Democracy, Elections and Voting — Part 3

Winston Churchill’s pithy observation that “the best argument against democracy is a five-minute conversation with the average voter” is unfortunately too accurate to be dismissed lightly. We are often acutely reminded of that by the results of elections, in developed as well as in developing countries. It is a marvel that the myth of the enlightened voter persists against all evidence to the contrary.

The problem is that voters are not enlightened beings — but then no one is. The best we can hope for is informed voters. Fortunately, that is sufficient for our purposes which is, to put it briefly, choosing good policymakers. Although there are no theoretical impediments to the task of educating voters to the degree required for fully informed voting, it is impractical to do so in a world of limited resources, complex issues, and very large number of voters. That’s a problem, but like all problems of human societies, there are ways to work around them satisfactorily, if not solve them entirely.

India’s system of choosing policymakers is one of representative democracy with universal adult franchise. People generally accept that almost as if it were an unalterable fact of nature, and if not actually the best way of choosing a government, the widespread belief is that it works sufficiently well that there is absolutely no need to question it or seek alternatives. I think this is profoundly mistaken. I believe that we have to recognize the inherent, deeply embedded flaws in the system, and replace it to suit the reality of India.

We often hear about the “wisdom of the crowds.” The phrase has a comforting assurance to it which arises from the counter-intuitive realization that while the individual is not particularly wise, the collective is surprisingly full of wisdom and insight. But that assurance is at best an illusion maintained only by a suspension of disbelief, and is ultimately cold comfort in the face of real troubles brought on by the real stupidity of people.

The more the merrier, it is said. Perhaps, if you are talking about a party with your dearly liked family and friends. But not quite so much fun if the people involved are people like them rather than people like us. In fact, the more the PLT, the sorrier. The assumption I make here is that the present company — the PLU — are the informed kind and the PLT are the uninformed kind. There’s no need for me to waste time justifying that assumption, as it is so self-evidently true. (Make what you will of that.)

Getting back to the matter at hand. Uninformed voters are a positive danger to society. One uninformed voter is just fine. A few even — not a huge problem. But when their numbers grow to the hundreds of thousands — god forbid, millions — then you are asking for trouble. The theoretical argument for this is summarized by the Condorcet jury theorem (formulated by the Marquis de Condorcet in 1785, Essay on the Application of Analysis to the Probability of Majority Decisions.)

The theorem addresses the question of the optimal size of a decision-making group where the rule is that majority vote determines the decision. The model assumes that the individuals in the group have a certain (and equal) probability of making a good decision. If that probability of an individual making a good decision is more than half, then “adding more voters increases the probability that the majority decision is correct. In the limit, the probability that the majority votes correctly approaches 1 as the number of voters increases.” But if the probability of an individual making the right decision is less than half, “then adding more voters makes things worse: the optimal jury consists of a single voter.”

In real life, of course, voters are not homogeneous in their knowledge and cognitive abilities. But that does not alter the fundamental point that the larger the collection of uninformed voters, the higher the probability that the majority decision may turn out to be a bomb.

A few paragraphs up, I wrote, “of real troubles brought on by the real stupidity of people.” Stupid people are dangerous.

Allow me to briefly digress at this point. Prof Cipolla codified the basic laws of human stupidity thusly:

• First Basic Law: Always and inevitably everyone underestimates the number of stupid individuals in circulation.
• Second Basic Law: The probability that a certain person be stupid is independent of any other characteristic of that person.
• Third (and Golden) Basic Law: A stupid person is a person who caused losses to another person or to a group of persons while himself deriving no gain and even possibly incurring losses.
• Fourth Basic Law: Non-stupid people always underestimate the damaging power of stupid individuals. In particular non-stupid people constantly forget that at all times and places and under any circumstances to deal and/or associate with stupid people always turns out to be costly mistake.
• Fifth Basic Law: A stupid person is the most dangerous type of person.
• Corollary to the Fifth Basic Law: A stupid person is more dangerous than a bandit.

(See this post of Feb 2006, “The Basic Laws of Human Stupidity” for details.)

While it is quite true that stupid people cause us needless troubles, thankfully not all people are stupid–only a small fraction of humanity is stupid. But you really don’t need a plane load of stupid people when the same negative effects of stupidity can be duplicated by a sufficiently large collection of uninformed people. A sufficiently large collection of uninformed people are indistinguishable from group stupidity in their effect on society. (With apologies to Arthur C Clarke.)

Stupidity is a congenital problem rooted in the brain. It cannot be cured. Being misinformed or uninformed is not similarly incurable. Nothing prevents us from making fully informed all the citizens who are eligible voters — nothing except that it would be too costly in term of time and money.

But wait! Do we really have to inform and educate all voters? Can we do something which does not involve educating everyone but that will have the same outcome as if we were to fully educate all the voters? Yes!

Imagine choosing a random sample of voters from the population. Then you educate this subset of voters intensively about the issues, the political parties and their manifestos, about the candidates, about the pros and cons of various proposals, about everything that a voter should be aware of before voting. Finally, you let these people cast their votes and figure out the winners of the election.

How large does the sample size has to be so that its choice is statistically close to the choice of the population? This always comes as a surprise to those of us who are unfamiliar with statistics, but the number is relatively small.

Take a look at this handy table (Source):

Let’s examine one line in there. For a population of 5,000, if you need a 95% confidence level and a margin of error of 2.5%, then you have to have a sample of 1,176 — that is, over 20% of the population will have to be sampled. But for the same confidence level and the same margin of error, for a population of 300 million (an increase of 60,000 times in population over 5,000), the sample size goes up to only 1,537 (an increase of only only 1.3 times), or about 0.0005% of the population.

From the same table, if you need to have a confidence level of 99% and an error margin of 1%, you can sample on 16,586 to get the population estimate of 300,000,000 people. That is, you need to get only 5 out of every 10,000 people.

Imagine that. If 300,000,000 people were to vote, the results would be indistinguishable, for all practical purposes, from the results of a properly randomly selected subset of 16,586 voters. If it costs $1,000 to properly educate a voter, then educating 300,000,000 is an impossibility. But it will cost less than $17 million to educate the sample voters.

Three hundred billion dollars is a number too large for us to comprehend, leave alone spend. But $17 million we can understand: it’s what Mukeshbhai spent on the bathroom sink in the smallest of the guest bathrooms in his fugly mansion (if one goes by the reported $2 billion he spent on it.)

I will go into some details of this idea later. In the next post on the topic, I will look into “deliberative democracy.” Go to Stanford University’s Center for Deliberative Democracy to understand what it is.

Be well, do good work, and keep in touch.

Previous posts in this series: Part 1, Part 2