A Mathematical Way to Describe Different Forms of Government

We know that there is a field of study that is called “political science.” But we also know that it is not really a science. The field of economics is not a science either, but because everything it involves can be expressed as a number, it can cloak itself in complex mathematical formulas and models that can predict every important economic event in history except the next one. The stock market is thought by many to be governed by predictive processes, which, once discovered, can lead to great fortunes. And, this one happens to be partially true. The fact is that in the long run the winners on Wall Street fall into two categories: those who are lucky and those who have an unfair advantage over everyone else—the rest of us are net losers. “This is a moral that runs at large. Take it. You’re welcome. No extra charge.” But this fact does not stop all kinds of theorists who claim that they have found some market data formula that will lead to riches. In fact, these theorists are so sure of their formulas that they will sell them to you for 4% of the money you invest, but not 4% of the money you make.

Political scientists should get into the formula game as well. It appears to be much more profitable than writing books about parties, policies, elections, and the various forms of government. In fact, we can start the process right now. If we attempt to make a general formula that describes the various forms of government we might try this:

Government of a group of humans, by a group of humans, and for a group of humans.

That’s not very mathematical. Let’s try this:

Government of x, by y, and for z

And we might get fancy and say that governments can be expressed as a three-variable function: G(x,y,z) where G is the function that operates on the three variables to predict, or determine, the form of government.

Now we are getting somewhere. It sounds, and looks, more mathematical doesn’t it? But we need to define, or describe, the three variables. So, x=who is being governed, y=who is doing the governing, and z=who reaps the lion’s share of the benefits of the government.

So we can restate our original formula in a shortened form:

G(x,y,z) = the form of government.

Abraham Lincoln was talking about a democracy when he said, “government of the People, by the People, and for the People.” Let’s substitute “the People” for “x y z” in our formula, and while we are at it we can make a few other substitutions.

• G(the People, the People, the People) = Lincoln’s Democracy
• G(German People, Adolf Hitler, Adolf Hitler) = Nazi Germany
• G(American Colonies, George III, George III) = British Monarchy
• G(Americans, the wealthy elites, the wealthy elites) = Madisonian Republic
• G(Russians, Josef Stalin, Josef Stalin) = Communist Russia
• G(Southern Whites and Blacks, Slavers, Slavers) = Confederacy
• G(Athenians, Athenians, Athenians) = Athenian Democracy
• G(Americans, Americans, Americans) = Faction-Free Democracy

We can make many similar substitutions for governments throughout human history. And in the eight examples immediately above we can easily see that our formula works; those who did the governing also benefited most from government. Those who were governed got very little, if they got anything at all. Adolf Hitler did the governing and he benefited more than any else. So, the people will be the biggest beneficiaries of our faction-free democracy. Such a government has happened only once in human history. It happened in ancient Athens. We could be, should be, next. We want our government to be a special case of G(x,y,z)—we want it to be: G(p,p,p) where p is the People. The People govern themselves and the People reap the benefits of their government.

So, our little exercise shows that the best thing that can happen to a people is that they govern themselves. James Madison was experimenting with a “theoretic” form of government: a representative republic, which became our Madisonian republic. He gambled, and we lost. But we don’t have to experiment. We can model our government after that of ancient Athens.

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