Risk and Rationality
Thursday, April 24, 2014 -- 12:00 AM
John Perry

The world is a risky place where all sorts of nasty things could happen.  So, how do we decide what to do when there are risks at every turn?

Luckily, there’s a widely accepted theory that tells me when it’s rational to take a risk. It says that a rational person is someone who maximizes  expected utility.  The basic idea is that an agent does something and, depending on circumstances, it may have several outcomes we can rationally assess.

For an example, suppose I’m considering a sky-dive -- that is, jumping out of a plane and parachuting to the ground. If the parachute doesn’t open, there’s a good chance I’ll die. So, when I jump, I’m taking a risk. 

I jump out of an airplane. That’s my act. One possible outcome is the parachute opens, I glide to earth, and have a great time. The other is that my parachute doesn’t open, and I plummet to the ground, and die.  Each outcome has a value. Floating to the ground, seeing things from that perspective, the whole experience, would be amazing. Falling and dying, of course, would be terrible.   And each outcome also has a probability. Let’s suppose that parachutes fail to open once in ten thousand times. The probability of the great outcome is 99.99 %.  The probability of the terrible outcome is .01 %  So, to get the expected utility of the act, we take the value of each outcome.  Let’s say the good outcome is worth 1000 points and the terrible one is worth a negative 100,000 points.  Then we multiply it by the probability of it being the outcome and then add them together, getting, by my rusty math 989.

Now suppose the value of not jumping is minus-25. Everyone will think I’m a wimp if I don't jump. So the expected utility of not jumping is minus-25, compared to plus-989 for jumping.   So, it’s rational for me to jump, and risk my life, rather than not jump, and risk derision.  At least, it is once I've put my self in a position to make this choice, by getting in a plane with a bunch of risk-loving friends.

Is that the whole story?  I learned this theory in graduate school, so it must be right.  However our guest has some doubts.