Decision Analysis: Interpretation

If a decision tree is to be valid, the outcomes must be mutually exclusive and collectively exhaustive.

"Mutually exclusive" means that the branches extending from the nodes mustnot overlap (they must be "well defined," in mathematical terms). It will not do to try to analyze a chance node with options of "low interest loans," "tax abatement," and "TIF bonding," since TIF bonding overlaps with low interest loans. If the probabilities are properly calculated, theymust add up to more than <1> (since at least part of the same outcome is included in two outcomes); if the probabilities only add up to <1> they cannot be properly formed (since that would ignore the overlap).

Collectively exhaustive" means that the branches from a node represent all the choices or outcomes that are possible. In the previous examples, if a city had 3 categories for Industrial land use, analyzing only Light and Heavy would distort the results (since the probabilities will not add o <1>, at least not if they are well formed).

A decision tree becomes more useful as the probabilities in it are more carefully defined. Using probabilities based on an informed opinion is better than drawing numbers out of the air, but better yet are probabilities based on empirical estimation. But gathering additional information may not always be advisable. Sometimes additional information cannot change the decision. For example, getting more precise estimates on the probabilities for a choice node which has a "best" outcome less than the expected value of a competing node is a waste of effort--even in the best case, one would not choose it. At other times the cost of the additional information may be more than it is worth. The "cost" of information is the difference between the expected value from the information less the value of the next best option. If two choices are fairly close (say, a choice between two housing projects, one with an outcome of $1 million and the other with an outcome of $1.01 million, and you could improve the accuracy of your analysis by commissioning a survey for $10,000) the cost of the additional information may eat up any benefit it could bring to the analysis.

Finally, the analyst must consider the characteristics of the decision makers for whom the analysis is being done. Most of the time, a rational decision maker will be "risk-neutral." The risk neutral position uses the expected value for chance nodes. Recall that the expected value need not(usually, will not) actually occur. It represents the point at which the probable gains are just offset by the probable losses. However, sometimes even a rational decision maker will be "risk-averse." Sometimes the "probable losses" (the downside of the "expected value" gamble) are simply too important to risk. For most people, a game of Russian Roulette fits this description. Some would argue (for example) that threatening wetlands or endangered species are similar examples. In this case, rather than evaluating payoffs in terms of dollars one converts to an ordinal system of values, called "utility" (see Stokey & Zeckhauser, 1978, pp.237-254). Note that there is no hard criterion for determining when an analysis shifts from a risk-neutral to a risk-averse basis.

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