Here's how the system could work:
- Expand the size of the House to 540 districted members. This means the smallest district (Wyoming's) is everyone's size--about 600,000 constituents. The current number of House districts--435--has been fixed since 1911. Some things have changed since then... (I guess this isn't strictly necessary to a mixed-member system.)
- Have independent commissions in each state draw the districts, with a first priority to keep communities of interest together, although districts need to have the same 600,000 people, so it won't be perfect. This means you'll have some heavily African-American districts, heavily Latino districts, and big rural districts. Geographical compactness can take a back seat. Yes, that's right--we might have some ugly, squiggly districts. Trust me, this will work. Independent commissions' proposal should be approved by 2/3 of the votes in the state legislature, which should be easily achieved because everyone can recognize that districts are reasonable communities of interest.
- Modify ballots to include two questions for the House races: (a) Which candidate do you support for your House district? This could use approval voting to allow selection of more than one candidate in multi-candidate races. (b) Which party would you like to see control the House? This must be a single selection.
- Winners on question 1 win their district and get the seat. Because of the way we've drawn the districts, we're more likely to see black representatives run and get elected, Latino representatives, etc.
- We've got district races done and can look at the composition of the entire House so far. For example, the House might be 290 seats for party A, 250 for party B. This establishes the seat share for party A of 53.7%. In the next stage--the mixed member part--votes on question 2 are now compiled nationally. If the vote share and the seat share are not the same, then the party that is underrepresented in the House has at-large seats added. Seats are added until the seat share is within 1% of the vote share. In our example, let's say party A won 55% of the vote. Party A would have 4 seats added: 294 out of 544 seats is 54.04%. If two or more parties are underrepresented, whichever one is farther behind has a seat added first. Two parties might ping-pong back and forth in adding seats.
- Once the total number of at-large seats each party gets is decided, then those new members are selected. The at-large members are chosen from the party's candidates who lost but received the most votes. In other word, party A's four additional seats would go to whichever of its candidates lost very close district races.
Stop and think about the incentives of this proposal. There's actually a triple incentive to draw fair districts. Independent commissions want to get the districting plans to supermajority status; there's no reason to draw unfair districts, as you'll lose any gains in the at-large seats part of the plan; and having several competitive districts might increase your state's representation in Congress. States would want to draw at least a few competitive districts to get one over on the neighboring states.
In theory, it's possible that you have to seat 519 additional members (party A wins 49.9999% percent of national House votes but loses every single district race), but in all likelihood, we're talking about an extra 5% of seats--perhaps 20-30 additional seats. Altogether, a 570-member House is about 30% larger than today's. It's big but still manageable. And it's gerrymander-proof. The incentive to gerrymander disappeared.
And here's the most exciting part: You can vote for a third-party to have seats in Congress, even if no one runs (or has a shot) in your district. Let's say you want to vote for the Democratic candidate but throw your party support to the Greens. Or for the Republican candidate and put party support behind the Libertarians. Nationally, those parties will pick up enough votes to amount to at least a few seats. All they have to do is field some candidates in some districts, who will lose, but get picked up in the at-large representatives process.
My hope would be that third parties win enough support to deny either of the two major parties an outright majority, forcing the major parties to form coalition governments with third parties. Suddenly, we're looking at a system that doesn't freeze third parties out of power entirely; we're looking at a system that gives third parties enough seats in Congress to be involved in some leadership decisions. Support for a major party's Speaker might come at the cost of a committee leadership position. The Green party might demand leadership of the Natural Resources committee to support a Democratic speaker. The Libertarian party might demand leadership of Judiciary to support a Republican speaker. It seems likely, though, that this system creates more third party involvement.