Composition by DEA Distance to the Frontier - Probabilistic Composition of Preferences, Theory and Applications - page 62

have subsequent effects on the others. For such strategies, the optimistic joint
probability approach and the DEA algorithm may be contemplated.
Differences between these two last approaches must also be noticed. The use of
DEA corresponds to a more radical option for valorization of a marked advance in
one of the indicators isolated. In the optimistic probabilistic approach, less signif-
icant advances combined in two different dimensions have a positive effect on the
overall rating that does not appear in the composition by the DEA algorithm.
For example, countries like Liechtenstein and Qatar, which stand out for income,
but do not have such a good behavior in the educational dimension, have a better
evaluation when the ef

ciency in reaching DEA frontier is applied, but have a
worse evaluation by the optimistic joint probabilistic composition, though not as
bad as by the pessimistic composition.
It is also interesting to consider the cases of Japan and Iceland, which reach the
DEA frontier and are rated in the pessimistic approach that rewards consistency of
evaluations according to all criteria in a better rank than when evaluated by the
optimistic joint probability composition. Under this approach they are overtaken by
countries with scores close to the position of excellence in more than one criterion.
At the other extreme, call attention the positions of Eritrea and Sudan, with the
last positions in the pessimistic ranking, but escaping that position in the optimistic
probabilistic composition and in the assessment by the DEA algorithm, due to their
longevity scores. On the other hand, Sierra Leone, Congo and Central African
Republic, despite the worst performance by this criterion, have a relatively better
evaluation under the pessimistic assessment, due to a relatively better position by
other components.
The largest discrepancy between assessments for the same country in Table 6.2
is provided by Equatorial Guinea, a country for which the indicator of per capita
income ensures the fortieth position in the optimistic probabilistic classi

cation,

while by the pessimistic classi cation, taking into account more strongly the

proximity to the frontier of worst performance in the other indicators, is placed
among the countries with the worst scores.

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1950 - 2010. National Bureau of Economic Research Working Paper 15902. Retrieved 2010
from http://www.nber.org/papers/w15902 .
Charnes, A., Cooper, W., & Rhodes, E. (1978). Measuring the efficiency of decision making units.
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UNDP. (2014). Human Development Report. UNDP - HDRO, New York. Retrieved 2014 from

http://hdr.undp.org/en/reports .
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