D.3.3 ALGORITHMS FOR INCREMENTAL ... - SecureChange

12 F. Massacci and L.M.S. Tran
RM
5%
5%
5%
45%
RM1
A
RM2
A
…....
RM11
A
RM12
B
Fig. 4 The long-tail problem.
6 Quantitative Metrics: Max Belief and Residual Risk
As consequence of actual occurences of evolutions possibilities, a final design
choice may or may not be able to fulfil the enterprise’s objectives. In order to
select among the various alternatives we need a quantitative metric that can guide
the decision maker.
The first intuitive measure is the total probability that a final configuration
survived, called Total Belief : the sum of probabilities of all possibilities where
the final choice fulfill the enterprise’s objectives. If complexity is not a problem
it is also easy to compute: just unroll all probabilities combining them into one
big observable rule. Then gather every possible model that (i) is resulting from the
evolution, (ii) includes the final design choice and (iii) fulfils the root objectives of
the enterprise.
Unfortunately, this measure might lead to a severe long-tail problem. This
problem, firstly coined by Anderson [1], is present when a larger than normal population
rests within the tail of the distribution. A long-tail example is depicted in
Fig. 4 where an enterprise model EMmight evolve to several potential possibilities
with very low probabilities (say, eleven possibilities with 5% each), and another
extra possibility with dominating probability (say, the twelfth one with 45%).
Suppose that an element A appears in the first eleven possibilities, and an element
B appears in the last twelfth possibility. Apparently, A is better than B due
to A’s total belief is 55% which is greater than that of B, say 45%. Arguing that A
is better than B or versa is still highly debatable. Ones might put their support on
the long tail [1], and ones do the other way round [10].
Our game semantics allows us to make an informed choice: at the end of the
day, only one possibility becomes effective (i.e. chosen by Reality). If we thus
consider every single possibility to be chosen, the twelfth one (45%) is the one
with the highest pay-off by the Domain Expert. The other possibilities offers a
substantial less chance of making money: Domain Expertwill only pay a 5% ROI
for any of the other possibilities. It is true that globally A might be chosen by any
of the 11 alternatives, but reality will not realized them all together. It will only
chose one and each of them only have a ROI of 5%. Choosing the largest ROI is
one of the possible alternatives.
However, we need to be careful since Designer must invest M to build B before
knowing whether it would pay off. So what is interesting for the Designer is a
measure of the risks that its choice might turn out to be sour. We are currently
investigating a number of alternatives. A possible solution is to consider the dual
of the MaxBelief and namely the MaxRisk as the highest chances of a possibility