Democracy is Always Right (That’s Just Math)

by Tim Sommers

Why have a democracy? Because democracy is always right.

There are two kinds of arguments in favor of democracy: intrinsic and instrumental. Intrinsic arguments try to show that democracy is good in-and-of-itself – and not as simply a means to some other end or ends. Instrumental arguments try to show that democracy is good because it leads to some good.

There are two main kinds of intrinsic arguments: those based on liberty and those based on equality. The most straight-forward kind of liberty argument says that we should be free, but to be free means not only to govern ourselves, but to have some control of our larger social and material environment. Democracy gives us that control. The trouble is that in actually existing democracies very, very few people are able to exert any real influence on society or their material conditions via the political process. Democracy does not make most of us free, at least in this way.

Here’s a different kind of liberty argument. We all have certain basic rights. Among the basic rights, liberties, and freedoms we possess in a liberal democracy – freedom of religion, free speech, the right to the rule of law, etc. – there are also rights of political participation – political speech, a right to free assembly, etc. What does this kind of pro forma right to some kind of political participation really amount to, though?

There’s no right to vote in the US Constitution. And Arrow’s Impossibility Theorem shows there is no way of counting votes that can satisfy all of the seemingly simple and reasonable conditions voting must bear. To oversimplify a bit, there is no way of voting that always gives us an answer, always depends on the input of more than one person, gives a way of deciding between candidates based on voting (and nothing else), and insures that the choice between any two candidates is independent of how the voter feels about other candidates.

Fortunately, there are also equality-based arguments for democracy. Many political philosophers have argued that democracy is a way of treating people equally. But lotteries treat people equally too.

Here’s an instrumental argument for democracy from Thomas Christiano:

“The modern democratic societies of Europe, North America, and East Asia have actually been quite successful…Democracies do not go to war with one another and respect the rules of war better than other societies. They are responsible for the creation of the international trade system, the international environmental law system, and the human rights regime. In fact, democracies do massively better on basic human rights than other societies, and it appears to be more their majoritarian character that explains this than their systems of checks and balances. Democracies prevent famines and, since the onset of universal suffrage, have developed powerful welfare states that have been enormously productive, have greatly reduced poverty, and have smoothed out the disastrous economic crises that occurred in their more free market ancestor societies.”

But why?

Here’s a different kind of instrumental argument for democracy, one that may well explain all these good outcomes to boot. The epistemic – or the acquisition-of-knowledge-based – argument for the instrumental value of democracy is based on the claim that democracies are more epistemically efficaciously than the alternatives. Which is just to say that, if we have to decide an issue, or choose a leader, doing it democratically will give us the best chance of getting the right answer.

Deliberative democratic theorists give a variety of epistemic arguments. But we need only one. And it’s just math.

The Marquis de Condorcet was a moderate democrat during the French Revolution. He advocated universal suffrage and was an early advocate of universal primary education. He went into hiding after voting against the death penalty for Louis XVI, but was captured and died in his cell nine months later. Ironically, his warders had lost track of who he was by the time he died and he was identified only by the copy of Horace’s “Epistles” he had been carrying when he was arrested.

Condorcet had studied voting and concluded that, under the right circumstances, it is an extremely effective procedure for getting right answers. This was a consequence of his famous “Jury Theorem”. On an issue with two alternatives, where the decision is made independently by each participant, where there is also an objectively right decision, and each decision-maker has a greater than 50% chance of making that right decision a group of 5 or more people have a high likelihood of making the correct decision, a group of 12 has a higher likelihood of giving the correct verdict, and a group of a 1000 or more is nearly certain – out to several decimal places certain – to make the right call. In other words, if we think of a voting as a kind of procedure to determine the truth of a question, as long as we add competent voters the more the better.

And the Jury Theorem is just math. It’s not an empirical claim. Certain simple assumptions lead you inevitably to its conclusion: Democracy is always right.

More than a hundred and fifty million people voted in the recent presidential election. That’s a staggering number from the point of Condorcet’s Theorem. That many people cannot possibly be wrong. It’s just math.

Well. There are a couple of caveats. I’ll just mention one. While it’s true that for each person that you add, with enough information and good judgment to vote for the better candidate even 50.00000000001% of the time, you increase the odds of electing the right person, but this cuts both ways.

For every person you add who has a slightly worse than average chance of picking the right person (even 49.999999999%), you decrease the odds of electing the right person. In fact, with too many incompetent people, it becomes a virtual certainty that the voting will give you the wrong answer, choose the wrong person. Virtually certain.

Thankfully, we don’t have to worry about that. Right?

After the Columbia space shuttle explosion in 2003, astronaut Mark Kelly, classmate to all three of the astronauts who died, ended a conference call on the subject with a line that’s now a poster on a conference room wall at NASA’s Huston complex. It says, “None of us are as dumb as all of us.”