Mixed member House

I've written about gerrymandering before (and solutions to it), but the more I think about it, the best way to fix the problem is to remove the incentive. Proportional representation is good (and here), but the simplest change to the system is mixed member representation.

Here's how the system could work:

1. 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.)
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.

Proportional representation 2

I write this with trepidation, since I think people invest a lot in their own preferred voting schemes. But I believe I have a novel proportional representation voting method, so I'd like to share it whether it is good or not. I have not encountered an approval voting method for multi-seat elections, so here goes.

Let's say there are three seats in a district. Let's also say there are three parties, each nominating three candidates, for a total of nine. Each voter chooses his top three candidates (because there are three seats). The voter may vote straight down a party line, or he may pick and choose from the different parties. The results are tallied like so.

1. All possible three candidate combinations are listed.
2. For each combination, each voter's ballot is used to score it. If there is one candidate he approves of, it gets a score of 1 point from him. If two candidates, 1.5 points. If all three candidates, 1.75 points.
3. This is repeated for every voter's ballot for every possible combination (obviously, this must be done by computer).

This is somewhat like a jungle primary, except there is no runoff. (The top two system does seem intriguing.) Here is an example.

The columns headers show the sizes of voting blocks. Out of the 90 total voters, the biggest plurality, 35 voters, prefer Party 1. A block of 10 voters prefer candidates B, E, and H; a block of 5 voters prefer C, F, and I. Obviously, Party 1 deserves at least one seat, possibly two; Party 2 might deserve just one seat; and Party 3 might be below the threshold to get a seat at all. But which candidates from each party?

There are 84 possible combinations, so let's focus on the highest scoring combinations.

The "1 pt" column indicates what would happen if only the voter's first approval counted. The next column indicates the tally method I described above. Some comparisons are interesting: ABF is a higher-scoring combination than ABE -- sure, the block of 10 voters is happier having two candidates of whom they approve, B and E, but the ABF combination brings in a candidate whom the block of 5 voters like.

The ultimate winners are B, C, and E: two seats for Party 1, one seat for Party 2, and zero for Party 3. Now, before anyone says that this is unfair for this or that reason, just remember that no voting system is perfectly fair. Kenneth Arrow wrote about voting systems and proved that no system could simultaneously meet all three of his sensible criteria. Instead, let me just lay out some of my choices in creating this method.

Why did I choose approval voting? A: I think you open it up to a lot of strategic voting if you allow people to rank candidates -- people can choose to tinker with their votes down toward the bottom of their list to give their own preferred candidates at the top of their list the best chance of winning. I'm not sure that the same can be done with approval voting. Let's say I'm a hard-core partisan of Party 1. I know that realistically my party is likely to win one or two seats, but not three. I might be tempted to use my third vote to influence the candidate who gets chosen in Party 2 (thus voting, perhaps, ABD in the above scenario). But I have to realize that the voting method cannot tell that I dramatically prefer A or B to D. It makes the gamble riskier, I think.

Why did I choose only three votes? Short answer: Because there were three seats. Long answer: I think that this constraint forces people to think carefully, and my gut says it makes it even harder to vote strategically. As a variant system, I think it might be interesting to consider giving each voter (seats - 1) votes, so in this case, two approval votes. The reason would be to force each partisan voter to indicate which candidate in his own party he least likes. This actually puts more power into the party supporters', not the party leaders', hands.

Why did I choose the "first candidate approved of equals one point, while second candidate approved of equals 1.5 points?" A: The reason that I set up the point values that I did is so that it is worth more to get voter A one candidate whom he likes than to select for voter B the second candidate whom he likes. In this way, this voting method tries to get everyone one representative, before it tries to get anyone a second representative. The pattern would continue: 1, 1.5, 1.75, 1.875, 1.9375 . . .

I have not done the math to see what all the ways to strategically vote are, but my guess is that in the end, the smart "game play" for a party is to nominate candidates who can attract swing voters. In my scenario, the 15 total swing voters ended up deciding where the third seat went and also deciding which candidates got elected from each party. In the real world, perhaps this would mean that a multi-seat district could be representative (in the sense that most voters approve of at least one of their representatives) AND competitive (in that the swing voters always produce some fluctuation). The idea I'm most attracted to is that even a popular party's incumbent could be thrown out. In the above scenario, just assume for a second that candidate A and B are their party's incumbents. Perhaps A was involved in a scandal. Party 1 still might retain one or two seats [they have the block of voters to do it], but disgusted swing voters can make clear that candidate A must go.

I welcome any scenarios readers come up with to show weaknesses to strategic voting in this system. Please share them.

On an interesting note, ranked choice has the problem of complicating things too much for voters. Of course, in the article, the larger point is the critique that a desire to change elections is often actually motivated by a desire to change politics. But repressed interests won't always naturally bubble out. People might not spend the time to learn about the candidates. People might still vote in habitual, not considered ways.

This is a fair point. A new system of voting should be simple. Approval voting, with the option to vote down a party line, fits that bill. If one was really concerned about overvoting, one could drop the limit on how many candidates a voter could approve of; even if a voter approved of every candidate on the ballot, it would still be valid. Certainly, approval voting would have far fewer problems with incorrect ballots that ranked choice. And it doesn't require extensive knowledge of the candidates like range voting.

As to the other part of the critique, I do think proportional representation would actually change our politics. So I'm guilty of some optimism there. The reason is simple, though: proportional representation would probably create a 45-45-10 political system, where the numbers stand for Democrats-Republicans-Third parties. I think the Green Party, the Libertarian Party, and on and on would bring policies to the table that are missing. Nothing magical. Just a more open debate.

UPDATE, March 15, 2019: As my good friend Dr Paul Snell pointed out, my system definitely creates an opportunity for voters to vote strategically. A voter who wants to give their favored candidate the best possible chance should only vote for that candidate. That means there's only one way for the method to "score" a point for that voter, as opposed to someone who's voted for three different candidates. The latter voter's approval is more diffuse and the voter can be "satisfied" by more different outcomes. If everyone votes in this strategic fashion as the first voter--voting for only their top candidate--then the method reverts back to first-past-the-post.

proportional representation

The gerrymandering of U.S. congressional districts is a problem. First, it is simply at odds with democratic principles to have our representative choose us. Gerrymandering can lead to extraordinarily safe districts and can slightly tilt the balance of the whole state delegation. We get less turnover (fewer competitive races) AND skewed results. (Vox has a great series on gerrymandering.)

Second, there's the appearance of corruption, unless the redistricting process is handled transparently by a nonpartisan committee (and these are few and far between). Even when a nonpartisan committee does try to do the redistricting fairly, it's hard to do: districts are supposed to be geographically compact (a smaller perimeter/sqrt[area] is better); minorities are supposed to be given a voice (so create some minority-majority districts); and some districts are supposed to be competitive (so, near 50-50 splits). But here's the key problem: a district can be represented (a representative speaks for the overwhelming majority in that district) OR competitive but not BOTH at the same time. I have a simple solution: Elect U.S. congresspeople in at-large races in each state, like senators. (Article here.)

There's nothing in the U.S. Constitution to prohibit it: it's up to states how to elect their representatives: "The Times, Places and Manner of holding Elections for Senators and Representatives, shall be prescribed in each State by the Legislature thereof..." (Art. 1, Section 4)

This change would allow states to use a proportional allocation method. There are all sorts of methods, but the simplest one to imagine starts with each party putting forward a list, in order, of its potential delegation. If the Democratic party wins 4 seats, the first four people on the list become U.S. representatives. (Obviously, being toward the end of the list is an honorary thing, since it's very unlikely one party would win all the seats in a state.)

Again, there are all sorts of ways to let people vote in these kinds of elections. One way is that a voter could receive a ballot that gave him one of two options in voting: a straight party line vote, and picking and choosing from the various parties. Say John is voting in Colorado's election (7 representatives). He could vote down the Democratic line, for their 7 candidates, or he could vote for any 7 candidates he liked, regardless of party. I think for simplicity and to avoid strategic voting, it's best to make the voting unranked; this would be approval voting. (The mathematics of proportional representation tallying are fascinating.)

Proportional representation gives third parties a better chance to win at least one seat. It allows ideologically unified but geographically spread minorities to build a voting block. And there are no districts to draw.

Well, not quite.

While it would be reasonable for Colorado to treat the state as one delegation, it's hard to imagine California (53), Texas (36), Florida (27), New York (27), Illinois (18), Pennsylvania (18), or Ohio (16) doing it. I think electing no more than a dozen at-large representatives is best: it gives third/minority parties a good chance, but isn't overwhelming to the candidates and voters. These large states would need to be subdivided. The key criteria would be creating geographically and economically cohesive units, transparency, and stability (with luck, the zones could exist without modifications for two or three census cycles).

Perhaps the most obvious way is to divide along county lines. Here's a possible zoning map for California:

Zone 1 is the Bay area counties: population 6.1 million, 9 representatives. Zone 2 is L.A. county: pop. 9.8 m, 14 reps. Zone 3 is San Diego/Empire: pop. 8.4 m, 12 reps. Zone 4 is N. California: pop. 7 m, 10 reps. Zone 5 is S. California: pop. 5.6 m, 8 reps.

It's possible to imagine other ways to partition it (FairVote recommends 3-5 seat districts), but the voters/reps ratios are fairly consistent across the different zones. How did I do on geographic compactness? (One random note: apparently U.S. courts do not have an agreed-upon formula for measuring compactness! Follow the link to a very informative website.) Using my own formula perimeter/sqrt[area], most of the zones are decent:

Zone 1 is the most compact, with about 4000 sq. miles in 260 miles of perimeter. I calculated a compactness factor of about 4.2. To put it in perspective, that's only 1.2 times worse than a circle. Zone 5 is the worst, about 58,000 sq. miles in 1400 miles of perimeter (it has to go around L.A. and Fresno counties). I calculated a compactness factor of about 5.7. That's about 1.6 times worse than a circle. That's worse than an equilateral triangle. In the grand scheme of things, it's not terrible. Certainly, not as bad as this:

or this:

It's hard to know which is my most favorite ridiculous district. Districts 3, 10, 11, 15, and 18 are misshapen lumps. Districts 27, 29, 32, 39, and 40 are odd. Is it just me, or does 42 look like Italy? But the most bizarre must surely be 38.

Texas might divide itself into three zones (western; central: Dallas, FW, Austin; and coastal, including Houston). New York: upstate and city, perhaps. Illinois: Chicago and the rest. Pennsylvania: Pittsburgh, middle, and Philadelphia. Ohio: perhaps northern and southern.

For those who think computer programs can repair the problems, think again. And I reviewed critically a different possible solution, hands-off redistricting, here.

Perhaps a side benefit of allowing third parties a shot at national elections (breaking the national duopoly) is that it would encourage more competitive state elections (breaking the state-level monopoly). Here is an argument to that effect.