I’m not sure that “twice as much is twice as good” is a necessary property of utility functions. Though I guess it may be true by definition?
IIRC, utility functions are only unique up to positive affine transformations. And also I think only the gaps in utility between lairs of options are meaningful.
100⁄200 utility is meaningless without a “baseline” with which to evaluate it. And even then, it’s the gap between the baseline and a given utility value that would be meaningful not the utility value itself.
Suspect your last claim about the coherence of utility functions is just wrong.
The system can trade the resource in equal proportions to utility
Human utility functions over money are very much non linear (closer to logarithmic in fact) and utility functions over energy may also be sublinear.
John seems to assume that there is one resource that is equally valuable for maximizing utility for all systems. Why is that?
Resources like energy may seem useful for transforming the whole universe, but maybe my utility function is not about making such large-scale transformations.
Take humans as examples: most humans experience strong diminishing returns in almost all (or maybe even all) resources.
I think this is only an issue because you assume that for a resource to qualify as a “measuring stick”, the quantity of the resource possessed must be a linear function of utility.
I think that’s an unnecessary assumption and not very sensible because as you said, diminishing marginal returns on resources is nigh universal for humans.
Also I don’t think making large scale changes is relevant/load bearing for a resource to be a measuring stick of utility.
I think the only requirements are that:
The resource is fungible/can be traded for other resources or things the agent cares about
Agent preferences over the resource are monotonically nondecreasing as a function of the quantity of the resource possessed (this is IMO the property that Wentworth was gesturing at with “additive”)
I’m not sure that “twice as much is twice as good” is a necessary property of utility functions. Though I guess it may be true by definition?
IIRC, utility functions are only unique up to positive affine transformations. And also I think only the gaps in utility between lairs of options are meaningful.
100⁄200 utility is meaningless without a “baseline” with which to evaluate it. And even then, it’s the gap between the baseline and a given utility value that would be meaningful not the utility value itself.
Suspect your last claim about the coherence of utility functions is just wrong.
Human utility functions over money are very much non linear (closer to logarithmic in fact) and utility functions over energy may also be sublinear.
The law of diminishing marginal utility suggests that sublinear utility over any resource is the norm for humans.
I think this is only an issue because you assume that for a resource to qualify as a “measuring stick”, the quantity of the resource possessed must be a linear function of utility.
I think that’s an unnecessary assumption and not very sensible because as you said, diminishing marginal returns on resources is nigh universal for humans.
Also I don’t think making large scale changes is relevant/load bearing for a resource to be a measuring stick of utility.
I think the only requirements are that:
The resource is fungible/can be traded for other resources or things the agent cares about
Agent preferences over the resource are monotonically nondecreasing as a function of the quantity of the resource possessed (this is IMO the property that Wentworth was gesturing at with “additive”)
See also my top level comment.