Probabilities permeate our lives: they show up in weather reports, science, popular reports of science, predictions about election results, chances for surviving diseases, prices on futures market, and of course, in casinos. Probability plays such an important role in modern life that it is no surprise that philosophers are interested in them.
Evolution is principally a probabilistic concept. There is a plevelent strain of Darwinism, called naive Darwinism, that believes that any species or member of a species that dominates at any point has been selected by evolution because they have an advantage over others. This results from a common misunderstanding of logical and global optima, mixed with an inability to get rid of the belief in the law of small numbers. Just put two people in a random environment, say a gambling casino, for a weekend. One of them will fare better than the other. To a naive observer the one who fares better will have a survival advantage over the other. If he is taller or has some trait that distinguishes him from the other, such trait will be identified by the naive observer as the explanation of the difference in fitness.
Some people do it with traders-make them compete in a formal competetion. Consider also the naive evolutionary thinking positing the "opitimality" of selection-the founder of sociobiology does not agree with such optimality when it comes to rare event. Wilson writes:
The human brain evidently evolved to commit itself emotionally only to a small piece of geography, limited band of kinsmen, and two or three generations into the future. To look neither far ahead nor far afield is elemental in a Darwinian sense. We are innately inclined to ignore any distant possibility not yet requiring examination. It is, people say. just good common sense. Why do they think in this shortsighted way? "The reason is simple: It is a hardwired part of our Paleolithic heritage. For hundreds of millennia, those who worked for short-term gain within a small circle of relatives and friends lived longer and left more offspring- even when their collective striving caused their chiefdoms and empires to crumble around them. The long view that might have saved their distant descendants required a vision and extended altruism instinctively difficult to marshal.
Miller says:
Evolution has no foresight. It lacks the longterm vision of drug company management. A species can't raise venture capital to pay its bills while its reseach team. Each species has to stay biologically profitable every generation, or else it goes extinct. Species always have cashflow problems that prohibit speculative investments in their future. More to the point, every gene underlying every potential inovation has to yield higher evolutionary payoffs than competing genes, or it will disappear before the innovation evolves any future. This makes it hard to explain innovations.
The concept of rationality is not so easy to handle. As the concept has been investigated in plently of fields, it has been developed the most by economists as a normative theory of choice. Why did the economists develop such an interest in it? The basis of economic analysis is a concept of human nature and rationality embodied in the notion of homo-economicus. The characteristics and behavior of such homo-economicus are built into the postulates of cunsumer choice and include nonsatiation and transitivity. For instance, Arrow writes,
It is noteworthy that the everyday usage of the term 'ratinality' does not correspond to the economist's definition as transitivity and completeness, that is maximization of something. The common understanding is instead the complete exploitation of information, sound reasoning, and so forth.
Perhaps the best way to see it for an economist is the maximization leading to a unique solution.Even then, it is not easy. Who is maximizing what? To begin, there is a conflict between collective and individual rationality. "Tragedy of the common" seen by Keynes in his parable of the stadium where one's optimal strategy is to stand up, but collectively the optimal strategy is for everyone to remain seated. Another problem is seen in Arrow's voter's impossibility theorem. Consider also the following voter problem: People vote but the probability adjusted gains from voting can be less than the effort explained in going to the polling place.
Note that the literature on rational choice under uncertainty is very extensive, cutting across fields, from evolutionary game theory to political science. But as John Harsanyi put it bluntly, it is normative, and meant to be so. This is a heroic statement: Saying that economics has abandoned its scientific pretentions and accepted that it does not describe how people do act but rather how they should act. It means that it has entered the realm of something else: philosophy though not quite ethics. As such, an indivisual can accept it fully and should aim to act like the neoclassical man.
Most of the conventional discussion on probabilistic thought, especially in the philosophical literature, present minor variants of the same paradigm with the succession of the following historical contributions: Pascal, Cardano, De Moivre, Gauss, Bernouilli, Laplace, Bayes, von Mises, Carnap, Kolmogorov, Borel, De Finetti, Ramsey, etc. However, these concern the problems of calculus of probability, perhaps fraught with technical problems, but ones that are hair-splitting and, to be derogatory, academic. They are not much concern in this essay, because, they do not seem to provide any remote usefulness for practical matters. For a review of these, I refer the reader to Gillies, Von Plato, Hacking ,or the more popular and immensely readable 'Against the Gods' by Bernstein, itself drawing heavily on Florence Nighttingale David. I recommend Bernstein's 'Against the Gods' as a readable presentation of the history of probabilistic thought in engneering and the applied hard sciences but completely disagree with its message on the measurability of risks in the social science.
To philosophers operating in probability per se, the problem seems one of calculus. The problem of probability is largely a matter of knowledge, not one of computation. The real problem is: Where do we get the probability from? How do we change our belief? It is far more important to figure out what dice we are using when gambling than to develop sophisticated computations of outcomes and run the risk of having, say, dice with nothing but 6s. In economics, for instance, we have very large models of risk calculations sitting on very rickety assumptions. They smoke us with math, but everything else is wrong. Getting the right assumptions may matter more than having a sophisticated model.
An interesting problem is the "value at risk" issue where people imagine that they have a way to understand the risk using "complicated mathematics" and running predictions on rare events-thinking that they were able from past data to observe the probability distributions. The most interesting bahavioral aspect is that those who advocate it do not seem to have tested their past predicting record, another Meehl type of problem.
Perhaps the most insightful book ever written on the subject remains the great John Maynard Keynes's Treatise on Probability, which surprisingly has not collected dust- somehow everything we seem to discover appears to have been said in it. In the usual supplied lists of thinkers of probability, Shackle, who refined subjective probability, is often undeservedly absent. Most authors also omit the relevant contributions of Issac Levi on subjective probability and its links to belief, which should be required reading in that area.
