Composition by DEA Distance to the Frontier - Probabilistic Composition of Preferences, Theory and Applications - page 55

output and the probabilities of minimizing some measure of cost of acquisition of
each input. In the other form, which takes as criteria the output/input ratios, the nal

scores will measure ef ciency in a manner more similar to that traditionally used in

DEA.
Preference scores for the cars in the example models in the preceding chapters
can be obtained by employing DEA algorithms to combine the probabilities of
preference according to the different criteria. As there are not causal relationships
between the attributes considered in this model, a constant inputs DEA model with
one output for each attribute must then be used. However, the result of the appli-
cation of the DEA algorithm will present as fully ef cient, i.e., with a global score

of preference of 1, all the alternatives. This follows from the fact that, with a large
enough number of criteria, it becomes possible to find for each alternative one

criterion for which the alternative is better than all the others, which is enough to
guarantee full ef

ciency.
A similar situation is that of the bus schedules example. Because the goal
intended in that case is raising quality and not productivity in the use of any inputs,
the process variables T 1 and T 2 should be maximized in the frontier of excellence,
as well as the outcome variables. This may be dealt with again inside the DEA
framework by applying the constant inputs approach.
In that case, a majority of the alternatives will again be fully ef cient. It is easy to

see, for instance, that the drivers of the second shift, which maximizes the last
output, will be in the frontier and, consequently, have an efficiency score equal to 1.
It may be noticed anyway, even in the simple examples above, that the con-
stancy of the results is limited to the conceptual approach taken. It would be
con rmed if, for instance, criteria to globally evaluate the performance of each shift

with respect to the process variables already in the analysis were added. If, on the
contrary, the change extends beyond the scope of this analysis to take into account
other variables, such as contribution to vehicle maintenance or careful driving, for
instance, the results might be entirely altered. In that case, the simplicity of the
vector of scores generated by the DEA approach may be an advantage.

6.3 A Human Development Index

This example shows how, even with the same criteria, the form of composition may
be employed to stress different points of view. Here, the probabilistic composition
is employed to offer diversi ed options of computation to the Human Development

Index HDI (UNDP 2014 ). This index was designed to provide a single counter-

point to the per capita Gross National Product (GNP) as a development measure, as
this does not take into account important aspects of quality of life that do not
depend on the volume of goods traded in the market.
Social values are complex and cannot be measured directly. Social indicators are
objective measures of simple attributes that are supposed to be in some way

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