A Savage-Like Axiomatization for Nonstandard Expected Utility
Abstract
Since Leonard Savage's epoch-making "Foundations of Statistics", Subjective Expected Utility Theory has been the presumptive model for decision-making. Savage provided an act-based axiomatization of standard expected utility theory. In this article, we provide a Savage-like axiomatization of nonstandard expected utility theory. It corresponds to a weakening of Savage's 6th axiom.
Cite
@article{arxiv.1701.03500,
title = {A Savage-Like Axiomatization for Nonstandard Expected Utility},
author = {Grant Molnar},
journal= {arXiv preprint arXiv:1701.03500},
year = {2018}
}
Comments
The alleged result of this paper is incorrect, the transfer principle applies only to first-order statements over standard structures, but I attempted to apply it over second-order statements as well. I believe a proof in the same vein as the one in this paper could be developed, but much greater care would need to be taken to respect the difference between internal and external sets