The Efficient Market Hypothesis states that it is not possible to trade in a market with the expectation of gain on the basis of public information. An efficient market may be defined as one in which all public information is instantly reflected in prices. As such, the Efficient Market Hypothesis is really a definition. The hypothesis is that real markets are close to being efficient.
I propose an Intelligent Adversary Corollary, that it is not possible to make useful predictions about the acts of an adversary on the basis of public information. The adversary has access to this information, and can perform the same analyses we can, and can therefore anticipate our conclusions and our responses, and can act with knowledge (at least statistical) of what they are likely to be. As a result, the adversary can negate the predictive value of our conclusions.
Of course, this is almost trivial. If we perceive a vulnerability, we defend against it. As long as the nature of that defense is public, the adversary is fully aware of its strengths and weaknesses. If strong, he will find some other place and means of attack. If weak, he may choose to attack there.
Strong public defenses can be effective (there have been no hijackings since September 11, 2001, and the Israeli security fence has reduced suicide bombings by about 90%); the Corollary only asserts that attempts to predict the time, place and nature of attacks on the basis of public information are not useful. Secrecy is a force multiplier, most obviously for the offense (whose attacks would be readily thwarted if the defense knew when or where they were planned), but also for the defense. For example, even lax pre-September 11 airport security could have been effective if supplemented by a secret program of ethnic profiling. Overt ethic profiling would have been less effective, because it could have been thwarted by using operatives, such as the ``shoe bomber'', without the expected ethnic characteristics.
The validity of the Efficient Market Hypothesis in actual markets is a matter of controversy among economists. To some extent, this is a controversy over the definition of public information--if information can be obtained only by extensive statistical analysis of public data, requiring computing capabilities not generally available, is that information public? In an earlier era, one might have asked if a specialist's order book was public information.
It is possible to profit from small deviations from the Efficient Markets Hypothesis because gains of fractions of a percent per transaction are sufficient. In contrast, for predictions of military attacks or terrorist acts to be useful the Intelligent Adversary Corollary would have to be qualitatively wrong, rather than merely inexact. A ten percent reduction in the likelihood of been the victim of a surprise attack or in the rate of successful terrorist acts would be impossible to demonstrate because of the intrinisic rarity of these events and fluctuations in their frequency, and would not satisfy those responsible for controlling these threats.
The Intelligent Adversary Corollary doesn't make public information, or the collection of open-source intelligence, useless. These are necessary to set the context of secret information, and may be important in themselves. For example, the public information (well-known historic facts) that Sunni Arab cultures have ineffective conventional militaries was essential to planning the spectacularly successful liberation of Iraq by small American and allied forces in March, 2003. Not recognizing the equally public information that Sunni Arab cultures do not accept defeat, do not readily compromise, and enforce this by the assassination of any of their own leaders seen to be willing to compromise was a strategic failure. Not acting on the public information that these cultures use informal networks of terrorists and suicide bombings as weapons led to a tactical failure, and our present difficulties.