Archive for July, 2007

risk: uncertainty and probability chains

July 25, 2007

Think fast: would you rather face a 50/50 chance of a single positive outcome or a positive outcome that required three things to happen, each with .80/1 chance of happening?

If you chose the latter, you would be mathematically justified by a narrow margin. Three occurences with .80 probability happening has a net 51/100 probability.

I take away two points from this. One, in reality, the former choice is likely preferrable because you can focus on just one variable. In the latter, your best resources’ attention may be stretched to cover all the bases. Even though both choices have the same mathematical probability, if you have some level of control to affect outcomes, all other things being equal, the simpler proposition is better.

Two, it’s human to exaggerate the certainty of things, and this gets ugly as variables pile up. Let’s say you have a 90% chance of something happening. Most people would say that’s a pretty sure bet, assuming it’s not a life and death type of matter. If you’re an optimist, you might not think twice about the uncertainty. But as we chain “sure things” together, the ultimate outcome gets increasingly uncertain. In fact, when you chain 10 of these sure things with 90% probability together, the desired outcome drops to only 35%!

There’s a third point here that’s for the pessimists out there. Sometimes longer chains are better. Sometimes not everything has to go perfectly to get to the ultimate outcome. And, although this is a little abstract, it’s generally easier to positively affect an event with 90% probability than one that is 50/50. For instance, the higher the probability the more likely we can look to someone else to transfer the risk. Not too many insurance companies will insure against a 50/50 risk, but the higher you scale, the more likely they will.

Bottom line? Map out the critical variables to achieving your positive outcome. Look at each variable for how manageable it is first. The more manageable they are, the more reasonable it is to “stretch out” the chain of variables. Otherwise, try to reduce the number of variables you’re dependant upon.