A decision tree is a popular tool to use to share information about risks using expected value. Every decision has an outcome and something will happen as a result of the decision. The decision “tree” helps us decide whether we can live with the choices we make; if we choose to eat lunch out or stay in for lunch, whether to build or buy, whether to pursue a line of business or not. These events are out outcomes of whatever decisions are made – not on probability. However, the outcomes of events do have a probability associated with them. There is a chance they will occur, as well as a chance they will not. It’s important to acknowledge that the outcomes from a single event are mutually exclusive of one another. If outcome 1 happens; outcome 2 cannot. If outcome 2 happens, outcome 1 cannot. For that reason, we can determine their probabilities clearly. If there are only 2 outcomes, and there’s a 40% chance of outcome 1 occurring, then there is always a 60% chance of outcome 2 occurring. The multiple of the outcomes will always sum to 100%.
Here is an example. We have a decision called “where to eat lunch”. We have 3 possible choices which lead to an outcome. The outcome is either “keep customer” or “lose customer”. For this example, we are associating some probabilities and some values of the outcomes. These values are not “Expected values”, but simply values of the outcomes if they come to pass. The costs of the meals are also included. Costs associated with the outcomes represent lost business through negative word of mouth communication. Revenues associated with outcomes represent newly acquired business by virtue of the positive experiences associated with the meal.
So we have 1 Decision – Where do we eat? There are 3 choices, we can eat at a hot dog vendor for – $10, fast food for -$20, or Fine dining for -$150. If we eat at the hot dog vendor we stand a 10% chance of keeping the customer which leads to outcome 1 ($500). That gives us a 90% chance of losing the customer if we eat at the hot fog vendors place (-$600). Choice 2 is eating at a fast food place costing -$20. It leads to a 40% chance of keeping the customer valued at $750 and a 60% chance of losing the customer valued at -$300. The third choice is fine dining costing -$150 leading to a 60% chance of keeping the customer valued at $1000 and a 40% chance of losing the customer valued at -$100.
Now we have enough information to figure out the best outcomes for our company. If for example, we select a hot dog vendor for this client lunch and achieve a positive outcome, the total benefit for the company will be $490 (outcome of event – cost of lunch). If we choose last food and have a positive outcome with the customer, the net benefit to the customer is $730.
When looking at risks, we need to also take the potential losses into consideration. Returning to the hot dog example, the negative impression generated may cost an additional $600 in lost business. That combined with the initial cost of the lunch would mean losses to the company on the order of -$610.
Stay tuned for part 2.