Imagine you are part of a competition where you put your hand in a pot of water and it is heated. Your pain threshold is quantified as the temperature (T) where you withdraw your hand. The person with the highest pain threshold wins a rediculous sum of money.
Now, we know there will be variability in T. My question is whether this variability in T primarily reflects differences in the ability to tolerate pain, or simply differences in the amount of pain produced by a given temperature (i.e., neurological differences). If the former is the case, then this competition will truly find the person with the most "grit". However, if the latter is true, all we are doing is identifying people with particularly insensitive neurology, and they may actually be no "tougher", mentally, than the others.
I would expect that the utility of the reward would play some part in each subjects willingness to tolerate pain. That is why the reward is a very large sum of money, such that the utility of the reward effectively "saturates" each subjects tolerance for pain (i.e., assume each subject is very motivated to accept pain).
Can we decide between the two options?