Geoscience Reference
In-Depth Information
Chapter 5
Composition by Joint Probabilities
Abstract
culty involved in the composition of the criteria by weighted
average, due to the dif
The dif
culty of assigning weights to criteria and to sets of criteria,
was already signaled in the preceding chapters. The probabilistic approach allows
forgo the weighting of the criteria and get overall scores of preference by calcu-
lating joint probabilities.
Keywords Being the best
Being the worst
Conservative
Progressive
Optimist
Pessimist
All the criteria
At least one criterion
5.1 Approaches by Joint Probabilities
The choice between possible forms of composition of preferences in terms of joint
probabilities is facilitated by its probabilistic character. For example, the alterna-
tives can be ordered according to the probability of being the best by all the criteria
simultaneously. To calculate this probability, assuming that the random compo-
nents involved in the application of the different criteria are independent, it is
enough to multiply the probabilities of being the best according to each criterion.
The form to obtain joint probabilities of preference depends on the point of view
taken by the decision maker. Four forms of composition can be obtained according
to the position taken by the decision maker on two questions, the
rst about
conservatism and the second about pessimism. It is much easier to identify which of
these views should guide the decision than choosing a set of weights to the criteria.
In the
first aspect, the decision maker in the progressive side pays attention to
maximize the probabilities of preference according to the criteria examined, while
for that in the conservative side the odds that matter are of not minimizing such
preferences. The progressive decision maker pays attention to the differences
between the alternatives near the frontier of excellence; for the conservative one
what is important is to differentiate those near the frontier of worst performance.
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