The Mathematics of Social Ethics: Reflexive Theory and 'The Torturer's Dilemma'

I recently read a fascinating opinion piece by Jonathan David Farley, a mathematician working on developing mathematical models of terrorism -- San Francisco Chronicle: The torturer's dilemma: the math on fire with fire. The conclusion of the op-ed was that, if the United States adopted torture as an acceptable tactic in the war on terrorism, based on mathematical and logical criteria (as opposed to purely ethical or moral considerations), America will become the kind of strife-ridden society -- e.g., Saudi Arabia, the Soviet Union, etc. -- that the U.S. has traditionally been at odds with. Prof. Farley relies on a somewhat obscure branch of applied mathematics (or, perhaps it's better to call it mathematical psychology) called "reflexive theory" to make his points.

Applying reflexive theory to social ethics (or morality) leads to the conclusion that a society that is willing to compromise on issues of good and evil is a society where "individuals would often seek the path of confrontation with each other." This conclusion is somewhat counterintuitive because many people tend to assume that the willingness to compromise on principle is an almost necessary condition to cooperation, and the lack of compromise is what leads to conflict.

Unfortunately -- in an otherwise excellent article -- Prof. Farely doesn't directly address the last point. Let me try to explain how reflexive theory could work in spite of the objection just raised by using an example Prof. Farley uses in his piece. Prof. Farley uses the example of two roads to illustrate the conclusions of reflexive theory. In the first road, drivers are more highly esteemed by society if they are willing to yield to other drivers on the road. On the second road, drivers "lose face when they yield." Not surprisingly, Prof. Farley argues that it "is clear that traffic will move faster on the first road than on the second."

On the surface, the example of the two roads may seem more consistent with the intuitive objection to reflexive theory rather than bolstering the theory. However, deeper thought reveals that the two roads example is consistent with reflexive theory. In the case of the first road, the drivers are holding fast to the principle that courtesy and politeness on the road is a societal 'good' that should not be compromised. This unwillingness to compromise on a moral/ethical principle (paradoxically to those with more cynical intuitions) leads to the emergence of cooperative behavior. In the case of the second road, the willingness to compromise on a moral/ethical principle for self-serving purposes leads to conflict and, thus, gridlock.

All of this leads to Prof. Farley's stark conclusion -- again, based on mathematical logic:

What does this mean? If Americans begin to accept the use of torture, American society might turn into a society of individuals in conflict.

....

It can be argued that repressive states like Saudi Arabia, which bred most of the Sept. 11 hijackers, are on the second road. If the United States moved to accept torture, it could veer toward the second road, too -- the road of the Soviet Union.

And we know where that road ends. The Soviet Union no longer exists.

In other words, America would be heading down a dark and perilous road -- both morally and mathematically -- if the U.S. accepts torture as a legitimate tactic in the war on terror.

By the way, reflexive theory was developed by Vladimir Lefebvre, a mathematical psychologist formerly of the Soviet Union but now at University of California, Irvine. One of the advantages that reflexive theory has over its better known alternative, game theory (at least the traditional approaches to game theory), is that reflexive theory, from its inception, attempted to take into account behavioral and moral considerations into its calculus. Traditional approaches to game theory (unmodified by behavioral economics) made little or no attempt to take those important considerations into account.