The Utility of Probability

We intuitively understand probability, but its application is incredibly complex. For the record, probability is defined as the likelihood of an event occurring, expressed in % terms. Textbook explanations talk of rolling a dice and predicting the chance of getting a 6. These are benign experiments with results of little consequence. But when probability is applied to real events, interesting, if slightly unnerving, possibilities emerge.

Let’s take power cuts as an example. In most Indian metros, we are used to 24-hour power, but there is always a probability of grid failures that will cause a blackout. I don’t think even power equipment manufacturers provide 100% uptime guarantee, although the probability of failure is extremely low. So if we didn’t have any grid failures in the last five years, the probability of such failure increases with each additional day. Yet, the way we look at it, if something hasn’t failed in the last five years, it probably won’t in the future.

This paradox is explained to an extent by the framing of the situation. Underlying every probability data is the assumption of a very large number of observations. We think five years is large enough, when apparently it is not, as is seen from the recent crisis. If property prices are rising over the last few years, it is probably time for a correction, but we believe otherwise. However, we do grasp probability pretty well in other areas. For example, when a batsman hits a century, we expect that he will soon get out. We know scores above 150 are very rare. (Why so many batsmen get out between 100 and 150 is another question altogether.) In a game of cricket, with a definite start and end, we can easily imagine possibilities and compute probabilities. But in life, defining a start and end period is easier said than done.

We shouldn’t feel too sorry for the theory itself is weirdly structured. It says, for example, that the probability of getting heads or tails when tossing a “fair coin” is 50% when the experiment is repeated a large number of times. So if I take a random coin, what’s the probability of heads? This dilemma is beautifully captured in one of my favorite Jay Leno punch lines, “George Bush’s popularity rating hit a low of 25%, which means, now only one in four people support his presidency. So when the President is having dinner with his wife and two daughters, he is the only one that thinks he is doing a good job.” The second statement logically flows from the first one, but one can immediately see the fallacy. So if autism affects 1 in 10 children, we know there is no way to rule out our kid by gathering a group of 10 children. The statistic is chilling, but it has no practical utility, which leads us to believe that our child is not the “1”, resulting in complacency and complications.

So what to do with probability data? One could argue that we should strive to minimize the probability of adverse events (or failures). For example, the probability of traffic snarls can be minimized through electronic monitoring of traffic patterns and adjusting the timing of signals or diverting traffic through alternate routes. This will work, and brilliantly so, but here’s the problem. Once these things work on a consistent basis, we assume that they will never fail. So when they do fail for whatever reason, we are caught unawares. And my uneducated opinion is that as we keep minimizing the probability of failure, the magnitude of failure goes on increasing. If the traffic signals were coordinated and centrally controlled, a break down will result in unmanageable chaos. And with every day such a system works brilliantly, the probability of failure, infinitesimal as it may be, keeps mounting. But a high probability doesn’t mean the event will occur:)

Game Theory and Traffic Rules

Game theory attempts to explain our behavior in situations where the success of our choices are impacted by the choices of others. Price wars are the most common example. If Pepsi cuts prices, assuming elastic demand, sales will increase and so will profits. But if Coke follows suit, Pepsi's action will be neutralized such that both Coke and Pepsi end up with lower profits than what they would make if prices werent cut in the first place. So letting prices be is the best course of action for both, which is the conclusion they will eventually reach after the game is played multiple times.

I got thinking if this explains the problem with our traffic rules. When we all follow rules, then it gives those who break them an advantage. Let's say the rule is that we stick to our lanes regardless of traffic. Now, if the traffic is slow, someone can cut across lanes and weave through traffic, assured that everyone is driving in their lane. But once that happens, the rest will naturally feel cheated and start doing it too, and we end up with massive chaos.

I see two ways of addressing the problem. One is to remove the incentive for breaking rules, by imposing hefty and consistent fines, which is impossibly difficult to do in our country. The second is to let people play this "game" enough times until they realize that we are better off following the rules. It doesnt mean every single person has to experience chaos before sanity returns. Once enough people decide to follow rules, a critical mass is reached. You have - tada - a tipping point. You see people following rules, then more people follow rules and so on. The concept of social proof kicks in.

Its not as far-fetched as it sounds. I think it partly explains why Mumbai has better lane discipline and civic sense than other cities - people here have seen traffic chaos so many more times.

I think the unfortunate part is when everyone starts to follow the rules, some of us will be tempted to break them and get an unfair advantage. And when there is no system of fines or penalty, more people will start doing it creating another tipping point and the cycle continues...