The key properties that make money a useful measuring stick are:
It’s fungible: agents can purchase things they want through money (including other resources).
Agent preferences over money are monotonically non decreasing as a function of quantity (more money is not worse [it may not always be better: e.g. some agents may have bounded utility functions]. I think you alluded to this by describing money as “additive”, but I don’t think that’s the right property; additive resources aren’t a useful measuring stick if the agent doesn’t want more of the resource.)
Something that you did not address is how the measuring stick relates to the utility function.
Consider five resources {A,B,C,D,E}, and functions that measure the utility to the agent of a given quantity of each resource. (RA,RB,RC,RD,RE)(RX:R→R).
RA∈Θ(logn)
RB∈Θ(√n)
RC∈Θ(n)
RD∈Θ(n2)
RE∈Θ(2n)
Which of the four resources is a measuring stick of utility? Are all of them?
I don’t think this is a significant hindrance. If we know how utility of the resource grows as a function of quantity, we could back out a linear measure of utility by applying said function to the quantity of the commodity possessed.
As for the question of how to identify measuring sticks of utility in the wild, I think the two conditions highlighted earlier purchase a lot of mileage:
Any commodity that:
Can be traded for known resources (e.g. energy, money [specifically, it’s commensurable with every other resource]) or is otherwise fungible for things the agent cares about
This fungibility should be in such a manner as to preserve the “monotonically nondecreasing as a function of quantity” property
Agent preferences over the commodity are monotonically non decreasing as a function of the quantity of the commodity possessed
The key properties that make money a useful measuring stick are:
It’s fungible: agents can purchase things they want through money (including other resources).
Agent preferences over money are monotonically non decreasing as a function of quantity (more money is not worse [it may not always be better: e.g. some agents may have bounded utility functions]. I think you alluded to this by describing money as “additive”, but I don’t think that’s the right property; additive resources aren’t a useful measuring stick if the agent doesn’t want more of the resource.)
Something that you did not address is how the measuring stick relates to the utility function.
Consider five resources {A,B,C,D,E}, and functions that measure the utility to the agent of a given quantity of each resource. (RA,RB,RC,RD,RE)(RX:R→R).
RA∈Θ(logn)
RB∈Θ(√n)
RC∈Θ(n)
RD∈Θ(n2)
RE∈Θ(2n)
Which of the four resources is a measuring stick of utility? Are all of them?
I don’t think this is a significant hindrance. If we know how utility of the resource grows as a function of quantity, we could back out a linear measure of utility by applying said function to the quantity of the commodity possessed.
As for the question of how to identify measuring sticks of utility in the wild, I think the two conditions highlighted earlier purchase a lot of mileage:
Any commodity that:
Can be traded for known resources (e.g. energy, money [specifically, it’s commensurable with every other resource]) or is otherwise fungible for things the agent cares about
This fungibility should be in such a manner as to preserve the “monotonically nondecreasing as a function of quantity” property
Agent preferences over the commodity are monotonically non decreasing as a function of the quantity of the commodity possessed