A Quantitative Model of
the Amplification of Power Through Order and Implications for Defense Against
Why was a minority of 15 barely armed terrorists on September 11 able to hijack 3 planes with several hundred passengers on board and fly them into buildings committing mass murder? The hundred or so passengers and crew were only able to resist in one of the planes, thwarting the intention of the hijackers to kill even more. In the end nobody on that plane survived either. One might have expected that the passengers and crews on all flights would have resisted and been able to overwhelm the terrorists and fly the planes to safety.
In this contribution I propose a simple quantitative model of how the power of a leader over a group is amplified when the group is ordered. This model implies that a small well-informed minority can easily govern an ordered majority and suggests the importance of a new concept, "group defense" that may be helpful in preventing fatal hijackings of the September 11 type.
How power is amplified through order
Consider a drill sergeant trying to line up her recruits. This maneuver imposes order on a group and, as we will see, greatly increases the power of the drill sergeant. Assume we measure the power a particular drill sergeant displays over a lone recruit to be P per time interval. Consider two situations which includes all the recruits: none of the recruits lined up and all the recruits lined up - in other words, no order or perfect order among the recruits. In the case of no order, each recruit experiences P/N displayed power from the sergeant because her attention and intimidation has to be equally shared among the N recruits. The sum over all recruits, the displayed or "real" power is then P, same as for a single recruit.
Preal = P
In the case of perfect order among the recruits, the drill sergeant's total displayed power stays the same, P, but through the ordering process she now has added a new kind of power over the ordered recruits, "virtual" power. Each recruit knows that if he gets out of line, as long as he is the only one doing it, he has to face a P confrontation with the sergeant. This threatened power of the drill sergeant is not actually displayed by her until the recruit gets out of the line. Before it is displayed or "real" we call it "virtual". It is important because it is considered to be real and prevents recruits from moving out of the lineup. How large is her virtual power? It is N*P*d (P per recruit, with d likelihood of discovery adding up to N*P*d for all recruits). In the case of perfect order we approximate d=1 and obtain:
Pvirtual = N*P
This is quite extraordinary: a sergeant can enhance her or his virtual power 10 - 100 times without doing anything but lining up the recruits. No additional weapons or backups are needed. The sergeant's virtual power comes about because and only because the recruits are ordered. The more ordered they are, the larger is her virtual power, in other words, the order amplifies her virtual power. The virtual power varies as the number of recruits get out of the lineup. As she orders the recruits into the lineup, her virtual power rises from 0 to NP.
The increase in virtual power due to the ordering of the recruits is but one of the several sources of power through order. Another source of power results from the tendency of most people to copy the behavior of the people around them (Asch, 1956). If we label this power also as virtual, it can be quantified as c*P*n per recruit in the situation of perfectly ordered recruits where c is the conformity power a recruit has over another in units of the power the sergeant has over a recruit, and n is the number of neighbors he has eye contact with. In some instances n is about 8, in some instances this can become much larger depending upon the formation of the recruits. For all the recruits the result is:
Pconformity - virtual = N*c*P*n
Two other types of power result from the successful threat of collective punishment and the planting of spies among the recruits. Suppose our sergeant imposes collective punishment. If the recruits don't want to be punished, they will look around to make sure any dissenters get in line. A single unaligned recruit faces the real power P from the drill sergeant and the real power (N-1)*P*s from the other recruits, where s is the power a recruit has over another in units of the power the sergeant has over a recruit.
Pcollective punishment = (N-1)*P*s
The corresponding virtual power is (N-1)*P*s per recruit or, for all recruits:
Pcollective punishment - virtual = N*(N-1)*P*s
The role of spies is to keep the power of the sergeant intact when he or she is not present. The more spies, the higher the probability that the sergeant will find out about individual deviations, for simplicity we assume that there are enough spies to make the probability 1. The power from spies is then:
Pspies - virtual = Pvirtual
In total, the power of the sergeant in the case of all ordered recruits is all virtual and is:
Ptotalordered = Pvirtual + Pconformity - virtual + Pcollective pusnishment - virtual + Pspies - virtual = N*P+ N*c*P*n + N*(N-1)*P*s
The power amplification resulting from ordering the recruits is then:
Amplification = N+N*c*n+N*(N-1)*s
If we pick s = 0.1, n = 8, and c = 0.1 the amplification for 100 recruits is then:
Amplification (N = 100, s = 0.1, n = 8, c = 0.1) = 1170 thus the sergeant's power has increased more than 1000 times.
Implications for Hijacking Victims
If a lightly armed hijacker is an experienced fighter and can evenly battle say four passengers, four hijackers should not be able to control more than sixteen passengers. The model of power amplification through order, however, suggests otherwise. Once the hijackers order the passengers, their virtual power Pvirtual is amplified 100 times if there are 100 passengers. The passenger group would then act as if the hijackers could evenly battle 1600 of them.
Strategies for Group Defense Against Hijackings
The informed minority we have alluded to is one which has experienced the amplification of power through order. Such informed minorities would presumably include the hijackers of September 11, but also school teachers, flight cabin crew and other people who are in charge of groups and who have seen the consequences of the ordering of groups.
The majority of passengers and crew members may not be aware of this phenomenon, however. The model of power amplification through order suggests that to prevent hijackers from taking control of a passenger/crew group, the passengers and crew have to become more informed about "group defense".
A group can defend against ordering in two ways, by not ordering or by counteracting ordering with a more powerful opposing ordering.
To not be ordered, the passenger population should be instructed as a whole not to respond to hijackers' ordering requests. The judgement of which orders can be followed and which cannot should probably not be left open to individuals; that would allow the hijacker to begin to order some passengers, immediately making it more difficult for the remaining group to prevent further ordering. Leaving the judgement to group consensus is probably even worse: it is very difficult for any group to quickly organize a common response to an ordering request, let alone if one of the ordering requests is not to communicate within the group.
If the group did not succeed in preventing the ordering of itself, the group will be in a difficult position because of the amplified power of the hijackers. The group then has to try to counteract the ordering by either removing the ordering or imposing an opposing ordering.
Finally, here are some ideas for what possible group defenses would be.
Once a plane is hijacked, the cabin could be fed prerecorded messages pertinent to hijackings. Such messages could help preventing the hijackers from ordering the passenger group. These messages could also start to introduce a counter-ordering of the group by publicly or privately identifying, for example, which rows of passengers should take what kind of action. With a little more technical preparations the cabin audio visual equipment could be taken over irrevocably by ground control, giving them equal access to the passengers. Planes could also be outfitted with individual feedback systems making it possible for ground controls to instruct and get feedback from the plane passenger by passenger. This could also be used to instruct both ground control and the passengers about the particular hijacking. The passengers succeeded in counter-ordering (rebelling) in one of the planes of September 11 because they found out via their cell phones that the hijackers were planning for all of them to die.
We should also find out which of the particular architecture and furnishings of an airplane are useful to the hijackers taking control over the passengers and then change them. For example, the more private each seat is, the harder it is for the hijackers to enforce their ordering of the passengers. The less public space there is, the harder it is for the hijackers to communicate with the passengers and with themselves. Hijackers seem to prefer to move all the passengers to the back of the plane, creating a buffer between them and the passengers. This buffer should be used by the plane manufacturers as well to aid the counter-ordering of the passengers under such circumstances.
Eugen Tarnow is a management consultant with a degree in physics (Ph.D. M.I.T., 1989). He has published some twenty-six articles in physics and organizational behavior. His interests include groupware as a tools for communication and efficiency and the performance of cockpit crews. He is the Director of Consulting with Avalon Business Systems, Inc. He can be reached at 718 884-1819 (phone & fax); www.avabiz.com , email: email@example.com .