In his blog, Luther Martin has been advising caution about the use of risk assessment and risk management methods for information security. In many posts, he’s out-right skeptical, and seems to be advising against it. Here’s the most recent example, from the post “The two-envelope problem in risk management” [emphasis added]:
Does it make sense to never change your information security strategy? That’s a possible consequence of the so-called two-envelope paradox. This is a problem in probability theory that has confused students of probability theory for over 50 years.
[explanation of the problem and how it applies to InfoSec investments]
The bottom line is probably that probability is a complicated and subtle concept, which means that risk management, which relies on it, also is.
Luther and I agree on his bottom-line statement. This stuff can be complicated and subtle. It is easy for college-educated professionals and executives to make mistakes that lead to erroneous conclusions. In fact, Luther’s own blog post is a case study in how easy it is to make mistakes.
Luther uses the “Two Envelopes Problem” in probability theory as an example where Bayesian (subjectivist) probability methods seem to break down in paradox. Here’s the problem and paradox, leaving out the math for now (details at the end):
The player is given two indistinguishable envelopes, each of which contains a positive sum of money. One envelope contains twice as much as the other. The player may select one envelope and keep whatever amount it contains, but upon selection, is offered the possibility to take the other envelope instead ["switch"].
[...Bayesian analysis, leading to the decision to "switch", and then "switch" again, ad infinitum...]
As it seems more rational to open just any envelope than to swap indefinitely, the player is left with a paradox.
Following Wikipedia, Luther points out that ”There’s a problem with this argument, of course, but it’s fairly subtle. Even specialists in probability theory don’t agree what the problem actually is,…”. Luther then applies Two Envelopes Problem structure to an analogous problem in information security (I’ll call it “Two Technologies”):
Now let’s suppose that we can’t find a flaw in the above argument and we apply it to our information security strategy. Let’s suppose that we have some initial set of technology, policies and procedures that end up giving us some exposure to risk that we’ll denote R, and if we change to a different set of technology, policies and procedures, we might either increase the risk to 2R or decrease it to R/2. If we apply the same reasoning that we applied above, we find that it never pays to change, because the alternative always has a greater than the risk than what we have now. This clearly doesn’t make sense, but it’s what you might get if you do a risk analysis that isn’t as careful as it could be.
This seems OK on the surface, but Luther has made a mistake in framing the Two Technologies problem. Simply put, his Two Technologies problem is not structured the same as the Two Envelopes problem. Therefore Bayesian formulas for the Two Envelopes does not fit his Two Technologies problem. Even if it did, a proper framing of the Bayesian analysis avoids the paradox. (For math details, see below).
So, yes, probability and risk management can be complicated and subtle. But Luther’s use of the Two Envelopes Problem and his attempt to construct the same problem in InfoSec only supports this conclusion through the “covert channel” of his own mistakes.
Is Luther implying that we shouldn’t even try risk assessment and management because it’s beyond our ken? “Yes” seems to be the answer, if I understand his posts in the “risk” category. What alternative to risk management is Luther proposing? In another post, he suggest that we should just use trial-and-error to muddle through:
In the absence of reliable risk information, a similar approach to information security may be the best that we can do – just try different things and see which works the best. You might call this approach “experimental security.” There may be no better approach.
If someone can prove that risk assessment/management for InfoSec is impossible in principle, then Luther would be right. But I know of no such proof of impossibility. Just because we currently find risk management to be “complicated and subtle” doesn’t mean we should dump it. We do need tools and frameworks that are up to the job and sufficiently usable to help ordinary people avoid the paradoxes and ratholes in the analysis. As our academic colleagues would say: “further research is needed”.
(For mathematical details, read on…)
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