Theory of deterrence: potentials of conceptual models.

Scientific methods used in finding regularities in the behavior of sides involved in military conflicts are based on carrying out studies, on different levels of abstraction, depending on the objectives of these studies. The first among them is the so-called conceptual level. The main objective pursued on this level is to establish a system of views on questions of rational behavior (rational strategies) of sides in wars and armed conflicts, which makes it possible to identify, early on, unworkable strategies and select avenues of more detailed studies.

Studies as a rule use simplified models, including mathematical models based on taking account of a small number of most important factors. It is customary to refer to them as conceptual. Such models can be very rough and it is only important that they should be constructed accurately, that is to say, they should be useful in drawing accurate conclusions from the results of studies. Among the important advantages of conceptual models are their transparency and the possibility to clearly observe the mechanism of substantiating rational strategies of behavior of sides in military conflicts.

To confirm the above statement, let us, from the positions of modern deterrence theory, analyze the activities of the United States and its allies in Iraq in the spring of 2003 and try to think what could have happened otherwise. Our analysis will be based on a mathematical model of a conceptual level.

Let us suppose that the U.S. military-political leadership took into account, at the time of making the decision to launch the Shock and Awe operation in Iraq, the experience of previous military operations of the previous decade and started from the possibility to win by "blitzkrieg" while not ruling out the possibility of a prolonged war. Based on this assumption, the war in Iraq could have had three phases.

* Phase one is an offensive air operation involving air and missile strikes to destroy military-economic and military targets, eliminate the country's military-political leaders, and first of all Saddam Hussein, and crush the Iraqi's will to resist.

* Phase two is a fluid airland operation with an objective to crush resistance of the Iraqi army and achieve its surrender.

* Phase three is a prolonged land operation with an objective to occupy Iraq and completely eliminate the Hussein regime.

Further analysis is based on the following concept of modern theory of deterrence: the aggressor can embark on escalation of the conflict if the expected gain would far outweigh the losses. (1) At the same time, decision in every phase should be based on expected long-term consequences. For this reason, a mathematical escalation of conflict model that would characterize its advantageousness in this or that phase could be mathematical expectation of function F expressing the "gain-loss" ratio. The mean expected value of this function F, as has been mentioned, is determined with taking into account remote consequences of the unleashing (continuing) of aggression, for which reason it is given by the following expression:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1)

where [P.sub.i] is subjective probability of the aggressor's belief that the conflict can be over in phase i of the conflict;

[F.sub.i] is a function characterizing the "gain-loss" ratio in phase i of the conflict.

Function [F.sub.i] is found from the formula

[F.sub.i] = [g.sub.i][V.sub.i] - (1 - [g.sub.i])[D.sub.i], (2)

where [V.sub.i] and [D.sub.i] are respectively the values of the aggressor's gain or loss in phase i of the conflict;

g is the coefficient of relative importance of gain characterizing the aggressor's resolve to fight in phase i of the conflict despite losses.

It is clear that the criterion of gain (advisability, rationality) of escalating the conflict is condition

[bar.F] ae 0. (3)

Let us call function [bar.F] an escalation of conflict function.

We will take into account, in characterizing the aggressor's gain and loss in various phases of the war in Iraq, two generalized factors: factor one is the power of the opposing sides depending on their military and economic potentials; factor two is losses (in human, economic and military terms) and society's morale.

In this connection, the aggressor's gains and losses in every phase of the war can be characterized on the qualitative level as follows. Phase one--the gain is rather substantial and it is mainly political (the creation of yet another precedent of shaping the world order, stronger unity of the U.S. closest allies and a training for cooperation experience). The loss is substantial--a negative reaction of the world community, violation of norms of international law, economic costs. The aggressor's resolve to fight despite losses can be fairly high.

Phase two -- the gain is substantial and consisting primarily in demonstration of the power of American and British arms, the abilities of the coalition forces command to plan and carry out an effective airland operation. The political gain could have been greater in the event of an active involvement in the operation of armed forces from Germany and France; the loss is medium--military losses are growing imperceptibly whereas economic costs are more tangible. The aggressor's resolve to fight on despite losses remains high.

Phase three -- the gain is medium (the political gain, which could have been achieved in the preceding phases of the war, has noticeably declined because "blitzkrieg" tactics did not pan out. It remains to be hoping for the destruction of the Iraqi army, occupying the country and establishing a new regime). The loss (damage) is considerable--casualties and losses are climbing appreciably, likewise civilian casualties, financial costs are big, it becomes necessary to fight the guerrillas and there are considerable differences inside NATO. The aggressor's resolve to fight on is less than in the previous phases of the conflict, but it remains relatively high.

In accordance with the well-known methods of assessment, (2) let us introduce, for the purpose of quantitative appraisal of the aggressor's gains and losses in the various phases of the war, the following scale (based on points): 0 -- zero gains (losses), implying that there is practically no gain or loss; 1 -- insignificant gains (losses), implying meager gains or losses; 2 -- medium gains (losses), not small but not great; 3 -- substantial gains (losses), but it could have been greater; 4 -- very great gains (losses), they could not have been greater.

In determining the coefficient of relative importance of g . [0, 1] gain that characterizes the aggressor's resolve to fight on despite losses, we will use a method of individual estimation based on points (3): g = 1, if it is important for the aggressor to reach its objectives at any cost (that is to say the aggressor is only after the size of gain and cares not for losses); g = 0.75, if making decisions the aggressor is guided more by the possible gain than by possible losses, the resolve to fight on is high (that is to say, the size of gain is of more importance than the size of loss); g = 0.5 if in making decisions the aggressor gives equal consideration to possible gains and possible losses (i.e., the size of gain and loss is the same); g = 0.25 if in making decisions the aggressor gives more thought to possible losses than possible gains (i.e., the size of loss is more important to the aggressor than the size of gain); g = 0 when it is important to the aggressor to minimize losses at any cost (i.e., the aggressor considers only the size of loss and ignores the size of gain).

Table 1 brings together the results of calculations of [F.sub.i] from the formula (2) taking into account the gain (loss) scale and the coefficient of relative importance of gain.

Let us consider how the U.S. military-political leadership's decisions to begin Operation Shock and Awe could have influenced Iraq's expected strategy of opposing (deterring) aggression. For the well-known reasons, Iraq was unable, in the wake of Operation Desert Storm to appreciably build up the capability of its air defense system and for this reason the U.S. military-political leadership must have expected that Saddam Hussein would be able to hold out only through phase one of the war. Let us call this 'an "optimistic" (from the aggressor's viewpoint) strategy of deterrence (strategy I).

At the same time, in terms of Desert Storm as a "realistic" deterrence strategy, the U.S. military-political leadership had to consider that Saddam Hussein would move to take the military conflict into phase two (strategy II). This proved correct: it is in phase two of the above operation that Iraq made concessions. Finally, we can presume the existence of a "pessimistic" point of view with regard to the duration of the military conflict--taking it into phase three (strategy III).

Let us find the values of the escalation of conflict function (1) for each of these strategies. In accordance with strategy I, the U.S. military-political leadership must have thought it most probable that the war would end in phase one, or at least in phase two or, least probably, in phase three. By placing the war phases in this order and ranking them accordingly (phase one--1, phase two--2, phase three--3), the values of objective probabilities of [P.sub.i] can be obtained using a relative frequency of ranks method. (4) In accordance with this method, every phase of the conflict in the ordered sequence is assigned a reverse rank [r.sub.i]--3, 2 and 1, respectively. In that case we have:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (4)

Thus, under strategy I, subjective probabilities [P.sub.i] calculated from formula (4) take on the following values:

[P.sub.1] = 0.5; [P.sub.2] = 0.33; [P.sub.3] = 0.17.

Thus, the escalation of conflict function will be as follows:

[bar.F] (I) = 0.5 2.75 + 0.33 1.75 - 0.17 0.5 = 1.87.

Under strategy II, the U.S. military-political leadership should have thought it most probable that the war would end in phase two and less probably, in phase three. In this case, subjective probabilities [P.sub.i] take on the following values:

[P.sub.1] = 0.33; [P.sub.2] = 0.5; [P.sub.3] = 0.17.

In this case

[bar.F] (II) = 0.33 2.75 + 0.5 1.75 - 0.17 0.5 = 1.7.

Under strategy III, the most probable thing to expect should have been the ending of the war as late as in phase three and the most improbable, in phase one. In this case we have:

[bar.F] (III) = 0.17 2.75 + 0.33 1.75 - 0.5 0.5 = 0.79.

Thus, Iraq's presumed "deterring" actions did not induce the U.S. military-political leadership to cancel the launching of Shock and Awe on account of an acceptable ratio of expected gains and losses.

It became clear in phase one that the adversary was not going to give up resistance. This provided grounds for the U.S. military-political leadership, as it was deciding on further escalation of the military conflict, for considering two opposition strategies: "optimistic" (strategy IV) and "pessimistic" (strategy V).

Plainly, a hypothesis of the most probable end of the war in phase two was proposed in accordance with strategy IV, and that it would end in phase three in accordance with strategy V. Calculations of the conflict escalation function in connection with these deterrence strategies lead to the following results:

[bar.F] (VI) = 0.66 1.75 - 0.34 0.5 = 0.98,

[bar.F] (V) = 0.34 1.75 - 0.66 0.5 = 0.26.

As can be seen, the values of the escalation of conflict function for both expected strategies turn out to be positive. Therefore, further escalation of the military conflict proved quite acceptable to the U.S. military-political leadership owing to the ratio of expected gains and losses. As a result, the Hussein regime could hold out only through phase two of the war. The Iraqi army surrendered, Saddam Hussein in his inner circle went into hiding.

Had Saddam Hussein's prewar statements on the Iraqis' resolve to fight to the bitter end been backed by a high level of Iraq's military might and high morale of society (strategy VI), then the aggressor's loss in phase three of the war could have been estimated by the U.S. military-political leadership as big (the size of loss [D.sub.3] = 4) and the aggressor's resolve to fight on despite losses as relatively low (g = 0.25). In this case, [F.sub.3] function that characterizes the gain-loss ratio would have this value:

[bar.F.sub.3] = 0.25 2 - 0.75 4 = -2.5.

With regard to strategy VI, it would be natural to think that the war would most probably end in phase three or, less probably, in phase one. The escalation of conflict function would then take on the following value:

[bar.F] (VI) = 0.17 2.75 + 0.33 1.75 - 0.5 2.5 = -0.2.

In this situation, the U.S. military-political leadership would have hardly ventured to go ahead with Operation Shock and Awe because the ratio of expected gains and losses was unacceptable.

In summed up form, the results of calculations of the escalation of conflict function for the above strategies are presented in Table 2.

The main purpose of this paper was to use as an example a retrospective analysis of the war in Iraq in the spring of 2003 in order to show the potentials of conceptual models of modern deterrence theory in substantiation of strategic-level decisions.

One of the criteria used in estimating the quality of such models was that the results of modeling should not contradict the past events. From this point of view, the results of analysis presented here make it possible to conclude that the conceptual apparatus of today's deterrence theory is quite workable not only in describing the mechanisms of decision-making on a strategic level, but also in substantiating such decisions and, in particular, in devising rational deterrence actions.

These authors realize that the results of their analysis are subjective to a certain extent because the quantitative assessments used in this analysis were based on simplified expert judgements. They can be refined with regard to the conflict in question; in other instances, it is possible to take into account various sets of conditions, but the main provisions of the body of concepts of modern theory of deterrence generally apply and thus will remain valid.

NOTES:

1. Ye.S. Yegorov, Sovrenmennaya teoriya sderzhivaniya, VAD, Moscow, 1995.

2. Nadezhnost i effektivnost v tekhnike: Spravochnik, Vol. 3, Effektivnost tekhnicheskikh system, Mashinostroyeniye, Moscow, 1988.

3. Ibidem.

4. Ibidem.

Maj. Gen. V.V. VASILENKO

Doctor of Technical Sciences

Col. V.I. KUZNETSOV (Ret.)

Doctor of Technical Sciences

Col. V.D. ROLDUGIN

Candidate of Technical Sciences

Table 1

Phase  Gain         [V.sub.i]  Loss           [D.sub.i]  g     [F.sub.i]

1      Big          4          Insignificant  1          0.75   2.75
2      Substantial  3          Medium         2          0.75   1.75
3      Medium       2          Substantial    3          0.5   -0.5

Table 2

                            Deterrence doesn't exist
        Strategies           I                     II
Phases  [F.sub.i]   [r.sub.i]  [P.sub.i]  [r.sub.i]  [P.sub.i]

1        2.75       3          0.5        2          0.33
2        1.75       2          0.33       3          0.5
3       -0.5        1          0.17       1          0.17
        F                1.87                   1.70

                             Deterrence doesn't exist
        Strategies           III                   IV
Phases  [F.sub.i]   [r.sub.i]  [P.sub.i]  [r.sub.i]  [P.sub.i]

1        2.75       1          0.17
2        1.75       2          0.33       2          0.66
3       -0.5        3          0.5        1          0.34
        F                0.79                   0.98

                    Deterrence doesn't exist  Deterrence exists
        Strategies           V                  VI/[D.sub.3]=4
Phases  [F.sub.i]   [r.sub.i]  [P.sub.i]      [F.sub.i]  [r.sub.i]

1        2.75                                  2.75      1
2        1.75       1          0.34            1.75      2
3       -0.5        2          0.66            --        3
        F                 0.26                      -0.2

                    Deterrence exists
        Strategies  VI/[D.sub.3]=4
Phases  [F.sub.i]   [P.sub.i]

1        2.75        0.17
2        1.75        0.33
3       -0.5         0.5
        F           -0.2