So to recap, the main problems of the bipartisan system are:

1) Two parties aren’t enough to represent the different viewpoints of the American people.

2) A two party system inherently decays to a tyranny of a single party.

Having established the problems, it’s easy to see the solution.

To the first:

As I noted before, a number of parties already exist to better represent the views of the American people. On the “right” these parties include the Libertarian Party, the Conservative Party, the Right to Life party, and quite a few others- feel free to suggest and I’ll expand the list. Parties on the “left” include the Working Families Party, the Green Party, the American Populist party, and others. There are parties representing moderate and centrist views, and parties representing fringe and extreme views. Although it’s impossible for every single view to be represented, there are more than enough parties out there to represent, well, more perspectives than the two parties represent, and more accurately at that.

So the solution to poor representation is actually very, very simple: get multiple parties in place.

To the second:

Tyranny of the majority inherently occurs whenever a party holds more than 50% of the seats. The solution is mathematical. The only way to prevent one party from holding more than a majority, excepting an improbably tie (mathematically impossible roughly half the time) is to transfer some seats to additional minority parties. It’s actually, again, very simple: limit each party to 49% or fewer seats by electing minority parties to at least 1% of the seats.

Now, 1% will do the trick sometimes, when things are close to begin with. A congress of 49.5%-49.5%-1% is enough to take away the bloc. Even in that case, there is still the risk of just spitting the minority- say, 51%-48%-1%. A number closer to 10% is more likely to secure true representative, because that would become the margin by which the majority party would need to exceed the second-place party.  

So that’s the short version. Get other parties into congress, break the majority. I will be glad to post more math including charts, but I have a feeling nobody wants to see it.