Verifying vNM-rationality requires an ontology
It is impossible to verify that an agent is vNM-rational by observing its actions without access to the domain of its utility function.
Alphonso and Beatriz both go the market to buy fruit.
Alphonso prefers grapes to oranges.
He fills his basket with grapes and pays for them.
Beatriz carefully picks through the fruit and purchases some oranges and some grapes.
Callisto arrives with a package of grapes.
“Say, Beatriz, would you like to trade some of your oranges for this package of grapes?” Callisto offers.
“Gladly.” Beatriz replies, exchanging some of her oranges for the grapes.
A few moments later, Alphonso notices Beatriz giving Deion some grapes in exchange for some oranges.
“You are acting irrationally, Beatriz!” Alphonso exclaims. “Your unstable preference between oranges and grapes makes it possible for a malicious agent to exploit you and exhaust your entire grocery budget!
“Ah, but I am acting rationally.” Beatriz replied with a smile. “I prefer fruit that is fresh enough to last more than seven days. Thus, I trade away fruit that will spoil before that time.“
Consider an agent A.
We are interested in verifying whether or not A is vNM-rational.
However, we are only able to observe A’s decisions without any access to the domain of A’s utility function.
Without this access, it is impossible to distinguish between vNM-irrational choices (i.e. choices that violate one of the axioms of vNM-rationality) and choices that are vNM-rational but made under an unexpected ontology.
In other words, we need to know how A perceives outcomes of the world before we can verify that A’s preferences over those outcomes are vNM-rational.