This is the most intuitive, but highly impractical, measure of global robustness. According to this criterion, the robustness of a decision/system is the (if necessary, normalized) “size” of the set of “acceptable” outcomes.
More generally, the robustness of a decision/system is the fraction of “acceptable” outcomes associated with the decision/system. That is,
where
The larger the more robust .
It is assumed that for any nonempty set and that entails that . Note that since is a subset of , it follows that .
If the sets under consideration are finite, then we can let , where denotes the cardinality of set . In this case
