A republic, if you can fix it (with math)

Our republic is sick. To heal it, we must think about the oxymoron at its heart: outstanding representatives.

As the famous story goes, when Benjamin Franklin was leaving the Constitutional Convention, a woman asked him what kind of government they’d made. “A republic, if you can keep it,” he responded. In few words, he conveyed the sustained vigilance that democracy requires of its citizens. But even that does not go far enough. We must not only be vigilant against threats; we must be willing to actually improve our democratic republic. To keep our democracy, we must be ready to fix it.

The constitution Franklin had just crafted would not exist today if the American republic had stayed unchanged all these years. The injustice of slavery corrupted the original constitution, and without the improvements in the 13th, 14th, and 15th amendments, I believe it could not have continued to exist today. Of course, there are other key amendments—the 17th, 19th, the 24th—that have also helped renew and preserve our constitution. And these sustaining improvements do not have to be amendments: for instance, the Voting Rights Act helped protect the constitution by outlawing some of the worst abuses of Jim Crow.

I think most of you reading this will agree that our country is at another crisis point, and that our republican form of government is again in need of renewal. I believe that one of the touchstones of that renewal should be the oxymoron at the heart of the idea of a republic. And while the executive branch may draw more headlines, the true heart of the concept of a democratic republic is the legislature.

Philosophically, a republic consists of a sovereign people who elect to give power to a set of democratically-elected outstanding representatives. These people should have 3 characteristics:

They should have more time to think about the problems of government than the average citizen. This is easy; it’s their job.

to think about the problems of government than the average citizen. This is easy; it’s their job. They should represent the citizens. Ideally, each citizen (or group of citizens) should be able to look at the legislature and see a legislator (or a proportionally-sized group of legislators) who represents them. This goes for ideological groups such as political parties, but there’s reason to believe it also goes for demographic groups. Research suggests that, as long as communication is good, groups of people with diverse points of view can be better at problem-solving than more-homogeneous groups. Voting methods which optimize for this are called proportional representation .

the citizens. Ideally, each citizen (or group of citizens) should be able to look at the legislature and see a legislator (or a proportionally-sized group of legislators) who represents them. This goes for ideological groups such as political parties, but there’s reason to believe it also goes for demographic groups. Research suggests that, as long as communication is good, groups of people with diverse points of view can be better at problem-solving than more-homogeneous groups. Voting methods which optimize for this are called . They should be outstanding. Clearly, all else equal, we all want legislators to be smarter, more articulate, better listeners, harder workers. Representativeness is fine in many ways, but there’s no value in going out of our way to ensure that lazy assholes have a proportional share of the seats. Voting methods which optimize for this are called majoritarian.

These last two characteristics are somewhat in tension. I believe that understanding that tension holds the key to fixing our democracy. And resolving that tension means thinking about elections.

(I’m afraid that from here on this essay gets a bit technical. I’ll still try to use everyday language, but to do so in a way that is based on a rigorous underlying model. That’s a difficult balancing act, so I’m sorry if I err on one side or the other.)

The point of a democracy (aside from simply providing a structure for regular, orderly changes of power) is to make good decisions. In order to quantify this, we can use utilitarianism as our model. Each person, we will suppose, has a numeric utility they expect from each outcome; the best outcome is the one with the highest summed utility. Like any model, this is imperfect, but it does the job a model should, capturing useful complexity while still being simple enough to use.

This utilitarian model definitely gives philosophical support to the idea democracy. “Greatest good for the greatest number” and “majority rules” are not always the same, but they overlap substantially; both are based on the wisdom of the crowd.

And, from this utilitarian model, we can get a deeper understanding of the above tension, between a legislature that’s representative and one that’s outstanding.

The advantage of representativeness is clear. If the legislature is truly representative, it will decide any question it faces in the same way that the citizens at large would have, if they had the time to consider the question as deeply. Each legislator might find different allies on each question, but in every case the majority of the legislature would reflect the majority of the citizens.

To get a legislature that’s truly representative in that way, you don’t even need elections. You could just randomly select legislators; the law of large numbers would guarantee that, for a big enough legislature, the proportions on each side of each issue would be about the same for the sample and the larger group. This idea is called “sortition”, and it’s been used more than you might think; from ancient Athens, where they’d use a marble machine called a kleroterion, to Oregon, where “citizens’ juries” evaluate proposed ballot initiatives to provide recommendations to voters.

A modern reproduction of a kleroterion, a sortition machine

But a randomly-selected group isn’t always the best way to make decisions. Sometimes, it’s important for the legislators to have outstanding talents or skills which most randomly-selected citizens would not easily develop. In that case, you’d like to make the best possible choice for each legislator.

In some cases, representativeness and elitism are not at odds. Say that there were just two opinions (30% orange and 70% purple) and two levels of intelligence (20% smart and 80% dumb). As long as even dumb voters tend to prefer smart representatives, it would not be hard to find a proportional voting method that would elect the correct 30/70 balance between colors while simultaneously ensuring that all the winning representatives are from the 20% of smart people.

But in a more complex world, where both partisan opinions and nonpartisan suitability exist on continuous spectra, and where those spectra can be correlated in complicated ways, there is some degree of tradeoff between representativeness and outstandingness. To maximize representativeness, each winner should be chosen only by the subset of voters they will represent; to maximize outstandingness, every voter should get some say on every winner. In essence, this is a tension between a multi-winner (proportional) voting method for representativeness, and an iterated single-winner (majoritarian) voting method for outstandingness.

But remember the example of the oranges and purples. Even a purely proportional method can be designed to elect more-outstanding winners than sortition would. So one way to resolve this tension would be just to choose such a proportional method; though it would use just one slice of the ballots at a time to choose each winner, it would still choose the most-outstanding winner among those that represented those ballots. The fact that the voting method focused on one slice of voters at a time would still tend to ensure that the representatives could make the right majority choice on multiple crosscutting issues; but their outstanding skills would also tend to be good at finding non-obvious win/win compromises.

Some might argue, however, that when it comes to certain extremist groups, an outstanding representative from the groups’ own perspective is actually outstandingly bad from the point of view of the majority. We’ve all been in a group where one unreasonable extremist got in the way of the whole group dynamic. Is there some way to avoid that?

It turns out that there’s a continuum between proportional and majoritarian election methods. In particular, it’s possible to start with a pile of ballots, to choose each winner by a majoritarian method using that pile, but then eliminate a proportional number of ballots that supported that winner. Such methods give a proportional/majoritarian hybrid outcome that, hopefully, has the best of both worlds.

In the end, maximizing utility means thinking in both proportional and majoritarian terms. Since majoritarian aspects of a system can be designed more subtly, that probably means that the ideal election system will look more proportional than majoritarian at first glance. I have three specific election methods in mind as I write this: PLACE for larger, partisan elections such as US Congress or state legislatures; PAD for smaller, nonpartisan ones such as city councils; and proportional STAR for the smallest elections of all, when all voters have a good understanding of all the candidates, such as internal organizational elections.