Probability Tree

13 The Probability Tree

Probability is one of the more difficult concepts for humans to understand and deal with effectively. Morton Hunt explained why in The Universe Within. He wrote:

Most of the concepts and patterns that are difficult for the average person to grasp and use are “nonintuitive”—that is, they cannot be derived, or are not easily derived, from everyday experience, and therefore are not part of the normal mind’s repertoire. Probability is one such [concept]; most people can intuitively see the answer to only the simplest problems involving probability.

Jeremy Campbell in The Improbable Machine made a similar observation:

People do not seem to learn, easily or at all, the rules of probability … just by having repeated experiences of them…. [One explanation for this] seems to be that the rules of… probability fly in the face of common sense. And “common sense” in many cases turns out to mean the way in which human memory is organized and how it processes information.

Thinking in Time by Harvard professors Neustadt and May was equally discouraging:

Judging by our students, millions of Americans are either unfamiliar with numerical notations of probability or are uncomfortable at the idea of stating a subjective judgment [in terms of probability].

Jones explains these difficulties through the metaphor of a missing “probability module.” We can intuitively and fairly accurately estimate the height of most objects, like a tree or ladder. We can estimate distances like the dimensions of a room. These estimates rely on visual perceptions, with which we are innately comfortable and confident. But when it comes to the nonvisual, intangible process of estimating probability, we are notoriously unreliable. What it comes down to is that the human mind was not designed to think in terms of mathematical probability. For that reason we must be wary of our intuitive judgments involving probability because they can drastically mislead us.

For example, we humans tend to believe that, because an event took place, it was highly likely to take place. If the weather bureau forecasts only a 5 percent chance of rain, and we go on a picnic and get drenched in a downpour, we instantly conclude that the weather bureau goofed. Obviously the probability of rain was higher than 5 percent. More likely 100 percent. Look at us! We’re soaked! But what does a 5 percent chance of rain really mean? A calibrated forecast would mean that rain occurs about 5 percent of the time across comparable forecasts for the specified event. Expressed another way, if these exact weather conditions are repeated many, many times, 5 percent of those many, many times it will rain. It means the downpour that soaked us was one of the 5 percent. That one outcome does not establish whether the forecast was well calibrated; evaluating it requires a record of forecasts and outcomes.

Understanding and dealing with probability are crucial because probability permeates analysis both explicitly and implicitly. It lies hidden in the information we analyze and is a crutch for our analytic judgments. Unless we are sensitive to probability’s influence and accurately define its meaning and significance, it can, like a computer virus devouring computerized data, devastate our analytic findings and make a mockery of our recommendations and decisions.

The most difficult analytic problems are of the random and indeterminate type, where, because facts are scarce, our analytic product depends heavily on subjective judgments. For that reason, there can be no certainty when dealing with random or indeterminate problems. No certainty at all! The moment our analysis moves from facts to judgment, we leave certainty behind and enter the arena of estimates. “Estimating is what we do when we run out of data. The language of estimating is probability, and the laws of probability are the grammar of that language.” So said the late Sherman Kent, a U.S. intelligence officer widely regarded as the “father” of the National Intelligence Estimate.

Probability is difficult to deal with because the laws of probability, as Hunt observed, are often counterintuitive and the judgments resulting from the application of those laws are, more often than not, imprecise and ambiguous when expressed verbally.

The excerpt ends before the proposed exercise and the construction of a probability tree.