# Verifying vNM-rationality requires an ontology

Re­sult
It is im­pos­si­ble to ver­ify that an agent is vNM-ra­tio­nal by ob­serv­ing its ac­tions with­out ac­cess to the do­main of its util­ity func­tion.

Mo­ti­va­tion
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.”

Ex­pla­na­tion
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.

• Hmm. Un­der what con­di­tions does it mat­ter that an agent is vNM-ra­tio­nal with­out any more in­for­ma­tion about its goals? in­stru­men­tal ra­tio­nal­ity is defined in terms of goals, it’s not clear that it’s even mean­ingful to talk about it when the goals aren’t fixed, or mean­ingful to talk about know­ing it with­out know­ing the goals.

• Nit­pick: I think the in­tro ex­am­ple would be clearer if there were ex­plicit num­bers of grapes/​or­anges rather than “some”. Noth­ing is sur­pris­ing about the origi­nal story if Beatriz got more or­anges from Deion than she gave up to Cal­listo. (Or gave away fewer grapes to Deion than she re­ceived from Cal­listo.)

• Could you ex­plain the differ­ence (or re­la­tion­ship) be­tween on­tol­ogy and a util­ity func­tion? Is there a rea­son you change be­tween the two? And I thought on­tol­ogy is more to do with what ex­ists—would “ax­iol­ogy” be a bet­ter word?