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Single Trial Probability Applications: Can Subjectivity Evade Frequency Limitations?

 Author: David Howden  Date Published: 2009  File Size: 126.9 KB  Download

Crovelli (2009) argues that Richard von Mises was mistaken in defining probability in terms of frequency distributions confined by uniform trials (i.e., collectives). Mises (1957) demonstrates that data historically retrieved from collectives must have a convergent and stable distribution to be used statistically. Hence, this same data can only be applied to collectives, not to individual cases. It follows that the application of probability to a single trial (i.e., a boxing match) cannot be undertaken, even if we do have a series of historically similar boxing matches with which to create a proximate probability distribution. As an alternative, Crovelli posits that probability theorists, “must define probability subjectively; that is, as a measure of our uncertainty about the likelihood of occurrence of some event or phenomenon, based upon evidence which need not derive solely from past frequencies of ‘collectives’ or classes” (2009, p. 3).

Several ambiguities and confusions in Mr. Crovelli’s paper lead to erroneous conclusions regarding the use of frequency distributions in probability theory. This paper shall briefly clear-up these misunderstandings in four steps.

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