Since posting this, I’ve revised my paper, now called “Unbounded utility and axiomatic foundations”, and eliminated all the placeholders marking work still to be done. I believe it’s now ready to send off to a journal. If anyone wants to read it, and especially if anyone wants to study it and give feedback, just drop me a message. As a taster, here’s the introduction.
Several axiomatisations have been given of preference among actions, which all lead to the conclusion that these preferences are equivalent to numerical comparison of a real-valued function of these actions, called a “utility function”. Among these are those of Ramsey [11], von Neumann and Morgenstern [17], Nash [8], Marschak [7], and Savage [13, 14].
These axiomatisations generally lead also to the conclusion that utilities are bounded. (An exception is the Jeffrey-Bolker system [6, 2], which we shall not consider here.) We argue that this conclusion is unnatural, and that it arises from a defect shared by all of these axiom systems in the way that they handle infinite games. Taking the axioms proposed by Savage, we present a simple modification to the system that approaches infinite games in a more principled manner. All models of Savage’s axioms are models of the revised axioms, but the revised axioms additionally have models with unbounded utility. The arguments to bounded utility based on St. Petersburg-like gambles do not apply to the revised system.
Since posting this, I’ve revised my paper, now called “Unbounded utility and axiomatic foundations”, and eliminated all the placeholders marking work still to be done. I believe it’s now ready to send off to a journal. If anyone wants to read it, and especially if anyone wants to study it and give feedback, just drop me a message. As a taster, here’s the introduction.