Presidential primaries

There are a lot of ways we could alter with the U.S. government to improve it:

• proportionally elect the U.S. House;
• end the constitutional review powers of the U.S. Supreme Court;
• give the U.S. House and Senate different, separate jobs (one obvious split is to give the House domestic powers and the Senate foreign affairs powers; another split is to give the House budget-only powers and the Senate lawmaking powers);
• stop electing the President and go to a parliamentary-style selection of a prime minister;
• create a separate branch of government out of the Federal Elections Commission and actually give it real teeth to enforce election laws nationally;
• put all federal elections (House, Senate, and President) on a four-year cycle, doing away with the midterm slump.

But an easy-to-make reform I have thought about is to improve the presidential primary processes. One problem is that states want to be first, or failing that, as early as possible. This is for each state to maximize its own influence, but this creates an "arms race" among the states. There needs to be a national, coordinated solution that gives each state a fairly equal chance to each state to have a maximum impact.

One possibility is to draw states at random. Two states go every week for a 25-week process - about as long as the current six- to seven-month-long primary system. This is fair, but the only problem is that California or other big states could come early. The smaller contests really ought to come first. The small contests allow for a wide field and enable less-well-funded candidates to gain exposure. Some unheard of candidates might do well and attract support and funding and be ready to move on to bigger contests. But candidates who could not finish in the top half of smaller contests run out of chances and are eliminated. Allowing large contests at the beginning would be a prohibitive barrier for all but the most well-known, well-funded candidates.

My idea is to organize primaries into ten slots, each separated by three weeks. This 30-week process would start in January and finish in July, just before August conventions. The sensible thing would be to order the primaries into ever-larger blocks, so that the smallest contests are first and the largest contests come last. Here's one schedule I made up: 5, 6, 9, 13, 20, 31, 49, 78, 125, and 202. There could be a drawing of states every presidential election, and each state could be assigned in order to the earliest slot that is still available. For the first nine slots, the numbers are caps. If a state would push the number over the cap, it must go into a later slot. The last slot does not have a cap, so any state that cannot go in the first nine slots goes in the final slot.

Big states can only go at the end by definition. California can only go in slot 8, 9, or 10. However, California would rather get a good lottery number and go in slot 8 (when it would dominate the candidates' attention for three weeks) than in slot 10 (when it would be only 55 out of about 202 votes and be a much smaller part of the candidates' attention). Small states with good lottery numbers that year will go early and will dominate the conversation. It is bad luck for small states that get a bad number; they will be ignored in a big vote slot. It is clear that the large states have less variation in "dominance" than the small states do. But how much less? Are small states better off, on average, under this arrangement? This calls for a simulation. I ran 200 trials. Here are the results.

The average dominance is just under 20%, meaning that each state represents, on average, 20% of the Electoral College votes available in the given slot. But notice how even the small states have, at times, 100% dominance of the slot. Notice how the small states, mid-size states, and even some of the larger states have averages that are right around 20%. It is only the very biggest states -- Florida, New York, Texas, and California -- for which average dominance of their slots is above 20%. One could play around with the numbers a bit. For example, dropping slot 7 to a 48 would depress Florida's and New York's slightly too high chances a little (no longer could they share the slot if a 20 EV state got there first, so their odds would be slightly lower for this outcome). But my first attempt represents quite a substantial flattening out; each state has a reasonable chance of influencing the selection of the presidential candidates.

Otherwise, the problems just continue.

UPDATE, March 23, 2019: This article in fivethirtyeight takes a very different approach to re-ordering the primaries: they look at how similar a state's electorate was to the national Democratic electorate as a whole, then put the most similar states first. Of course, this would require (probably) that Democratic and Republican primaries go in a different order. There's a downside in that you can't get cross-over primary voters. But fivethirtyeight's analysis exposes definite problem with my proposal--none of the small states are especially representative of the nation as a whole.

I have two responses, but neither of them is completely satisfying. First: we can hope that clusters of small states can be, on average, more representative. Iowa and New Hampshire might be too white, and South Carolina more African American, than the nation as a whole, but the average of the three together is closer to the national average. True, but not perfectly close. The average of these three states in particular is still far less representative than Illinois of the national Democratic electorate. And if we want to try to randomize the selection of small states, then there are many combinations that are even less representative on average. Fundamentally, a "small states first" rule must involve some trade-off with a "most representative first" rule.

Second: maybe we're not so concerned that the initial states are representative. After all, I am making the case that the early states purpose is to keep costs low (by being a small state with cheap media markets) so the barrier to running for President is negligible AND then to narrow down the field by eliminating non-viable candidates. The low-performing candidates drop out, not because of money, but because they can't win votes; the high-performing candidates gain new enthusiasm and fundraising when they win early states. The real question is whether we think low-performing candidates can't win votes because they're just bad candidates--or because the early states' demographics tilt the playing field against them. The reality is probably a mix of the two effects, but I lean toward the "bad candidates" explanation. Yet I can't rule out the biasing effect either. There's no doubt that early states lean toward rural populations.

Perhaps the best solution is to pair or triple states up so as to "average" out to national demographics: e.g., Massachusetts and Mississippi. The randomly draw out the 25 pairs (or sixteen triples and one pair), using the same sort of ordering method I discuss above. I'm not sure which combinations would be made, so I'm not sure how few electoral votes the smallest pair would have, or how many electoral votes the largest pair would have. But perhaps it would work.

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.