The de.Finetti.Game function estimates the interval of a
subjective probability regarding a possible event in the near future.
de.Finetti.Game(width)This is the maximum acceptable width of the interval for the returned subjective probability. The user must specify a width between 0 and 1.
The de.Finetti.Game function returns a vector of length
two. The respective elements are the lower and upper bounds of the
subjective probability of the participant regarding the possible event
in the near future.
This function is a variation on the game introduced by de Finetti, who is one of the main developers of subjective probability, along with Ramsey and Savage. In the original context, de Finetti proposed a gamble regarding life on Mars one billion years ago.
The frequentist interpretation of probability defines the probability of an event as the limit of its relative frequency in a large number of trials. Frequentist inference is undefined, for example, when there are no trials from which to calculate a probability. By defining probability relative to frequencies of physical events, frequentists attempt to objectify probability. However, de Finetti asserts that the frequentist (or objective) interpretation always reduces to a subjective interpretation of probability, because probability is a human construct and does not exist independently of humans in nature. Therefore, probability is a degree of belief, and is called subjective or personal probability.