When You Come Upon A Fork In The Road, Climb A [Decision] Tree To See Which Way To Go

We make decisions under uncertainty every day.  We make them at home, at the office, and everywhere in between.  They’re called decisions under uncertainty because we have to make them with only limited information about their consequences and the future.

One simple example is deciding whether to take an umbrella with you when you leave home.  Since you do not know with certainty whether it will rain during the day you have to consider a few relevant factors, like the likelihood of rain and how uncomfortable you would be spending the day wet, and then make a decision.  Of course, at the end of the day you’ll know whether you needed an umbrella, but at the time you’re making the decision (in the morning) you have to make the decision despite uncertainty about the impending weather.

We face similar decision situations at work.  With only limited information about the future and the consequences of our decisions, we have to decide which customers to help, which products to sell, which buildings to construct, and which projects to pursue.  Given how significant these decisions can be, because they constrain our future alternatives, have major impacts on others, or involve large sums of money, it is important to structure our decision making process.  As Napoleon Hill once wrote, “Reduce your plan to writing.  The moment you complete this, you will have definitely given concrete form to the intangible desire.”

One way to structure our decision making process is to draw a decision tree and use expected value as the decision criterion.  An example of a decision tree is shown below:

A square represents a decision point, a point in time where you make a decision.  The circle represents a chance event, a point in time where you face two or more possible future states of the world.  The decimal numbers close to the circle show the probability that each of the possible states of the world could take place, and the dollar amounts show the monetary value of each of the possible decision paths.

Expected value is one decision criterion you can use to make a decision.  To calculate the expected value of a decision, for each alternative stemming from a chance event multiply the probability of an alternative by the value associated with that alternative and then add all of the products together.  For example, if you’re deciding whether to conduct a market survey before launching a new product nationwide there might be two alternatives stemming from the chance event, the market survey is favorable and the market survey is unfavorable.  Let’s say the probability the market survey is favorable is 0.60 or 60 percent, and the probability the market survey is unfavorable is 0.40 or 40 percent.  Remember, the sum of probabilities associated with a chance event is one.  Let’s also say the value of a favorable market is $100,000,000, and the value of an unfavorable market is $1,000,000.  In this case, the expected value of conducting the market survey is (0.60 * $100,000,000) + (0.40 * $1,000,000) = $60,000,000 + $400,000 = $60,400,000.  If this amount is greater than the cost of the market survey and greater than all of your alternatives, based on the expected value criterion, you should conduct the market survey.

Decision trees and expected value analysis are helpful tools for structuring your decision process; however, they do suffer from some weaknesses, like the possible amount of analysis required to derive the values and probabilities for the decision tree and the lack of consideration of your attitude toward risk, so you need to be careful when using these tools.  Incorporating your attitude toward risk into this type of analysis is an interesting and important capability, so I’ve decided I will discuss how to do so in a future article.  Wow, Rita Mae Brown was right when she said, “a peacefulness follows any decision, even the wrong one.”

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