Principal values and weak expectations

• Autores: Kenny Easwaran
• Localización: Mind, ISSN-e 1460-2113, Vol. 123, Nº. 490, 2014, págs. 517-531
• Idioma: inglés
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• Resumen

  • 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.