winning. If you deny the closest viable party your vote, they will just move rightward to try to capture votes they think they can feasibly win without alienating the middle. Stubbornly sitting in the extremes gets you little in situations where you have to compromise.
The problem is that leaves you with an unstable situation under FPTP. Let's say that our fictional third party, the Yellow Party, is to the point where 40% goes to Republicans (right), 30% goes to Democrats (center-left), and 30% goes to Yellows (left). Now Republicans are winning despite Democrats and Yellows forming a majority. So Democrats are going to split at some point, arriving back at an equilibrium of approximately a 50-50 split between Republican-Democrats and Democrat-Yellows. So in essence, you're right back where you started.
But you have a new party with better politics. Otherwise you argue that Democrats and Republicans already represent exactly the will of the population.
So make at least one of them a party with reasonable policies
Of course people care. That's the lock-in.
Give them a voting base that they can do that with. You can disagree with policy all you want, but if the votes aren't there then it's hard for politicians to justify voting against their constituents. You'll just get the present situation where a smattering of politicians support more left policies, but most Democrats are center-left.
Okay, but the problem is that those third parties have no chance of winning. If you deny the closest viable party your vote, they will just move rightward to try to capture votes they think they can feasibly win without alienating the middle. Stubbornly sitting in the extremes gets you little in situations where you have to compromise.
Yes, create the voting base.
If democrats move right, they take votes from Republicans and make it easier for third party to win.
The problem is that leaves you with an unstable situation under FPTP. Let's say that our fictional third party, the Yellow Party, is to the point where 40% goes to Republicans (right), 30% goes to Democrats (center-left), and 30% goes to Yellows (left). Now Republicans are winning despite Democrats and Yellows forming a majority. So Democrats are going to split at some point, arriving back at an equilibrium of approximately a 50-50 split between Republican-Democrats and Democrat-Yellows. So in essence, you're right back where you started.
But you have a new party with better politics. Otherwise you argue that Democrats and Republicans already represent exactly the will of the population.