This is the first post in a series of posts considering ways to design governments.
7 minute read
Typically when we consider “society”, we think about a giant mass of people – millions or billions depending on the scale. When we talk about rules for governing society, we usually consider the amount of people that would operate under a single government – in the US at the time of writing, 328.2 million people.
The problem we are going to discuss today is: How do we create the best possible government?
And in order to answer that question, I’d like to borrow the bones of a technique from mathematics known as proof by induction.
The essential idea of proof by induction is to look at the smallest possible example of a problem (known as the base case), come up with a solution for that small example, and then generalize the solution to all problem sizes.0
So what does this mean in the case of government?
First, let us define a government as a set of rules for conflict resolution among the participants of a society.1
In order to find the best possible government, we will first construct a government for the smallest possible society – a society of two people – and then see whether the rules we create will apply just as well to larger governments.
So let’s start designing our baby government!
To make this concrete, let’s consider a society of two roommates. How would they resolve conflicts and establish rules? Well, one reasonable way would be to simply not establish rules, and then when a dispute arises (“You left your clothes on the floor again. I demand you pick them up.”), it must be resolved by some expedient means (e.g., flipping a coin, engaging in debate, or playing a game of Super Smash Brothers to determine the winner). They may proceed like this indefinitely, without ever establishing a fixed set of rules. On one particular day, it might be perfectly legal to leave clothes on the floor, if the almighty coin flip determines it to be so. On a different day, the fateful coin might land on tails, forcing that good-for-nothing scoundrel to rid the floor of their soiled clothing at once!
This may seem silly. However, because the number of people in this society is small, this could actually work. But what happens if we increase the number of people to three?
If we assume that between a pair of people, C conflicts will arise per day, then with a society of two people, every single day those two people will have to resolve C conflicts. But with 3 people, because there are three unique pairs (Person A with Person B, Person A with Person C, and Person B with Person C), now there will be 3C conflicts to resolve per day! (And that’s assuming there’s no such thing as a three-way conflict, which is almost certainly false.) In a society of n people, there will be (C * n * (n – 1))/2 conflicts per day. If n = 100, that’s already 4950 * C conflicts per day! (Edit: Of course, in reality, not every person will interact with every other person in society on a given day, but let’s go with this line of reasoning because it’s fun anyways and that’s what I thought of while writing the post, and I like the rest of the conclusions anyway.)
So we can see that our simple government with no laws and case-by-case conflict resolution does not scale to large problem sizes.
The fundamental problem here is that these two roommates may end up resolving similar conflicts over and over again, and not always with the same outcome. This is a waste of time!
So, what if, instead of resolving the same dispute over and over again, the roommates were to document the resolution to that dispute, and refer to that for all future disputes of a similar nature? This would save them a lot of time, and probably a lot of anguish as well, by avoiding rehashing the same conflicts over and over again. Sounds like a win to me.
And so we say, let there be laws!
This way of forming laws is actually quite elegant, because it avoids another very difficult problem – agreeing on common principles. So on the one hand, the resulting set of laws may be intellectually unsatisfying or not perfectly internally consistent (especially in a system where laws are determined by coin flip); but on the other hand, this allows for compromise, even when the two people being governed operate by completely different moral frameworks. Pretty good, I’d say, for our tiny government of two!
(It turns out this is basically how common law works. It’s also related to caching.)
Now going back to our favorite question: Can we generalize this to larger societies?
Going back to the math – if we assume there are only M possible unique conflicts, then our society only has to reach a resolution to each of these conflicts once in order to create a law for each of the M conflict types, after which all conflicts will be able to be resolved by preexisting laws! So the size of the society and the conflict rate C do affect how fast this set of laws will have to be created – and at first, there will be an overwhelming number of laws created per day – but after all of the laws are created, assuming there’s not much overhead to resolving a dispute once a law is in place, there is no longer any daily time spent resolving conflicts! Of course, in practice resolving a dispute even according to an existing body of case law takes some effort, so for this to actually work, people would have to mostly follow the laws to limit the number of disputes.
There’s obviously a lot of detail missing here but given the size of the common law Wikipedia page, I’d say that yes, this way of making laws is actually practical in some sense.2
One fun thing to note about this is that the mechanism for the initial resolution of a novel dispute has been left completely unspecified, and yet we were still able to make some sort of a determination about the scalability of the rest of this legal system. Of course, in practice, it makes a difference whether this is done via coin flip or by a judge or by a popular vote, but allowing the initial law creation process to be abstract lets us consider the scalability of the rest of the system independently.
So, we’ve now seen how it’s possible, by considering a very tiny society of two people, we’re able to create general principles that seem to work well even as society grows larger. In a future post I’d like to explore how we might evolve this further and address more of the details and issues with what’s been presented so far. Stay tuned!
0 Proof by induction actually has a very formal definition which we won’t be following here. I’m more interested in the broad category of reasoning/intuition-building which works by starting with small cases and then moving to generalize that solution. I don’t know what to call that exactly and the closest analogy in my head is proof by induction. So, mathematicians, please forgive me.
1 This is my own definition and is probably wrong. If someone knows a better term for this than “government”, let me know. (Judicial system, maybe?)
2 As a fun aside, to get rid of the “startup delay” during the creation of all of the laws, you could agree on some set of base laws or rules to “bootstrap” society, but that would require a way to come to consensus on fundamental rules as a society, which currently is not required. But this would get us closer to something like the current government of the US which has a combination of case law and statutory law. (To be completely transparent, I’m talking based on 5 minutes of Wikipedia reading. I am not a lawyer or an expert in government.) But I want to derive everything from scratch, so who cares about the US! We can talk more about the introduction of statutory law if it’s required in future posts.
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