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2. The Meaning of ProbabilityThe problem of probable inference—that is, of reaching a decision in the face of incomplete knowledge—is a broad one that cuts across many disciplines. However, the formal treatment of probability by the mathematicians has seduced many people into believing they know more than they really do.
There are two totally distinct fields of probability, namely class and case probability. The former is applicable to the natural sciences and is governed by causality (i.e. mechanical laws of cause and effect), while the latter is applicable to the social sciences and is governed by teleology (i.e. subjective means/ends frameworks).
3. Class Probability
In class probability we know everything about the entire class of events or phenomena, but we know nothing particular about the individuals making up the class. For example, if we roll a fair die we know the entire class of possible outcomes, but we don’t know anything about the particular outcome of the next roll—save that it will be an element of the entire class. The formal symbols and operations of the calculus of probability allow the manipulation of this knowledge, but they do not enhance it.
The difference between a gambler and an insurer is not that one uses mathematical techniques. Rather, an insurer must pool the risks by incorporating the entire class (or a reasonable approximation to it). If a life insurance company only sells policies to a handful of people, it is gambling, no matter how sophisticated its actuarial methods.
4. Case Probability
Case probability is applicable when we know some of the factors that will affect a particular event, but we are ignorant of other factors that will also influence the outcome.In case probability, the event in question is not an element of a larger class, of which we have very concrete knowledge. For example, when it comes to the outcome of a particular sporting event or political campaign, past outcomes are informative but do not as such make the situation one of class probability—these types of events form their own “classes.”
Other people’s actions are examples of case probability. Therefore, even if natural events could be predicted with certainty, it would still be necessary for every actor to be a speculator.
5. Numerical Evaluation of Case Probability
It is purely metaphorical when people use the language of the calculus of probability in reference to events that fall under case probability. For example, someone can say “I believe there is a 70 percent probability that Hillary Clinton will be the next president.”
Yet upon reflection, this statement is simply meaningless. The election in question is a unique event, not a member of a larger class where such frequencies could be established.
6. Betting, Gambling, and Playing Games
When a man risks money on an outcome where he knows some of the factors involved, he is betting. When he risks money on an outcome where he knows only the frequencies of the various elements of the class, he is gambling. (The two activities roughly match up with the case/class probability distinction.) To play a game is a special type of action, though the reverse is not true; not all actions can be usefully described as part of a game.In particular, the attempt to model the market economy with “game theory” is very misleading, because in (most) games the participants try to beat their opponents, while in a market all participants benefit.
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Previous: Predictions can be precise but not accurate (and vice versa).
When a man (or woman or other creature, even) risks money on an apparent inefficiency, (s)he is arbitraging. When (s)he provides liquidity, (s)he is funding.