5

A Realistic Model of Interrogational Torture

I regard it in fact as the great advantage of the mathematical technique that it allows us to describe, by means of algebraic equations, the general character of a pattern even where we are ignorant of the numerical values which will determine its particular manifestation.

—FRIEDRICH VON HAYEK

Part of the purpose of Chapter 3 was to identify the constraints and limits on torture in the Bush program so as to avoid creating an easily criticized strawman model of interrogational torture. The BIT model in Chapter 4 hewed closely to the Bush ideal, but instead ended up producing an overly idealized, quixotic model distant from reality both in the way torture worked and in the outcomes it generated. Thus, building a realistic, but still fair, model requires navigating carefully between two types of caricature, between the Scylla of a strawman and the Charybdis of the quixotic.

As if this were not difficult enough, there is another set of extremes to avoid: analytical oversimplicity and realistic overcomplexity. The game theoretic model of interrogational torture must simplify—all models must do so—but it should not ignore essential features of the real world. That is, we must cut away some (well, a lot actually) of the extraneous detail in order to get at the fundamental dynamic that drives outcomes, but keep those details, those features of the real world of interrogational torture that are the factors actually doing the driving. Not just fenders, hubcaps, AC, and side view mirrors, but even doors, roof, and trunk must go. But the engine, wheels, transmission, steering column, and other necessary features must stay.

Some of these necessary features were missing from the idealized BIT models in the previous chapter, and to locate them we return to the basic elements of the BIT models: players, actions, information, and payoffs.

PLAYERS AND ACTIONS

The BIT game rightly portrayed the essence of interrogational torture as a game between a Detainee and an Interrogator. It got the number of players right. What it failed to capture, however, was the nature, or type, of each player. We saw that it made a big difference in terms of the interpretive link to the real world as well as the outcome of the game whether the Detainee was Cooperative, and so preferred to give up information to avoid torture, or was Resistant, and preferred to suffer torture rather than give up information. Although both the Cooperative and Resistant types exist in reality, and the interrogator never knows for sure which type she faces in an interrogation room, the BIT models forced us to choose one or the other. Once we chose, then all Detainees were of that type for sure, and that is what generated the bizarre outcomes. Neither the setup (knowing for sure a Detainee’s type) nor the outcome (information and no torture in the first model) corresponded to the real world—even according to torture proponents.

Recall from the end of the last chapter that we should consider the same possibility for the Interrogator. Might the Detainee be similarly uncertain about the nature of the interrogator across from him? Imagine that you have valuable information, have been captured, and are being threatened with torture. Among the many horrible things running through your mind might be a doubt whether you’ll be tortured even if you do provide information.

A scene from another classic Western, The Good, the Bad, and the Ugly, brilliantly illustrates this idea as well as the strategic effects when both players know this. If you are not familiar with the film, the character Angel Eyes has just had another character, Tuco, tortured for the location of some gold. Tuco provides the name of the cemetery but not the grave in which it is buried, since he doesn’t know. He tells Angel Eyes, however, that Blondie knows the grave. After sending Tuco away, Angel Eyes has Blondie brought in and the following exchange ensues:

BLONDIE: (after scuffing his boot on the floor stained with Tuco’s blood) “You’re not going to give me the same treatment?”

ANGEL EYES: “Would you talk?”

BLONDIE: “No, probably not.”

ANGEL EYES: “That’s what I thought. Not that you are any tougher than Tuco … but you’re smart enough to know that talking won’t save you.”

Angel Eyes is not a nice man (he’s the “Bad” in the movie’s title) and will execute and perhaps torture Blondie once Angel Eyes has the location of the grave. Blondie knows this and so does not talk.

In other words, is the Interrogator simply Pragmatic, and willing to torture only as a last resort to extract information from a noncooperative and knowledgeable Detainee? Or is the interrogator Sadistic, an Interrogator who tortures even after information has been obtained?¹ It is necessary to assume the (possible) existence of a Sadistic Interrogator in our real-life model not because it conforms to the pragmatic, normative model but because it (sometimes) conforms to reality.

More importantly, the Detainee will naturally be uncertain about whether an interrogator will refrain from torturing even if full information is provided. Interrogators who are nonsadistic in the psychological sense may also torture due to an organizational culture in which interrogators feel a need to prove their dedication by a willingness to “do what it takes” or by an incentive structure that rewards interrogators for the quantity rather than the quality of the information provided (or both).² It is simply not plausible to assume that a detainee would have no doubt that if he were to reveal information, even all of it, he would not be tortured anyway. This uncertainty will influence the behavior of the Detainee, so, in order to examine the effects of interrogational torture by a Pragmatic Interrogator, this perception must be taken into account, even if we are ultimately only interested in the behavior of a Pragmatic Interrogator, who only tortures as a last resort.

Together then, we have uncertainty about both player types. Each player will know his or her own type, of course, but neither will be certain of his or her opponents’ type, just as you wouldn’t be if you were an interrogator or a detainee. The Interrogator is uncertain whether the Detainee is knowledgeable and Cooperative, is knowledgeable and Resistant, or possesses no information (Innocent). The Detainee will be uncertain about whether the Interrogator is Pragmatic or Sadistic.

Game theory takes these uncertainties into account by adding a third player to the game, Nature, as in Figure 5.1.³ Just as Mother Nature “decides” on whether or not it will rain, so Game Theory Nature decides on whether the Detainee will be one of the three types and the Interrogator will be one of the two types. And just as we assign probabilities to Mother Nature’s choices, we will assign probabilities to Game Theory Nature’s moves.

Figure 5.1 Moves by Nature

Nature thus has three choices at her first move, with each selecting one of the Detainee types along one of three branches. In the top branch the Detainee is the Cooperative type, in the middle branch the Detainee is the Resistant type, and in the bottom branch the Detainee is the Innocent type. Similarly, to capture the Detainee’s uncertainty about which type of Interrogator sits across from him, Nature moves again, selecting the Interrogator’s type as either Pragmatic or Sadistic. Figure 5.1 captures these two moves.

Note three features about Figure 5.1. First, because all succeeding moves from Nature’s choice of the Resistant Detainee are identical to the Cooperative Detainee branch of the tree, in order to save space Figure 5.1 represents them with the single line from the Resistant Detainee continuing as a dashed line.

Second, notice the letters p and q along the paths of Nature’s moves. These are the probabilities that the Detainee is of that particular type. Neither we nor the players would know these probabilities, so there are no numbers attached; we let them take on any value between zero and one by labeling them with letters. (The convention in game theory is to use p and q for probabilities, but you could choose any letter or symbol you wanted.) Since probabilities always add up to one, if the probability that the Interrogator is the Pragmatic type is q, then the probability that she is of the only other possible type, Sadistic, must be 1 − q. Since there are three types of Detainees, we distinguish them by their subscripts, the little letters attached to the p, with p_C corresponding to the Cooperative Detainee type, p_R to the Resistant Detainee type, and p_I to the Innocent Detainee type. Of course p_C, p_R, and p_I together add up to one.

Finally, Nature moves prior to the two “main” players, the Detainee and the Interrogator, after which the Detainee and the Interrogator move. So you can think of the BIT game from the last chapter starting at the end of each of the lines on the right side of Figure 5.1. Figure 5.2 captures this by expanding the drawing in Figure 5.1 with the BIT games at the end of each combination of Nature’s moves.

Figure 5.2 Representing Uncertainty

Pause here for a moment. The game tree may look more complicated than it actually is. Remember that since each player is uncertain of the other, we have six possible combinations: two Interrogator types for each of three Detainee types. Each branch, or path, through the tree represents one of these combinations. The topmost path, for example, represents the case when a Cooperative Detainee faces a Pragmatic Interrogator.

The basic set of moves between the “main” players from this point forward, however, is the same as in the BIT model. (In order to keep the figure as neat as possible, the “no” in “no information” and “no torture” is represented with the symbol ~.) Since neither player will know for sure which branch of the tree he or she is on when he or she moves, we need to put the moves of the BIT game at every combination. Imagine, for example, that you are a Pragmatic Interrogator and you have just observed the Detainee’s move of “no information.”

Is this because the Detainee is Cooperative, but thinks you will not torture, perhaps because he thinks you think he is Innocent? Is it because the Detainee is Resistant and never reveals information, whether or not you torture? Or is it because the Detainee is Innocent and cannot even answer your questions?

In other words, the Interrogator will not know in which branch of the tree she sits as she prepares to make her choice. Because, however, the Detainee’s moves are identical—in this particular case, “no information”—and her own moves are identical, the game looks exactly the same in each of these three branches. Both facts—the uncertainty and the sameness of the choice—are represented by the dashed vertical lines connecting the Pragmatic Interrogator’s decision node after the Detainee has chosen “no information.” (Remember that while there are three nodes, one for each type of Detainee, only two are shown, one for the Cooperative Detainee and one for the Innocent Detainee, to keep the figure manageable.)

Similarly, a Cooperative Detainee, for example, will wonder whether he is in the upper branch playing against a Pragmatic Interrogator or the lower branch playing against a Sadistic Interrogator. This uncertainty is also represented in Figure 5.2 with dashed lines connecting the points where he must make his choice and is unsure which type of Interrogator he faces. Figure 5.2 shows just these two dashed lines as examples; the full game will have one for each combination, six altogether.⁴

After these moves by Nature setting up different possible states of the world (for example, a Resistant Detainee facing a Pragmatic Interrogator), the game proceeds just like the BIT model. The Detainee chooses to either reveal information (“Information”) or not reveal information (“~Information”). Following the Detainee’s choice, the Interrogator either tortures or does not torture. Keep in mind that at the point the Detainee and the Interrogator make their moves, neither knows which state of the world, which branch of the tree, he or she is making that choice from, captured by the dashed lines connecting their decision points (nodes).

QUESTIONING TYPE

One important aspect of interrogations in the real world that the BIT model did not consider was the nature of the questions asked by the Interrogator, namely whether they were leading or objective. Under objective questioning, the Interrogator does not tell the Detainee what she wants to hear. Under leading questioning, the Interrogator does let the Detainee know what would please her. While leading questioning clearly provides no new information, it is clear from the history of torture that it inevitably emerges when Interrogators torture.

We saw this in the case of John Clarke, who confessed in the Dutch Amboyna case only when his Interrogators fed him the particulars (East India Company 1665, pp. 10–12)). It is for precisely this reason that medieval European civil and Inquisitorial torture had rules prohibiting asking leading questions during torture sessions, though these were likely more honored in the breach than in the observance (Peters 1999, p. 68; Lea and Peters 1973, p. 111; also Langbein 1978, p. 7).⁵ Indeed, even the CIA’s own 1983 Kubark manual noted the “pitfalls produced by asking questions that suggest their own answers” in the annotated bibliography at the end of the document (Central Intelligence Agency 1983, p. 110). Nevertheless, the CIA’s and later the military’s reliance on SERE methods originally used by the KGB to extract forced (and false) confessions makes it even more likely that such questioning was used (Mayer 2008, pp. 158, 164).

There are thus two versions of the model: objective and leading questioning. Although the leading questioning variant does not provide new information, but instead can only confirm what the interrogator wants to hear, to the extent it is employed, it needs to be examined to identify what can happen when interrogators employ both torture and leading questioning. The goal is to model what happens in an interrogation room in which torture is permitted; and since leading questioning happens frequently, it must be modeled.

In the leading questioning version, then, each of the three types of Detainee can choose either “information” or “~information” (staying silent or providing information which is not valuable). Under objective questioning, when the Interrogator does not reveal what she wants to hear, the Innocent Detainee has only one move, “~information.” (Thus, the moves in the bottom half of Figure 5.2 portray the leading questioning version of the game, when the Innocent Detainee has the “information” option as well as “~information.”)

INFORMATION UNCERTAINTY

Before turning to how the players evaluate the outcomes of their choices (payoffs), it is first important to note two significant features of the move “information” by the Detainee in the model. The first is uncertainty about whether the Detainee has revealed all he knows. The second is the clarity of the information’s value to the Interrogator.

Information Hiding

At some point an interrogator must decide whether or not the detainee is still withholding information, whether the detainee had up to that point revealed a little or a lot. In addition to the information already provided, this decision will also be based on factors external to the detainee’s behavior, such as his or her hypothesized role in the organization or what other detainees have said about him.

In other words, under both objective and leading questioning, the Interrogator may believe that a Cooperative Detainee who chooses “information” may actually have more information, that the Detainee is still hiding something. If so, then the Interrogator would want to torture to compel full disclosure. This uncertainty is captured by the “information completeness” parameter f, which is just a number between zero and one, the probability that the Detainee has revealed all he knows. In other words, it’s the probability of full information disclosure. Multiplied by the payoffs, it weights the outcome to take into account the fact that getting that payoff is uncertain. Everything else being equal, an uncertain payoff is less valuable than the identical payoff for certain because there is a chance we may not get it.

Here is a very simple example of how it works. Suppose you come to my casino and I offer you the chance to play a very simple game. I flip a fair coin. If it lands on heads, you win $10; if it lands on tails, you win $1. How much would you pay to play my game?

If you are perfectly risk neutral, not more than $5.50.⁶

Here’s why.

You have to discount the value of each outcome by the likelihood that it actually occurs. Since my coin is fair, the chances of getting heads and thus $10 on any particular toss is 50% or .5. So you discount the $10 by the .5—that is, you multiply them together and you get $5. You also have a .5 chance of getting tails, netting $1, so you need to discount the value of that outcome in exactly the same way, by multiplying them, for $.50. Now you put both outcomes back together, by adding these products, and you have $5.50. This is the weighted average of the two outcomes.⁷

In other words, the expected value of this bet is $5.50. This is what you can expect to get in the long run, on average, if you played this game over and over again. Sometimes you’d win $10, sometimes you’d win $1, and over a long haul, you could expect to net $5.50.

Let’s apply the same reasoning to our game.

To keep the arithmetic simple, let’s say the maximum value of information the Detainee might have is 100. If the Interrogator believes he has provided all of it, she gets 100. But if he has not provided all of it, she gets something less. It might be only a little less, so that she gets 90. Or it might be a lot less, so she gets just 10. (Of course it might be any number less than 100; these are just easy examples.)

Now these amounts, these information values, are independent of the likelihood that he has provided everything, just as the coin toss was independent of the dollar amounts won for heads and tails. I could have raised the stakes to $20 for heads and $2 for tails, but that would not change the probabilities of getting heads or tails. A Detainee with valuable information may have provided a lot or only a little of the information he possesses. The same goes for a Detainee who possesses only a little valuable information.

Consider the two extreme cases when the Interrogator is absolutely certain. In the first case she is certain that the Detainee has provided all the information he has. In the second case she is just as certain that he did not, and is still hiding valuable information.

In case one, the Interrogator is convinced that this information is all the information he has. The Detainee has provided the maximum of 100. She is 100% certain that this is the maximum, so f = 1. Since one times whatever value the information given is the same as that value, in this case she gets 100. And since the probability that the Detainee has provided full information is 1, the probability that he is witholding anything is zero (i.e., 1 − f = 0). Zero times anything is zero, so the value of this possible outcome, whether it is 90 or 10, is zero. Adding them together, just as we did for the coin toss example, provides a payoff of 100. (Obviously in this case the Pragmatic Interrogator has received everything she wanted and so does not want to torture.)

Now suppose that she is absolutely certain the other way: that the Detainee is hiding information. There is some amount of information which he has not divulged, so she ends up with 90 or 10. She’s not on the fence about whether he is hiding information; she is 100% sure that he’s holding something back, worth, say, 10 or 90. If f is the probability of proving full information, then being positive that he is holding back means f = 0. Zero times anything is zero, so weighting the value of the full information outcome paying 100 makes it 0. Since the probability of full information disclosure is zero, then the probability of getting only partial information is 1 (it’s certain). This means multiplying 1 times whatever the value of the partial information is, which in our running example is 90 or 10. Obviously adding them together is just the same as this outcome, 90 or 10. The expected payoff, then, is 90 or 10, and the Interrogator would want to compare that value to what she would get if she decided to torture in order to see which is better for her.

We’ll return to those payoffs in a moment. For now, imagine an intermediate (and more realistic) case. The Interrogator is just not sure. She suspects that the Detainee is hiding information, but she is not certain. Maybe she thinks that it could go either way; it’s 50–50, reminiscent of the coin toss example. Of course, it could be 80–20, 25–75, or something else, but let’s stick with 50–50.

Applying the same weighting procedure as before, this time with f = .5, we multiply .5 times the value of getting full information (100), which gives us 50, and .5 times the value of getting partial information (since 1 − .5 = .5). If the value of partial information is 90, then this product is 45; if the partial information is worth 10 to the Interrogator, then this product is 5. So the expected value this time is (assuming partial information = 90) or (assuming that partial information is worth 10).

In short, the value of the move “information” to the Interrogator will be determined not just by the intrinsic value of the information actually provided but by the probability that the information provided was the maximum there is. At some point, f will be low enough that she will prefer to torture rather than be satisfied with a partial disclosure.

Note, though, that in the model, the decision to torture after a Detainee has revealed that information can be interpreted in two ways in terms of what it represents in the real world. On the one hand, it can be interpreted as the case in which a Detainee really is hiding more information and gets tortured. This would be “justifiable” torture on the pragmatic view. On the other hand, it can also be interpreted as the case in which the Detainee has revealed everything he knows but is tortured anyway because the Interrogator does not believe him. This would be unjustified torture, again, even for proponents. This outcome in the game, in other words, will be just as opaque and open to interpretation in the model as in the real world. This setup captures the fundamental problem of interrogation: The Interrogator can never be sure of what the Detainee actually knows. If he provides information, is it all of it or only a portion? If he fails to provide information or provides misleading information, is it because he is attempting to hide it or because he really does not have it? Of course, the Detainee is well aware of this fundamental uncertainty on the part of the Interrogator so f is common knowledge.

Information Clarity

The second feature of the move “information” by the Detainee is the clarity of the information provided. Under leading questioning, of course, this is irrelevant, since the Interrogator knows exactly what she wants to hear. Under objective questioning, however, the Interrogator may not always recognize “information” as valuable even when it is given. In fact, the less the Interrogator knows about the Detainee, the more this is likely to happen. In short, the Interrogator may recognize it as useful information, but might also perceive it as false or otherwise not valuable information. Thus, the “information clarity” parameter u represents the Interrogator’s uncertainty about whether the Interrogator understands that the information is valuable. Since u weights the Interrogator’s payoffs in exactly the same way as f, we need not go through that again.

There is a difference from f though, insofar as the Detainee will be unaware that the Interrogator has this uncertainty. A Detainee choosing “information” assumes that it will be recognized as valuable and plays accordingly. In game theoretic terms, u is the private information of the Interrogator; the Detainee is not aware of u.

This is an unorthodox assumption in game theory. I adopt it in this more realistic model because this happens in the real world of interrogation. While it seems likely that a Detainee will know that the Interrogator will suspect him of hiding information (i.e., that f exists) and that he cannot prove what he does not know, he is likely to believe that the Interrogator will recognize valuable information if he in facts provides it to her. Either it will be immediately seen as valuable or it can be verified later.

Indeed, there is no point to torture or to conduct any other form of interrogation unless the interrogator can recognize at least some information as valuable. What is an unorthodox assumption from the perspective of game theory is a natural and necessary assumption from the perspective of the real world of interrogation. In principle, both types of information uncertainty could be applied to the Sadistic Interrogator as well, but since (as we will see shortly) the Sadistic Interrogator tortures no matter what move the Detainee makes, this is irrelevant.

PAYOFFS

In the Prisoners’ Dilemma in Chapter 1, in the BIT models of the last chapter, and in the expected payoff examples above, the payoffs to the players were actual numbers: years in jail (the first example), numbers representing the preferred order of the outcomes to the players, with 4 better than 3, 3 better than 2 and so forth (the BIT models), or numbers representing cardinal (as opposed to ordinal) values. Cardinal values such as the 100 for complete information and the 10 for partial information show not just the ranking of the outcomes (one over the other), but how much one is preferred over the other, the intensity of that preference.

But what goes into arriving at this ordering or these values? Rather than just a number showing the relative preference for this outcome compared to the other possible outcomes, it would be nice to show what it is about this outcome that makes it more or less attractive. We can do this by substituting these numbers with (combinations of) variables (i.e., letters) which can take on a range of values and which are more closely tied to the actions leading to the outcomes. This is the x and y from high school algebra.

Detainee Payoffs

Take, for example, the outcome when a Detainee has provided intelligence information and has not been tortured afterward. Two things have happened to the Detainee. First, he has provided information. Since this is a knowledgeable Detainee, this is not good for him, a loss of some sort. We can represent this intuitively by representing this value as the quantity v, the value of the information he divulged. Giving it up means losing it, or . Second, the Detainee has not been tortured, and this means no additional loss. So in total, the Detainee gets in this outcome. We’ll apply this same idea of representing costs with negative signs to the other variables as well.

Now consider the outcome in which a Detainee has refused to provide information and has been tortured afterward. In this case, the Detainee keeps the information, so there is no , but he suffers torture. We can represent (not reduce!) this loss with (we need the symbols “t” and “c” elsewhere, so we’ll use “k” for the phonetic mnemonic kost of torture to the Detainee). So in total, the detainee gets in this outcome.

How about the other two possibilities? If the Detainee provides no information but is not tortured, then he suffers no losses at all and receives a payoff of zero. If he provides information and gets tortured afterward anyway, then he pays both “costs,” for a payoff of . Now go back to the Cooperative vs. the Resistant Detainee types in the previous chapter. This variables approach to payoffs gives us a neat and clear way to distinguish the two.

The Cooperative and Resistant Detainees are identical insofar as they most prefer not to reveal information and not get tortured, ending up with the best they can do, 0. They also both least prefer to reveal information and still get tortured anyway, which results in the worst payoff of . Where they differ and, indeed, what distinguishes them is the value of information relative to the costs of being tortured.

Both have information v they do not want to give up. But whereas the Cooperative type of Detainee prefers to give up information rather than be tortured, the Resistant Detainee is willing to suffer torture rather than give up information. As discussed in Chapter 4, Jeremiah Denton’s torture at the hands of the North Vietnamese provides a clear example of this.

The costs and are the same, but the difference between the two Detainee types is captured nicely by the way they order these payoffs. For the Cooperative Detainee we have , so that is a better payoff than, is preferred to, . For the Resistant Detainee , so that suffering the costs of torture is preferred to the costs of giving up information.⁸ If , then . Similarly, if , then .⁹

This makes sense; for the Cooperative Detainee, the value of the information is less than the pain of torture, whereas for the Resistant Detainee, the information is more valuable than magnitude of the torture. Thus, the full preference ordering for the Cooperative Detainee is , while for the Resistant Detainee it is . These orderings follow the numbers in the BIT models in the last chapter and capture neatly and compactly the differences between the two Detainee types.

What about the payoffs to the Innocent type of Detainee who has no v to give up? While it is theoretically possible for the Innocent Detainee to behave either like the Cooperative or the Resistant Detainee, depending on his aversion to lying and falsely confessing, we will assume that the Innocent Detainee mirrors the preference ordering of the Cooperative Detainee. Whereas the Innocent Detainee would prefer not to lie, to falsely confirm something he knows nothing about, he is willing to do so if the alternative is telling the truth (i.e., “no information” because he has none) and getting tortured. In other words, replacing the v of the Cooperative and Resistant Detainees with l for lying, the preference ordering is exactly the same: , for a full ordering of .

Variables have a third advantage beyond linking payoffs to actions and permitting the easy characterization of different player types. By not tying the results of the model to a particular set of values, the results will be more general. In the expected value example above, we specified two versions of partial information, one worth 90 and one worth 10 to the Interrogator, with expected payoffs of 95 and 55 respectively. It should be clear that they might lead to radically different outcomes—for example, torture in one case but not in the other. The model could (rightly) be criticized for assuming a particular set of values, and we wouldn’t know whether the results held true for a different set of values. Using variables makes the model more flexible, helping us understand, as Hayek says in the epigraph, “the general character of a pattern even where we are ignorant of the numerical values which will determine its particular manifestation.”¹⁰ In other words, we don’t need to know particular values of partial information, 10 or 50 or 90 or whatever, to examine the general effects of partial information. This makes the model more powerful because it provides more analytical leverage.

There is a fourth advantage. Using variables will also allow us later on to see what happens to the different equilibrium outcomes of the model as the values of different variables change. What, for example, happens to Cooperative Detainee truth telling as the value of the information goes up? What happens to outcomes in which there is no torture when the costs of torture to the Interrogator go down? By letting those values vary, rather than fixing them to particular numbers, we can (and will in Chapter 7) answer these and other similarly important questions.

Interrogator Payoffs

To assign variables to the Interrogator’s payoffs, we will use the first BIT model as our point of departure. In what follows we assume that the game is between a Cooperative Detainee and a Pragmatic Interrogator. The Interrogator seeks information from the Detainee; if he supplies it, she receives a benefit. Call this V for the value of the information. Recall that in the BIT model the Interrogator preferred not to torture if the Detainee had provided information. This was consistent with the real constraints and limits on torture we discovered in Chapter 3, in which torture is employed as a last resort.

A preference on the part of the Interrogator not to use torture if she can get the information otherwise suggests that using torture is somehow costly for the Interrogator as well. Even if she is willing to use it, torture does not come “free.” She pays a price every time she uses torture, even when she deems it necessary. Call this cost of using torture . The cost might represent psychological, reputation, morale, or other costs to Interrogators (and the government employing them).¹¹

Moreover, since the Pragmatic Interrogator uses torture only to extract information from knowledgeable Detainees, she bears an additional cost for “unnecessary” torture—that is, torture of an Innocent Detainee who does not reveal information (i.e., tells the truth) or of any Detainee who reveals full information. Adding the additional variable or parameter complicates the model a little but is necessary to be consistent with the ideal and pragmatic models of interrogational torture in Chapter 3, in which a Pragmatic Interrogator prefers to torture only when absolutely necessary and does not want to torture “unnecessarily” (again, from the proponents’ point of view). Thus, if the Interrogator receives information and does not torture afterward, she receives V; if she does torture afterward, she receives .

If the Detainee fails to provide information and the Interrogator tortures, she pays the permanent cost of torture but receives no information, leaving her with just . If she fails to torture after the Detainee has refused to provide information she “pays a price” . This captures an element central to the rationale for using torture: establishing the credibility of the threat to use torture if the Detainee does not provide valuable information. That is, it captures the idea that, once torture becomes an interrogation tactic, interrogators suffer reputation costs if Detainees fail to provide useful information but the Interrogator still does not torture. An Al Qaeda training manual captured in Afghanistan provides support for this belief. According to an Interrogator who read the manual, it viewed “America’s aversion to torture … as a symbol of American weakness” (Mackey and Miller 2004, p. 180).

Putting the cost payoffs together, then, we have . Alternatively, we have . Note that this means we are building in a strong aversion to torturing innocents by making the additional cost a larger than the reputation costs r. Given this aversion assumption favoring the proponents’ argument, it will be interesting to see whether and how often innocents are tortured in the full model. Figure 5.3 presents the BIT model with these payoffs in variable form.

Figure 5.3 Bush Interrogation Game with Variables for Payoffs

Even though this game replicates the same problems plaguing the original BIT, let’s take a closer look at it for a moment because it does provide a good and easy illustration of how to solve a game using variables for payoffs.

We solve this game just as we did before. It is clear that if the Detainee provides information (along the top branch), then the Pragmatic Interrogator will not torture because . She gets the benefits with no costs. So she does not torture.

What about the bottom branch, when the detainee has not provided any information? Her choice is to torture and receive a payoff of or not to torture and receive a payoff of . We know that torture is a last resort for the Pragmatic Interrogator, but this is precisely that time. In the post-9/11 world, the “gloves are off” and the costs of letting a suspected terrorist hide valuable information () are higher (that is to say, worse) than the costs of torture (). In other words, the Interrogator suffers losses in either case, but the losses from using torture are not as large as the losses from the reputation costs, or and the Pragmatic Interrogator will choose torture. More generally, once torture is admitted as an interrogation technique, it must be the case that using torture is preferred to not using torture for some level of non-information disclosure.

Note that these orderings are the same as in the BIT model and make sense in the same way they did in that model with numerical payoffs. The Pragmatic Interrogator prefers to get information without torture, but is willing to “do what it takes” (i.e., torture) to compel the Detainee to give up information, rather than let a suspected terrorist get away.

Finally, there are the payoffs to the Sadistic type of Interrogator. The Sadistic Interrogator receives the same value from information V as the Pragmatic Interrogator, but naturally enough considers the use of torture to be a benefit rather than a cost. Thus, there is no c or a, but instead the variable s, which represents the sadistic benefit the Sadistic Interrogator receives from torturing regardless of whether or not the detainee has provided information.

A REALISTIC INTERROGATIONAL TORTURE GAME (RIT)

We have made important and necessary changes to BIT while staying faithful to core features of the pragmatic model. We have retained the pragmatic model’s conception of torture as a last resort in the form of the Pragmatic Interrogator type who prefers not to torture if full information is provided and who suffers costs from using torture and even an additional cost from torturing innocents or those who have already provided full information. We have also assumed that there are indeed detainees who have intelligence information and are willing to give it up only under (the threat of) torture, as assumed by the Bush administration and advocates of interrogational torture more generally. Table 5.1 summarizes the variables and their symbols.

Table 5.1 KEY TO SYMBOLS FOR PAYOFFS

Element of Model	Symbol	Meaning
	v	Value of information to Cooperative and Resistant Detainees
Detainee	l	Lying cost to Innocent Detainee
	k	Torture kost to Detainee
	V	Value of information to Interrogator
	c	Cost of using torture to Interrogator
	a	Additional cost of using “unnecessary” torture to Interrogator
Interrogator	h	Value of hidden information to Interrogator
	r	Reputation losses to Interrogator for not torturing upon receiving no information
	s	Sadism benefit to the Sadistic Interrogator for using torture
	f	Probability the Detainee has provided full information
Uncertainty	u	Probability the Interrogator understands information is valuable

Other changes we have made add the realism necessary for us to know that we are dealing with windmills and not giants. In the first set of changes, we added the very real uncertainty that interrogators will have about how much the detainee knows and indeed whether he knows anything at all. We also added detainee uncertainty about whether the interrogator is sadistic and will torture him no matter how much information he gives up. We include this possibility not because we think CIA interrogators actually were sadistic—indeed we’ll assume they were pragmatic in what follows—but because it is very likely that detainees might worry they were sadistic. Any person subjected to torture in interrogations would wonder about this. In the second set of changes, we added the uncertainty that real-life interrogators actually have about the value of information and how much had been disclosed. Thirdly, we replaced numerical payoffs with the more general variable payoffs linked more intuitively to the actual actions the players take. Finally, distinguishing between objective and leading questioning results in two versions of the model.

Putting all this together generates the Realistic Interrogational Torture (RIT) game in Figure 5.4. Admittedly, it looks a bit messy and complicated, but it is really only the accumulation of all the individual changes we have made. Before we walk through the game, it is important to note that Figure 5.4 actually presents an amalgam of two versions of the game, with the payoffs for objective questioning in the upper branch (Cooperative Detainee) and the moves for the leading question variant of the model in the lower branch (Innocent Detainee).

Figure 5.4 Realistic Interrogational Torture Game (RIT)

In the objective questioning version, the Innocent Detainee does not have the move “information” as he does in the Figure 5.4. In the leading questioning version of the game, when the Interrogator tells the Detainee exactly what she wants to hear, uncertainty about the value of the information (u) makes no sense and would disappear from the payoffs to the Interrogator. The branches for the Resistant Detainee type are again omitted to keep the diagram manageable, but recall that they are identical to the Cooperative Detainee. The Resistant Detainee just has the different preference ordering.

The RIT game begins with Nature making two moves, first selecting one of the three Detainee types, Cooperative, Resistant, or Innocent, with the associated probabilities p, before then selecting one of the two Interrogator types, Pragmatic or Sadistic, with the associated probabilities q and . The uncertainty of both players about their opponent is captured by the dotted lines connecting their choice nodes and the fact that the game from those nodes are identical to each other.

At this point, then, there are six BIT-like games, one for each combination of Detainee type (3) and Interrogator type (2).¹² The games differ somewhat, however, in their payoffs, since the different player types feel differently about the actions and the outcomes. Start at the top-right branch of the tree, when Nature has chosen the Cooperative type of Detainee and the Pragmatic type of Interrogator. The Cooperative Detainee has chosen to reveal information and the Interrogator has chosen to torture.

What does each player get from this outcome? The payoffs are listed in this order: Detainee, Interrogator and separated by a comma. So, just as we described above, the Detainee gets because he has revealed information and also been tortured. The payoffs to the Interrogator are, to use a technical term, goopier, but then her job is more complicated in real life too.

First take a look at her payoffs from the inside out. You may have heard the expression “surrounded by uncertainty.” In the case of the Pragmatic Interrogator’s payoffs, this is literally true. At the core, or center, of her payoffs are the same payoffs from the BIT models, . Now, though, they are surrounded by uncertainty: the probabilities f and u on one side and their complements, and , on the other side. The fundamental idea is that the basic payoffs from the BIT model are now weighted by this uncertainty, just as in the simple examples above.

To see this, now look at her payoffs from the outside and work your way in.

The first thing to consider is whether or not the Interrogator has understood that the information is valuable. If she has not understood that the information is valuable (alternatively: she has understood the information to be not valuable), then she gets just , the costs of torture with no benefit of the information. Just as above, this outcome is weighted by the likelihood it occurs .¹³ If, on the other hand, she does understand the information to be valuable, then this outcome (everything in the brackets) is weighted (multiplied) by its likelihood, u.

The next thing to consider is whether the Interrogator believes that it is all the information the Detainee possesses—that is, that there has been full information disclosure. Just as with the clarity variable u, the probability of full information f weights that possibility, in which the Interrogator receives the value of the information minus the permanent torture cost and the additional cost of “unnecessary” torture , while the likelihood of the other possibility, less than full information , weights what she receives then, the value of whatever information is received minus the permanent costs of torture and the costs of hidden information .

Before we move down to the next branch and combination of moves, a word is in order here about interpreting “information” and “no information” in RIT versus BIT. In the BIT game of the last chapter, we interpreted “no information” to mean “not enough good (enough) information” along with the other three interpretations. We’ve made things a bit more realistic in RIT by bringing in . This means that any valuable information provided by the Detainee counts as “information,” unlike in BIT, where we excluded nominal but valuable information.

This is an improvement in another way as well: It provides greater benefit of the doubt to proponents. Now, even the smallest amount of information counts as valuable information. The Interrogator may still decide it’s not enough and torture, of course, but in RIT no valuable information is “lost” by counting it as “no information.” As a reminder, this leaves the following three interpretations of the move “no information” by the Detainee:

1. truthful, accurate, but nonvaluable information

2. false and misleading information

3. no information whatsoever

In the next branch down, everything is the same except that the Interrogator has chosen not to torture. In this outcome, the Detainee stills pays the cost for giving up information but does not suffer the loss of as well. Notice that the Interrogator’s payoffs are very similar to the first branch. There is still some uncertainty about the value of the information and whether or not the Detainee has revealed all he knows. There is also the penalty or cost of if it turns out the detainee has hidden information.

The differences are related—not surprisingly—to not using torture along this path of play. On the one hand, there are no costs or since the Interrogator did not use torture. On the other hand, if it should turn out that the Detainee failed to provide full information or the Interrogator failed to understand the information as valuable but did not torture, the Interrogator pays the reputation costs .

The payoffs to the remaining outcomes are much simpler. In the next two branches down, the Pragmatic Interrogator confronts a Cooperative Detainee, but the Detainee has not provided information to the Interrogator. In branch three (counting from the top down), the Interrogator tortures; in branch four she does not. If she tortures, the Detainee suffers the cost but keeps the information and thus pays no cost for that. The Interrogator pays the permanent cost of torture but receives no benefit V. This time, though, she does not pay the additional cost because torture after “no information” is considered “necessary” torture on the pragmatic view. If the Interrogator fails to torture, then the Detainee suffers no losses (the best the Detainee can do). The Interrogator, however, pays the reputation costs for failing to torture after receiving no information.

In the next set of four branches a Cooperative Detainee faces a Sadistic Interrogator. The payoffs to the Detainee are exactly the same; the payoffs to the Interrogator, however, differ. A Sadistic Interrogator still receives the benefit V from valuable information if the Detainee reveals it, but pays no costs from using torture. On the contrary, because this Interrogator type is Sadistic, she receives an additional benefit s whenever she uses torture.

The middle branch of the tree, in which the Detainee is the Resistant type, looks exactly like the upper branch just described. The lower branch of the tree, in which an Innocent Detainee squares off against both a Pragmatic and a Sadistic Interrogator, is much simpler. Here is why.

First, recall that if an Innocent Detainee has the option to provide information, then we must be in the leading question variant of the model. If I am an Interrogator asking leading questions, and the Detainee is answering them, then there is no uncertainty about the clarity of the information. Consequently, there is no u variable weighting the payoffs. Now it is true that V is not new information but instead confirmation of preexisting belief, but this is what an Interrogator asking leading questions values, so we keep the same payoff. The rest of the payoffs to both types of Interrogators are exactly the same as with the other detainees. As for the Innocent Detainee’s payoffs, he suffers the same costs from torture as the other types of detainees, , but since he has no information, his costs of providing “information” to the Interrogator are the costs of being forced to lie to avoid torture: .

With these more realistic moves and payoffs, we now have a more realistic model of interrogational torture that steers a middle path between the two sets of extremes identified at the outset of the chapter. It balances reality with fidelity to the pragmatic model on the one hand and incorporates what is necessary while abstracting away what is nonessential on the other. In order to see what happens in this model, we need to solve it, to which we now turn.

The argument thus far has shown that:

1. EITs are torture, and the effectiveness of interrogational torture is an open question. (Chapter 2)

2. The Bush program approximates closely the ideal model of interrogational torture and includes limits on torture; the Bush and ideal models provide benchmarks for comparison with the game theory models to come. (Chapter 3)

3. The Bush model generates strange, quixotic outcomes. (Chapter 4)

4. The Bush interrogational torture program is more realistically modeled as objective and leading question variants of an incomplete information game, with three types of detainees, two types of interrogators, and uncertainty about the amount and value of information provided. (Chapter 5)

The next step in the argument is to solve this more realistic model.