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Why Combinatorial Prediction Markets are Useful

By Joey Krug
You want to use combinatorial markets when you want more specific information.  For example "The patient will survive the infection." and "The patient should take clarithromycin or rifabutin?" and you can find out that if you gave the patient clarithromycin she has a significantly higher survival rate as predicted by the market.
Now a more practical example is: let's say Congress is deciding on whether to pass a stimulus plan.  The two options are a) spend it on a random grab-bag of kickbacks or b) spend it on public infrastructure.  Then you create a combinatorial market with those questions and "The GDP will be greater than it was last year."  If the market has 70 cents a share for yes on the GDP provided it is spent on public infrastructure, you have your answer (this is, btw, the answer I would certainly wager on as public infrastructure dollars have a 2x greater impact on GDP than the average government spending). 
Another classic example is: you're a boss and have 3 decisions to make, a or b, c or d, and e or f.  Now if you look at them independently you may end up choosing a, c, and e.  However, if you look at them all with respect to "Amount of free cash flow next year" you may find out that whilst individually they're not a good choice, together, b, d, and f are the best combination of choices to make. 
We tend to make decisions as if each one were in a black box, but generally speaking, this is a terrible approach.  To take this outside of the PM space, imagine you're a hospital admin and you have two choices on how to decide to tell your doctors to treat your patients.  You can a) hire hundreds of specialists and tell them their primary focus is on keeping their specialty under control (e.g. if the patient is in kidney failure, and you're a nephrologist, get them out of failure at all cost even if it's damaging to another part of the patient) or b) tell each specialist to keep their specialty's organs under control, but only at minimal expense to the rest of the patient. 
The choice is relatively simple, b is superior: if getting the patient off dialysis means putting him into
heart failure, you don't do it.  However, you'd be surprised at the number of medical institutions that do operate this way (even many of the "top schools" & associated hospitals).  Almost invariably,
especially in Zebra (rare disease) cases, the hospitals that take approach b have significantly superior patient outcomes.  The reason being, if you have a relatively healthy person who gets quite sick & screw up one part of their body whilst fixing the other, it's usually no big deal and the patient bounces back.  Do it to an extremely sick person and you kill them.  I'm almost certain the approach of "unblackboxing" decisions can be beneficial to other fields as well.