Principal Values and Weak Expectations

Mind 123 (490):517-531 (2014)
Kenny Easwaran
Texas A&M University
This paper evaluates a recent method proposed by Jeremy Gwiazda for calculating the value of gambles that fail to have expected values in the standard sense. I show that Gwiazda’s method fails to give answers for many gambles that do have standardly defined expected values. However, a slight modification of his method (based on the mathematical notion of the ‘Cauchy principal value’ of an integral), is in fact a proper extension of both his method and the method of ‘weak expectations’. I show that this method gives an appropriate value when the ‘tails’ of the gambles that are eliminated in the truncation are ‘stable’, but that the value is not appropriate when the tails are not stable. I do not attempt to give an argument for the use of this method, but just note that it is more general than Gwiazda’s method, and is mathematically quite natural
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DOI 10.1093/mind/fzu074
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References found in this work BETA

Strong and Weak Expectations.Kenny Easwaran - 2008 - Mind 117 (467):633-641.
Orderly Expectations.Jeremy Gwiazda - 2014 - Mind 123 (490):503-516.
Unexpected Expectations.Alan Hájek - 2014 - Mind 123 (490):533-567.

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Unexpected Expectations.Alan Hájek - 2014 - Mind 123 (490):533-567.

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