Decision trees are excellent tools most often used in a business context
for making financial or number based decisions where a lot of complex
information needs to be taken into account. They provide an effective structure
in which alternative decisions and the implications of taking those decisions
can be laid down and evaluated. They also help you to form an accurate, balanced
picture of the risks and rewards that can result from a particular choice. An economist
wants to know about "opportunity cost", i.e. the consequences of doing one thing
rather than another. Decision trees make these choices explicit and clarify risks
associated with those choices, especially where the real likelihood of a particular
outcome is poorly defined. Option A may have the best outcomes if it works and
the worst outcomes if it doesn't; you need to be clear about these things! If you
do decide to proceed with a higher risk option being able to link the outcomes to
a properly designed monitoring program gives you the best chance of responding
quickly if the best case outcome is not happening.
Decision trees have been used in environment management to clarify choices
and exactly what is known about a problem. Some decisions are informed by
"best guess" estimates and have the advantage that at least the guess is made
explicit rather than hidden in an assumption of what will happen.
How to Draw a Decision TreeYou start a decision tree with a decision
that needs to be made. This decision is represented by a small square towards
the left of a large piece of paper. From this box draw out lines towards the
right for each possible solution, and write that solution along the line. Keep
the lines as far apart as possible so that you can expand your thoughts.
At the end of each solution line, consider the results. If the result of
taking that decision is uncertain, draw a small circle. If the result is another
decision that needs to be made, draw another square. Squares represent
decisions, circles represent uncertainty or random factors. Write the decision
or factor to be considered above the square or circle. If you have completed the
solution at the end of the line, just leave it blank.
Starting from the new decision squares on your diagram, draw out lines
representing the options that could be taken. From the circles draw out lines
representing possible outcomes. Again mark a brief note on the line saying what
it means. Keep on doing this until you have drawn down as many of the possible
outcomes and decisions as you can see leading on from your original decision.
An example of the sort of thing you will end up with is shown below:
Once you have done this, review your tree diagram. Challenge each square and
circle to see if there are any solutions or outcomes you have not considered. If
there are, draw them in. If necessary, redraft your tree if parts of it are too
congested or untidy.
You should now have a good understanding of the range of possible outcomes.
Starting to Evaluate Your Decision TreeNow you are ready to evaluate
the decision tree. This is where you can calculate the decision that has the
greatest worth to you. Start by assigning a cash or numeric value to each
possible outcome - how much you think it would be worth to you.
Next look at each circle (representing an uncertainty point) and estimate the
probability of each outcome. If you use percentages, the total must come to 100%
at each circle. If you use fractions, these must add up to 1. If you have data
on past events you may be able to make rigorous estimates of the probabilities.
Otherwise write down your best guess.
This will give you a tree like the one below:
Note that the tree looks less confused when different colours are used for
numbers than for the structure of the tree.
Calculating Tree ValuesOnce you have worked out the value of the
outcomes, and have assessed the probablity of the outcomes of uncertainty, it is
time to start calculating the values that will help you make your decision.
We start on the right hand side of the decision tree, and work back towards
the left. As we complete a set of calculations on a node (decision square or
uncertainty circle), all we need to do is to record the result. All the
calculations that lead to that result can be ignored from now on - effectively
that branch of the tree can be discarded. This is called 'pruning the tree'.
Calculating The Value of Uncertain Outcome NodesWhere we are assessing
the value of an uncertain outcomes (circles on the diagram), we do this by
multiplying the value of the outcomes by their probability, and noting the
result. The total value of that node of the tree is gained by adding these
In the example above, the value for 'new product, thorough development' is:
0.4 (probability good outcome) x $500,000 (value) = $200,000
0.4 (probability moderate outcome) x $25,000 (value) = $10,000
0.2 (probability poor outcome) x $1,000 (value) = $200
This is shown across our example tree in the diagram below:
Note that the values calculated for each node are shown in the boxes.
Calculating The Value of Decision NodesWhen you are evaluating a
decision node, write down the cost of each option along each decision line. Then
subtract the cost from the value of that outcome that you have already
calculated. This will give you a value which represents the benefit of that
Sunk costs, amounts already spent, do not count for this analysis.
When you have calculated the benefit of each decision, select the decision
which has the largest benefit, and take that as the decision made and the value
of that node.
Calculation of decision nodes in our example is shown below:
In this example, the benefit we previously calculated for 'new product,
thorough development' was $210,000. This example shows that we calculate the
cost of this approach as $75,000. This gives a net benefit of $135,000. The
benefit of 'new product, rapid development' was $15,700. On this branch we
therefore choose the most valuable option, 'new product, thorough development',
and allocate this value to the decision node.
ResultBy applying this technique we can see that the best option for us
may be to develop a new product. What the analysis shows which we might not have
appreciated, is that it is worth much more to us to take our time and get the
product right than to rush the product to market. In fact, it is better just to
improve our existing products than to botch a new product, even though it costs
SummaryDecision trees provide an effective method of decision making
As with all decision making methods,
though, decision tree analysis should be used in conjunction with common sense.
They are just one important part of your decision-making tool kit.
- clearly lay out the problem so that all choices can be viewed, discussed
- provide a framework to quantify of the values of outcomes and the
probabilities of achieving them
- help us to make the best decisions on the basis of our existing
information and best guesses.
Anderson discusses the use of Bayesian statistics in an ecological situation based on predictions of outcomes, and it is easy to see how the decision choices could be translated to a monitoring program.
Lee and Bradshaw discuss the approach of specifically integrating management into the design of monitoring programs to ensure feedback to managers to improve environmental outcomes.