Frequentist and subjectivist approach

The word “probability” can be defined in different ways, which start from different ideas but lead to the same rules of calculation.

In brief — Two approaches

• Frequentist: the probability of an event $E$ is the limit of the relative frequency of $E$ as the number of trials repeated under the same conditions grows.
• De Finettian (subjectivist): the probability of an event $E$ is the price that a rational gambler is willing to pay for a ticket worth $1$ if $E$ occurs and $0$ otherwise. It is a measure of “confidence” in the occurrence of $E$.

Both definitions lead to the same formal rules. In the case of experiments with equally likely cases (the roll of a fair die, drawing from an urn, and so on) we obtain the elementary formula $P(E) = \text{casi favorevoli}/\text{casi possibili}$.

The subjectivist definition is due to the Italian mathematician Bruno de Finetti, one of the founders of the modern theory of probability.

Links

Topics: Probability
Concepts: Frequentist definition · Subjectivist definition · Probability
People: De Finetti