Why is a resource central here? Consider (if it helps, also change “upgrade” to “switch”):
Let’s start with the simplest coherence theorem: suppose I’ll pay to upgrade pepperoni pizza to mushroom, pay to upgrade mushroom to anchovy, and pay to upgrade anchovy to pepperoni. This does not bode well for my bank account balance. And the only way to avoid having such circular preferences is if there exists some “consistent preference ordering” of the three toppings—i.e. some ordering such that I will only pay to upgrade to a topping later in the order, never earlier. That ordering can then be specified as a utility function: a function which takes in a topping, and gives the topping’s position in the preference order, so that I will only pay to upgrade to a topping with higher utility.
Surely one can notice the circularity problem without using a measuring stick.
Transitivity is a fundamental axiom necessary for a consistent utility function, which is central to rational choice theory. Sure, the potential for resource loss makes it more problematic for the agents you’re studying, but if you don’t have a consistent utility function to support your modeling in the first place, it’s already problematic for your studying of the agents. Put another way, you don’t even need to “reach” the coherence argument if you can’t get over the consistency bar.
Why is a resource central here? Consider (if it helps, also change “upgrade” to “switch”):
Surely one can notice the circularity problem without using a measuring stick.
If there’s no resource loss in that cycle, why is it a problem at all?
Transitivity is a fundamental axiom necessary for a consistent utility function, which is central to rational choice theory. Sure, the potential for resource loss makes it more problematic for the agents you’re studying, but if you don’t have a consistent utility function to support your modeling in the first place, it’s already problematic for your studying of the agents. Put another way, you don’t even need to “reach” the coherence argument if you can’t get over the consistency bar.