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The propensity theory of probability is a probability interpretation in which the probability is thought of as a physical propensity, disposition, or tendency of a given type of situation to yield an outcome of a certain kind, or to yield a long-run relative frequency of such an outcome.
Propensities are not relative frequencies, but purported causes of the observed stable relative frequencies. Propensities are invoked to explain why repeating a certain kind of experiment will generate a given outcome type at a persistent rate. A central aspect of this explanation is the law of large numbers. This law, which is a consequence of the axioms of probability, says that if (for example) a coin is tossed repeatedly many times, in such a way that its probability of landing heads is the same on each toss, and the outcomes are probabilistically independent, then the relative frequency of heads will (with high probability) be close to the probability of heads on each single toss. This law suggests that stable long-run frequencies are a manifestation of invariant single-case probabilities. Frequentists are unable to take this approach, since relative frequencies do not exist for single tosses of a coin, but only for large ensembles or collectives. These single-case probabilities are known as propensities or chances. Hence, it can be thought of as "meta-probability".
In addition to explaining the emergence of stable relative frequencies, the idea of propensity is motivated by the desire to make sense of single-case probability attributions in quantum mechanics, such as the probability of decay of a particular atom at a particular moment.
The main challenge facing propensity theories is to say exactly what propensity means, and to show that propensity thus defined has the required properties.