# Size Criterion

 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, $\gamma(q):= \displaystyle \frac{size(A(q))}{size(O(q))}$ where $O(q)$ = set of outcomes associated with decision/system $q$. $A(q)$ = set of acceptable outcomes associated with decision/system $q$. $size(S)$ = size of set $S$. The larger $\gamma(q)$ the more robust $q$. It is assumed that $size(S)>0$ for any non-empty set $S$ and that $B \subset C$ entails that $size(B) \le size(c)$. Note that since $A(q)$ is a subset of $O(q)$, it follows that $0 \le \gamma(q) \le 1$. If the sets under consideration are finite, then we can let $size(S)=|S|$, where $|S|$ denotes the cardinality of set $S$. In this case $\gamma(q):= \displaystyle \frac{|A(q)|}{|O(q)|}$