If you think about pain as an incentive mechanism to stop you from hurting yourself there are some properties that would follow from that.

When I was pierced by a stingray, the pain was outrageous. The puncture went deep into my foot and that of course hurts but the real pain came from the venom-laden sheath that is left behind when the barb is removed. Funny thing about the venom is that it is protein based and it can be neutralized by denaturing the protein, essentially changing its structure by “cooking” it as you would a raw egg.

How do you cook the venom when it is inside your foot? You don’t pee on it unless you are making a joke on a sitcom (and that’s a jellyfish anyway.) What you do is plunge your foot is scalding hot water raising the internal temperature enough to denature the venom inside. Here’s what happens when you do that. Immediately you feel dramatic relief from the pain. But not long after that you begin to notice that your foot is submerged in scalding hot water and that is bloody painful.

So you take it out. Then you feel the nerve-numbing pain from the venom return to the fore. Back in. Relief, burning hot water, back out. Etc. Over and over again until you have cooked all the venom and you are done. In all about 4 hours of soaking.

A good incentive scheme is reference-dependent. There’s no absolute zero. Zero is whatever baseline you are currently at and rewards/penalties incentivize improvement relative to the baseline. When the venom was the most dangerous thing, the scalding hot water was painless. Once the danger from the venom was reduced, the hot water became the focus of pain. And back and forth.

Second Observation.  After three weeks of surfing (minus a couple of days robbed by my stingray friend) I came away with a sore shoulder.  Rotator cuff injuries are common among surfers, especially over the hill surfers who don’t exercise enough the other 11 months of the year.  The interesting thing about a rotator cuff injury is that the pain is felt in the upper shoulder, not at the site of the injury which is more in the area of the shoulder blade.  It’s referred pain.

In a moral hazard framework the principal decides which signals to use to trigger rewards and penalties.  Direct signals of success or failure are not necessarily the optimal ones to use because success and failure can happen by accident too.  The optimal signal is the one that is most informative that the agent took the appropriate effort.  Referred pain must be based on a similar principle.  Rotator cuff injuries occur because of poor alignment in the shoulder resulting in an inefficient mix of muscles doing the work.  Even though its the rotator cuff that is injured, the use of the upper shoulder is a strong signal that you are going to worsen the injury.  It may be optimal to penalize that directly rather than associate the pain with the underlying injury.

(Drawing:  Scale Up Machine Fail, from www.f1me.net.)