A formulation of the concept of probability based on the use of experimental devices. Issue 10 (19th May 2017)

• Record Type: Journal Article
• Authors: Bowater, Russell J.
• Is Part Of: Communications in statistics. Volume 46:Issue 10(2017)
• Page Start: 4774
• Page End: 4790
• Publication Date: 2017-05-19
• Subjects: Ellsberg paradox -- experimental devices -- probability wheel -- reference set -- similarity -- strength of probabilities -- subjective probability.; 62A01; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2015.1085564
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: This paper sets out to identify the abilities that a person needs to be able to successfully use an experimental device, such as a probability wheel or balls in an urn, for the elicitation of subjective probabilities. It is assumed that the successful use of the device requires that the person elicits unique probability values that obey the standard probability laws. This leads to a definition of probability based on the idea of the similarity between the likeliness of events and this concept is naturally extended to the idea that probabilities have strengths, which relates to information about the likeliness of an event that lies beyond a simple probability value. The latter notion is applied to the problem of explaining the Ellsberg paradox. To avoid the definition of probability being circular, probabilities are defined such that they depend on the choice of a reference set of events R which, in simple cases, corresponds to the raw outcomes produced by using an experimental device. However, it is shown that even when the events in R are considered as having an "equal chance" of occurring, the values and/or strengths of probabilities can still be affected by the choice of the set R .