It may at first seem rather strange to see this provocatively titled book included for review in a mathematics-oriented column like this one. Certainly, the efficacy and morality of torture have for years (especially since the tragic events of September 11, 2001) been the subject of heated discussion at all levels of American society, from barrooms to political debates to academic conferences and university lecture halls. But these conversations are not usually *mathematical* in nature.

The interesting idea motivating this book is to try and use the mathematical discipline of game theory to determine whether torture really does work. (The author concludes that it does not.) No prior knowledge of game theory or any kind of advanced mathematics is assumed, and although some technical details are included in the book, the difficult ones are tucked away in several easily-omitted appendices, so as not to frighten off the lay reader. The author makes very clear that it is not his intent to make any original contribution to the subject of game theory. “My goal is to say something about interrogational torture, and game theory is just a tool to that end.”

Of course, there will be some people who are offended by the very idea of reducing an issue like torture to mathematical analysis, particularly when the mathematics that is being used has the word “game” in it. These people will argue that torture is morally wrong and illegal, and therefore should not be used, whether it works or not, and that it is offensive to refer to torture as a “game”. On the other extreme, there are those who are perfectly willing to torture even if it turns out to be not useful. The author acknowledges both sides, but points out that there is a “third group of Americans for whom torture is justified only because, and insofar as, it is effective, and who would oppose it otherwise….”. These people (the author calls them Pragmatists) may, according to Schiemann, “be open to reasoned and logical arguments evaluating the supposed effectiveness of interrogational torture.” Hence, this book.

The use of mathematics to say something about issues like this is not without some precedent in the current literature. The second half of Suzuki’s book *Constitutional Calculus*, for example, attempts to use mathematics to address issues arising under the Bill of Rights. (The first half discusses issues like voting theory and apportionment.) Suzuki (who, unlike Schiemann, is a mathematician) does not discuss torture but does address other hot-button political issues such as detention, “three strikes” laws, the death penalty, jury composition, etc.

One of the problems I had with the second half of Suzuki’s book concerned the assumptions that he made in his mathematical discussions. We all know, of course, that mathematical conclusions depend on the assumptions on which they are based, and that the actual choice of assumptions, at least in this context, is not necessarily a mathematical endeavor. The choice of assumptions, therefore, can be outcome-determinative, and this may present a problem in books that attempt to use mathematics as a way of establishing the correctness of some political conclusion.

Reading Suzuki, I often had the impression that his assumptions favored a certain outcome. At one point, for example, Suzuki engages in a cost-benefit analysis to analyze the efficacy of racial profiling as a means of stopping future terrorist attacks. In considering the “costs” of such an attack, however, he explicitly refuses to consider intangible costs such as the emotional distress caused by such an attack; specifically, he considers “the costs paid by federal, state and local governments, but no personal losses incurred by those affected.” So, the cost to the government of “cleaning up the debris” (his phrase) is a legitimate item of cost, but the emotional distress suffered by a person who has lost a spouse or child is not. This seems absurd to me: terrorists don’t attack because they want to create big clean-up bills, they attack precisely *because* they want to create fear and emotional distress — the very form of “cost” that Suzuki refuses to consider in his analysis. Refusing to consider these kinds of costs also diminishes the cost of a terrorist attack and makes it more likely that a cost-benefit analysis of detention will reach the conclusion that such sweeping detention is not justified.

Schiemann’s text is, I think, superior to Suzuki’s, in that I did not get the impression, reading Schiemann’s book, of an author making these kinds of unreasonable and arguably slanted assumptions. Nevertheless, I am not wholly convinced by the mathematical arguments and conclusions reached herein. This is not to say that I think the conclusions reached by Schiemann are in fact incorrect; I merely think that they do not follow inexorably from mathematics. In fact, I have some doubt that issues like the one tackled by Schiemann are really suited to mathematical analysis in the first place. Before explaining why, I’ll quickly summarize the contents of the book.

Schiemann begins with what he calls the Bush Interrogation Torture (BIT) model, a simple model consisting of two players, the Detainee and the Interrogator, each with two strategies: the Detainee’s strategies are “Talk” or “Don’t Talk” and the Interrogator’s are “Torture” or “Don’t Torture”. Over the course of two chapters, this model is defined and analyzed, and certain defects in the model are observed: the equilibria “solutions” seem odd and at variance with real life.

This is quickly followed by a discussion of a more sophisticated model, which Schiemann calls the Realistic Interrogational Torture (RIT) game. The RIT model allows for several different types of players (for example, the interrogator can be pragmatic or sadistic) and also takes into account the fact that neither player knows for sure what type of person the other player is. Much of the rest of the book is devoted to the development of this game and the analysis of its equilibria. The conclusions reached, as noted earlier, are that torture does not work: it produces false information or no information at all.

Although I do feel that Schiemann took pains to try and avoid “cooking the books”, I am, as noted above, not convinced that game theory is particularly well suited to situations like this. Game theory, with its emphasis on analysis of strategic decisions, necessarily presupposes free and voluntary choice on the part of the players, and it is awfully hard to say that a certain strategic choice is voluntary if it is induced by torture. The issue of whether there is really rational choice in this context is a controversial one; see, for example, the article “Torture is Not a Game: On the Limitations and Dangers of Rational Choice Methods” by Dustin Howes, appearing on pages 20-27 of Volume 65 (2012) of *Political Research Quarterly*. (This article predates the book, but is subsequent to, and in response to, a previous article by Schiemann on this issue.)

Schiemann, to his credit, acknowledges and addresses this concern. He relies on the fact that some people have refused to divulge information even under torture, and concludes from this and first-person accounts of torture victims that people being tortured for information do exercise some choice. “Many victims, by their own accounts, think of themselves as having at least two actions, confessing or not confessing, providing information or not…. Finally, both sides understand, even if imperfectly and under uncertainty, how their actions lead to outcomes.” Thus, the author views the decision to be tortured as a form of “cost” in a cost/benefit analysis.

I remain skeptical, however — and so do the courts in the American judicial system. In *Ashcroft v. Tennessee*, for example, the United States Supreme Court considered a situation where a person confessed to a crime five days of prolonged interrogation, including a 36 hour period during which the suspect was not allowed sleep or rest. There was not even any suggestion in that case of the kind of physical abuse that is commonly associated with the word “torture”, yet the Supreme Court found the confession to be “not voluntary, but compelled.” As the Court said, “We think a situation such as that here shown by uncontradicted evidence is so inherently coercive that its very existence is irreconcilable with the possession of mental freedom….” The point is that undergoing torture is *not* just strategic choice with outcomes of its own. Even if a person literally has a “choice” to make, that choice is, by virtue of the torture, made so unpleasant that it is not in any realistic sense a voluntary one.

I see another potential problem with the use of game theory in situations like this. There is definitely a certain allure in attempting to justify a particular point of view not by reference to opinion and moral values but instead by appeal to the cold logic of mathematics. This gives the result a certain indicia of reliability that an opinion-based conclusion may not have. But at the same time there are, it seems to me, certain issues, particularly issues that are at the forefront of public policy, that *cannot* be divorced from things like individual value systems. We live on planet Earth, not Vulcan; logic can only take us so far. As noted earlier, there are many very logical people, including, I am sure, lots of professional mathematicians, who take the view that, regardless of its efficacy, the government should not torture people because torture is contrary to the values of this country. This point of view strikes me as entirely reasonable, and I certainly do not wish to be seen as disparaging it, but the point is that at some point the analysis inevitably diverges from mathematics.

Indeed, Schiemann himself eventually appears to fall back on a values-driven point of view. Chapter 13 of the text begins with a summary of what has come before; after stating that torture does not work, Schiemann goes on to say:

Does saying it does not work mean it can never work? No. It can work. Under conditions that hardly ever obtain in the real world, it can work (but only if we’re willing to torture innocent detainees).

And a little later in this chapter, Schiemann makes even more explicit his reliance on ingrained values:

Some will say we must torture even if there is a small chance that it will work. No. There are some things we cannot do because they run too much against the grain of our character. As Senator John McCain said on the floor of the Senate, the CIA torture program “stained our national honor.”

This point of view is entirely reasonable, but it is important to realize that the ultimate conclusions reached here are based to some extent on considerations other than mathematics.

These concerns notwithstanding, I think this is a useful and thought-provoking book. The idea of using game theory to analyze this problem is creative, and the resulting analysis, even if problematic (the author, of course, does not claim to be proving any theorems here; game theory is used as a tool, and mathematical models frequently are simplified versions of real life) is interesting. Moreover, the game-theoretic analysis, while not airtight, at least can be viewed as clarifying what assumptions are necessary to ensure that torture, at least as an institutional practice, can be made to work.

The book is also skillfully written. The author takes pains to make the development of material accessible; each chapter, for example, ends with a recap of what has been done to date, and explains what is coming next. The mathematics that appears in the book is slowly and clearly explained. It should be largely comprehensible to a lay audience.

From the standpoint of a professional mathematics educator, I can see this book being used productively as the springboard for an interesting discussion on the use (and limitations) of game theory. From the standpoint of a citizen, I see this book as raising questions and offering ideas that merit intelligent discussion.

Mark Hunacek (mhunacek@iastate.edu) teaches mathematics at Iowa State University.