Background

Procurement of defence systems is generally supported by analysis that uses constructive simulations to provide objective measurements of operational effectiveness for various systems concepts under consideration; however, these simulations tend to contain simplified representations of command and control (C2) decision-making. For analysis to support procurement of command information systems (CIS), it becomes more important to improve our simplified representations of C2 decision-making because it is difficult to address CIS design without a formal representation of the human decision processes. The aim of this work, then, is to improve current representations of C2 decision-making in constructive simulations to support operational analysis studies. It is not our aim to make the individual psychology of the decision-maker(s) a key driver.

This paper offers a theory that provides a framework for representing C2 decision-making in situations of threat, uncertainty and conflicting objectives. The framework will aid the formal definition of C2 conceptual models that are central to the development of CIS within network-enabled capability (Saunders and Miles, 2004).

Introduction

A new approach to the representation of military C2 in fast-running, constructive simulation models has been developed (Moffat, 2000, 2002) and is currently being incorporated into a new generation of simulation models with C2 at their core. The emergent combat behaviour produced by C2 agents has been validated by comparison with historical conflicts (Moffat et al, 2004). As part of this set of ideas, the rapid planning approach has been developed, which represents the decision-making process of experts under uncertainty, working in fast and fluid circumstances and as part of a C2 decision-making network or hierarchy. The rapid planning process first defines the set of key situation attributes (eg enemy combat power) that the decision-maker uses to 'frame' his problem domain (Perry and Moffat, 2004). These define a space that we can call the C2 'decision space'. Dynamic linear models (DLM), as defined in (West and Harrison, 1997), are then used to assess the significance of any changes in these key information attributes over time. The decision-maker defines particular areas of the decision space on which he places particular emphasis, and for which he has an understanding of the potential consequences of his courses of action. The process of pattern matching that lies at the heart of the approach is between the decision-maker's assessment of his current position in the space (as defined by the DLM) and the areas of emphasis in the space that are associated with potential courses of action. The DLM approach is Bayesian in nature and is driven by incoming information and subjective priors. The DLM approach has been extended to include a further set of factors driving the C2 decision process (Dodd and Moffat, 2001; Dodd et al, 2002; Moffat and Dodd, 2000; Moffat and Witty, 2002) based on non-linear utility theory (Smith, 1979; Smith and Harrison, 1979; Smith et al, 1981). The aim is to be able to represent the subjective variability in C2 course of action selection by formally considering differences in situation assessments owing to the different perspectives due to the level of command and individual predispositions to threat and risk. The factors account for adjustments in the attributes and adaptation of the areas of emphasis to accommodate the decision-makers' sense of 'comfort' with regard to the courses of action.

Overview

The next section introduces non-linear utility theory by briefly reporting the initial application of the theory in exploring the discontinuous nature of command decision-making. The section following it discusses recognition primed decision-making (RPD), which is the foundation for the rapid planning approach, and sets the scene for the experimental game. The next two sections describe two settings for the experimental game and present the results using 24 military commanders, aiming to validate the theory. The penultimate section explains the theory of non-linear utility and the geometry of competing objectives, using a peace-support example as an illustration. The final section presents the conclusions drawn from the experimental results and recommends how the formalisms we have developed may be used (i) to understand command decision-making performance in typical conflict situations and (ii) to aid the future design of CIS, communication protocols and training strategies.

Rapid planning and non-linear utility

Recent research programmes to investigate human factors in command effectiveness have used RPD or naturalistic decision-making (Klein, 1997) to form the hypothesis that course of action (CoA) selection is a direct consequence of pattern matching. The rapid planning process is based on RPD but was initially extended to represent, as distribution functions, the decision-makers' belief in future outcomes and his subjective evaluation of the losses associated with these potential outcomes. When the belief and loss functions are combined to give an expected loss function, it results in two minima that relate to the local and global decision options (Moffat, 2002). (Note that this analysis initially used only loss to represent a simplified evaluation of course of action outcome, but generally the utility values will include all aspects of loss, cost and benefit.) Changes in the beliefs in outcome and the loss values (due to changes in situation uncertainty, on-going operational activity or operational context) cause a change in balance between the two minima (Dodd and Storr Maj, 2001). This extension has been incorporated into the rapid planning algorithm to indicate whether or not the local commander should deviate from his current CoA. There are, however, obvious problems associated with the representation of commanders' loss functions, as it is difficult to elicit such subjective constructs. However, initial examination of the results of the command decision-making experiment showed that these subjective functions could be represented in terms of utility and that they are composed of assessments of decision outcomes from different mission-objective perspectives. This has led us towards a further extension into non-linear utility theory that allows us to explain why CoA selections differ qualitatively dependent on the decision-makers' experiences and preferences, as these are expressed in the parameters of their subjective probability densities and utility functions. It may then be possible to understand with more clarity and formal definition

1. how the objective inputs (based on in-coming information) and the subjective inputs (based on an individual's training, experience and personality) combine in the decision-making process, and
2. how considerations of utility (from the different perspectives) influence this process: in particular, when there are conflicting local and global values within the C2 decision-making structure.

At each level in the C2 structure, the mission statements, orders and rules of engagement must be interpreted by the commander and accommodated into his subjective utility attributes, with criteria weights representing operational priorities, at least approximately. The missions described in this paper are simplified to just two levels of attributes, although the general theory is not limited to two levels. The first set of attributes measures the local outcome of the mission in terms of relatively immediate, 'close-to-home' considerations (such as loss of tactical assets). The second set of attributes measures longer-term and more global concerns related to more strategic considerations (eg integrity of the NATO campaign). The analysis sets out a formal reasoning about a decision process when a commander's response to his local situation may be inappropriate from the perspective of higher-level command, and it describes how this tension between local and global concerns can formally be modelled.

The choice of course of action depends on the interpretation of mission orders (ie weighing of priorities in terms of utilities) and the subjective situation assessment (ie weighing of evidence derived from subjective informational attributes). The commander may be unable simultaneously to reconcile, even partially, the objectives associated with the attributes pertaining to the high-level mission objectives and his own local appreciation of immediate potential threat. When this happens he may be forced to choose an action that focuses on local, shorter-term success, marginalizing the longer-term implications of his action. Alternatively, he may place more weight on global concerns. This tension between objectives is the basis for the derivation of the subjective utility and depends on the subjective descriptors of the conflict situation, the interpretation of the mission orders and the general appreciation of the situation. The relative importance each commander places on the local and global objectives is central to a conceptual understanding of 'value' in decision-making. It seems that such qualitative relationships are enduring in this context and that they provide a useful framework for C2 modelling.

In practice, most Bayesian decision analyses usually begin by assuming that the decision-maker's utility function, U, has an associated set of value-independent 'situation' attributes (Keeny and Raiffa, 1976). In our application, these attributes are associated with situation features that are immediately local to the decision-maker and those that have a longer-term, more global impact. For a decision, d, a decision-maker's utility function has to capture the trade-off between the different goals by assigning weights, (₁)=(₁(₁), ₂(₁)), to reflect the importance of achieving the desired values of the attributes, whose achievement is evaluated by the utilities. (₁ is a set of shape parameters describing his utility function.)

Projected future values of the attributes are represented by a probability distribution function p_i(_i|d, ₂), which reflects the decision-maker's current (subjective) probability of outcome _i relative to goal attribute x_i, given decision d, where ₂ is a shape parameter for this probability distribution.

The decision-maker should thus choose d to maximize the expectation of U(d, ₁) (averaging over his beliefs about different outcomes _i and their utilities). The decision-maker also implicitly sets weights (₁) reflecting, for instance, his priorities and ambitions and even his fears. In most military settings a decision-maker will be acting within a C2 structure and will be held accountable for his chosen course of action d. It is therefore, reasonable to expect that the specific nature of the mission objectives and the previously absorbed general training and personal history will be reflected in the commander's setting of (₁). There is also a vector (₁)=(₁(₁), ₂(₁), ..., _m(₁)) that parameterizes the marginal utility functions and determines their shape. Such parameters might determine the functions' offsets, spreads and turning points and specify how well the decisions, d, achieve goals associated with respect to attribute x_i.

Note that the densities p_i(_i|d, ₂) can only, at best, approximate a commander's estimate of attribute values against his general beliefs about future outcomes. His information will be imperfect and incomplete. Resources in the HQ to process the available information will be limited and subject to mistakes through lack of training, expertise and failure to follow procedure or just lack of imagination. A formal representation of the CIS within the HQ is outside the scope of this work; however, related work on CIS entropy and plecticity (Perry and Moffat, 2004) (ie measures of performance for CIS process connectivity) will help to form the necessary conceptual link. It is nonetheless useful to maintain the formality of the theory at this point as this enables us to address the possible consequences of C2 decisions in an idealized framework, which can later be relaxed. A similar formal utility-based approach is taken in by Glimcher (eg Glimcher, 2004).

RPD and the experimental game

One part of the UK Ministry of Defence research programme to investigate the 'contribution of the human element to command effectiveness' used an RPD experimental game to examine the hypothesis that CoA selection is a direct consequence of pattern matching. RPD describes how experienced practitioners, under uncertainty and stress, make decisions in their domain of expertise. It consists of three phases: situation recognition, serial course of action evaluation and mental simulation. Situation recognition in the presence of plausible goals leads to the selection of appropriate action with little or no search through alternatives. Serial course of action evaluation is undertaken only if the first feasible course of action is rejected. Mental simulation is the process used to evaluate actions (serially) if course of action evaluation is necessary (see Mathieson (2001) for details of previous experiments).

A key feature of the RPD model is the idea that decision-makers recognize situations by matching patterns of cues and indicators, contained in presented information, to previous situations remembered from past experiences. This recognition process provides access to pre-learned knowledge about how 'best' to behave and what to expect in a given situation. This pre-learned knowledge shapes the decision-maker's process of situation assessment and provides the starting point for course of action generation. In terms of the rapid planning process, this relates to the subjectively pre-specified areas of the decision space on which the decision maker places emphasis. It also relates to how he then maps one of these areas onto a preferred course of action. The overall process is

1. to identify where you are in the decision space (based on tracking the values of the key information attributes over time),
2. to assess which of the pre-specified areas of the space the track pertains to (the pattern-matching process),
3. to map, from that identification, onto a preferred course of action.

The RPD game was thus designed to measure the predisposition of participants, in a situation in which they should be experts, by requiring them to make a rapid determination of a course of action. Participants were presented with an initial operational picture and situation brief. Following 10 min to appraise the situation, an intelligence report was briefed, which might (or might not) demand action. The participants were then asked to choose and write down a course of action without being given further time for analysis. The intelligence update was designed to give them some room for choosing different courses of action so that their pre-dispositions were allowed to surface as variations in choice.

After the course of action was selected, participants were invited to record their situation appraisal and assessments along with the key indicators considered relevant to their course of action choice. It was accepted that these data might reflect post hoc rationalization to some extent. To account for any changes in situation assessment due to the process of having to analyse and express it, the participants were also offered the opportunity to record any other courses of action that they may have considered.

The RPD experimental game results give us a context within which to explore and test the non-linear utility theory: in particular, the ways in which individuals' predispositions affect the weights given to the situational attributes. It appears that the extent to which each attribute is (or is not) considered in the pattern-matching process strongly determines the choice of course of action. The RPD experimental game was based on C2 decisions at battle group (BG) and company levels set in two different conflict scenarios: war fighting and peace support.

War-fighting scenario

The war-fighting RPD game was played after participants had taken part in a related Brigade-level planning exercise, which provided them with a good appreciation of the operational context. The participants were focused on a decision concerning a BG of three tank companies located in hides on a large wooded ridge feature called Elfas (top middle-left in Figure 1). Enemy armoured and mechanized units could be seen travelling along roads either side of the ridge. The Brigade's mission was to delay the enemy's advance by 24 h until bridges to the West could be secured. A full written brief was presented that described the current operational status of all units within the Brigade's area of interest. Then followed a situation update as depicted in Figure 1.

Figure 1.

Schematic map of the situation update.

Full figure and legend (388K)

The situation update indicates probable enemy airborne deployments to the West of the Elfas feature. The strength of these deployments is not known but is assessed as an augmented company. The participants were asked to write down immediately their course of action. As the BG commander in the field HQ there are several courses of action available, for example:

• remain in hides and do nothing;
• request more information;
• attack North/North-East (hoping for surprise) against the armoured enemy units;
• attack West directly against the reported deployment of airborne troops;
• maintain a South-east withdrawal route to join up with own forces.

The CoA choices across the 24 participants appear to vary according to the way that they have taken account of the situation attributes and the higher-level mission orders. Some participants choose to give very little (if any) weight to the higher-level mission orders and focus on achieving effects that satisfy local utility. This local view of the mission in some cases tends to extend to the use and interpretation of the situation attributes in terms of both space and time. So, for example, the situation may be appraised purely as a snapshot in time (ie little or no forward projection) so that decision outcomes are assessed only from the point of view of the BG, ignoring the overall Brigade mission.

Table 1 shows the association of the weighted utility values and attributes with the selected course of action (as deduced from analysis of the experimental results). The utility values indicate a need to initiate an active decision to move out of Elfas hides to attack, but this can be qualified and delayed if there is uncertainty. This reveals two concurrent, inter-dependent assessment processes: threat and risk assessment.

Table 1 - Utilities, attributes and CoAs for the warfighting scenario.

Full table

For those participants who are not so concerned about the uncertainty in the situation update, the relative weightings of the BG and Brigade mission priorities coupled with the practical consideration of employing tanks against dismounted airborne troops result in two very different courses of action. Some choose to attack West (employing tanks against dismounted troops and preventing link-up and closure of the gap West of Luthorst) while others choose to attack North/North-east using tanks against tanks and adhering to Brigade orders. Where there is uncertainty and lack of confidence, the participants choose: to either keep tanks in reserve or prepare for attack while doing further reconnaissance, or secure a withdrawal route to rejoin the southern BG, or simply do nothing, remain in hides and report to Brigade.

Peace-support scenario

The peace-support scenario is set in a fictitious federation and involves provision of armed support for conveyance of supplies and civilians to and from a NATO-protected enclave East of the 'Nettoyer Pass' (Figures 2a and b). Following the break-up of the federation, the two major factions have been left in a state of armed stand-off. The NATO Task Force, with the UK acting as the lead nation, is a Division-sized force with a task of disarming the ethnic militia. NATO forces have also undertaken to escort and protect all aid convoys. The broader NATO mission is to restore peace and stability to the area in order to create conditions for a free vote by the population on the future of the region.

Figure 2.

(a) Peace support situation overview. (b) Situation close-up and situation update.

Full figure and legend (109K)

The intelligence update (depicted in Figure 2b) is sent to the tactical commander in the form of a radio message from an armed unit with two Land Rovers escorting a civilian relief convoy of six vehicles. The armed convoy has been stopped at a probable illegal vehicle control point (IVCP) in a mountain pass as it returns from delivering supplies to the enclave. The IVCP consists of 12 men, armed with AK-47 assault rifles and at least two RPG-7s. The second escort Land Rover is 500 m to the rear of the convoy. We focus here on the decision-making of the commander back at the field HQ located at Var (see Figure 2a). There are several courses of action available, for example:

• order the UK troops to negotiate their way out of the situation;
• order a withdrawal to move the civilian convoy vehicles to a safe distance;
• do nothing and hope that the militia men let the unit and convoy through eventually;
• deploy the quick reaction force (QRF) and move artillery units to fire positions.

There are well-defined NATO rules of engagement: for example, personal, direct-fire and indirect-fire weapons may be used to engage a positively identified threat.

Here the immediate potential outcomes of the mission are measured against attribute x₁ and scored by utility function U₁. This evaluates features that have consequences local to the situation, such as an escalation of the immediate threat by ambush or weapon firing, the reduced security of the civilians in the convoy and likelihood of kidnap, theft of supplies, etc. The second attribute x₂ is scored by U₂, evaluating more global issues concerning, for example, the integrity of the NATO campaign and political perceptions of NATO's ability to show resolve while adhering to the rules of engagement. The nature of peace-support operations generally means that the C2 structure tends to be flatter and with a less explicit hierarchy of mission orders (in contrast to the war-fighting scenario). Therefore, we would expect the course of action selection to be driven more from the situation attributes than from the weighting of mission priorities.

The decision model then is as follows:

• ₁(₁) is the subjective priority weighting of local effects.
• ₂(₁) is the subjective priority weighting of global effects.
• U₁(d, ₁(₁)) is the utility of the decision with respect to local outcomes.
• U₂(d, ₂(₁)) is the utility of the decision with respect to more strategic consequences of the decision.
• ₂ is a vector of shaping parameters for the subjective distribution of probable outcomes, and represents the general level of the commander's uncertainty in the situation.

The local features for attribute x₁ typically concern the potential for

• escalation of threat (in particular an ambush or firing of weapons),
• loss of civilian life,
• own force casualties,
• theft of convoy assets,
• taking of hostages.

Another x₁ attribute, only explicitly mentioned by two participants, was time pressure in that there was only 40 min of daylight remaining.

The global features for attribute x₂ are typically

• show of strength against NATO resolve to restore stability,
• provocation to create over-reaction and heightened regional tension.

Table 2 shows the various utilities and attributes along with the choices of course of action. In order to plot (in two dimensions) the participants' decision space and situation assessments within the space in terms of x₁, the features are combined into two measures that represent the seriousness of the terrorist threat and the sense of provocation through a show of strength. The former reflects the indications for ambush and imminent need to address a real threat with direct force. The latter measure embodies the features concerned with protection of the convoy and the need to avoid escalation.

Table 2 - Utilities, attributes and CoA for the peace-support scenario.

Full table

Participants' course of action choices, d, can be set against a notional decision scale (reflecting the degree of overt force deployed) that ranges from 'deploy the QRF with all available support (such as artillery and helicopters)' to 'negotiate with IVCP troops and do NOT deploy QRF'. Several participants chose to 'find out more' by sending in reconnaissance assets. This supports the fundamental basis for the non-linear utility theory approach that there are two major control dynamics:

• the dynamics of the actual situation (in particular whether or not the situation is close to, or approaching, a critical condition that demands corrective action);
• the associated probability dynamic (situation uncertainty strongly inter-related with consequential utility and whose functional forms are captured by the parameters).

Figure 3 schematically represents the participants' situation assessments plotted in the two-dimensional space representative of x₁. Each letter in Figure 3 corresponds to the participant's assessment in the experiment. The position of the letter, and the associated arrow indicate the stated position (abstracted to be in terms of the two-dimensional representation) of their situation assessment, and the arrows attempt to show how they anticipate that the situation will develop. Overlaid onto this situation assessment plot is the grouping of the participants into their CoA choices. This representation goes some way towards an initial validation of the rapid planning process.

Figure 3.

Participants' situation assessments and grouping of courses of action.

Full figure and legend (77K)

The courses of action are associated not only with the static assessment of the situation but also with the projection forward in time and the associated potential (and maybe feared) consequences. The subjective utilities are 'folded' into the situation assessment to represent the question 'Is there going to be a significant change that will demand corrective action?' evaluated in relation to what is at stake. The 'significance' of the change is embodied in the subjective utility curves. So there is a utility score for each point in the decision space and, in general, for this example, the utility scores tend to become rapidly low towards the top right corner of the plot in Figure 3. The participants will have utility 'slopes' of differing shape and gradient.

In addition to the assessment of the situation, a degree of confidence is associated with the individual's training and previous experience. This confidence helps to manage uncertainty in the situation and allows the decision-maker to identify factors that help to discriminate between equally likely situation assessments. In Figure 3 we can see this through the differences in the actions taken by the [L,O,P] group of participants and the [G,C,R,T,X] group. The [L,O,P] group decides to negotiate and at the same time prepare (at first covertly) the QRF deployment so that if they detect an escalation of threat the QRF could be used either as a negotiation lever (now making the QRF deployment overt) or, if necessary, the QRF can be employed rapidly and decisively. The [G,C,R,T,X] group, on the other hand, deals with situation uncertainty rather differently and decide to delay any decision to act until more information is made available.

The other groups express confidence in their assessments of the situation (and its consequential projection) and hence choose an appropriate CoA. Differences in CoA result from the weightings placed on the utility values associated with the consequential situation attributes. For example, the [H,Q,M,D,V,I,K] group places a high weighting on the more global utility, U₂, associated with the broader NATO mission, that when balanced against U₁ (removing the IVCP and keeping the convoy moving) comes out in favour of negotiation with no QRF deployment.

Non-linear utility theory and the geometry of competing conflict decisions

Let the shape parameters of the decision-maker's utility function, U, be denoted by ₁. In practice, most Bayesian decision analyses begin by assuming that U is associated with a set of m value independent attributes x=(x₁, x₂, ..., x_m). This implies that a decision-maker's expected utility function has the form U(d, ₁, ₂) and can be written as

where 0_i(₁) for all i and , and ₂ is the vector of shape parameters of his joint distributions or attributes.

The criteria weights, _i(₁), are chosen to reflect the importance of achieving the goal of the ith attribute, as evaluated by the marginal utility U_i(_i|_i(₁)).

The vector (₁)=(₁(₁), ₂(₁), ..., _m(₁)) parameterizes the marginal utility functions and determines their shape. Such parameters might determine the functions' offsets, spreads and turning points and specify how well the decisions, dD, achieve goals associated with respect to attribute x_i. The decision-maker should then choose d to maximize U(d, ₁, ₂) (averaging over the perceived outcomes and their utilities). The decision-maker has a free choice of how to set (₁) and (₁), reflecting, for instance, his priorities and ambitions.

Formally, the decision-maker's optimal decision is a course of action d^*D that maximizes his expected utility U(d, ₁, ₂), where, for 1im, we calculate the marginal expected utility by averaging over the possible outcomes _i relative to attribute x_i as follows:

where p_i(_i|d, ₂) is the perceived probability of outcome _i relative to goal attribute x_i, given decision d, and ₂ is the shaping factor for this distribution. U_i(_i|_i (₁)) is the utility of outcome _i relative to goal attribute x_i, and _i(₁) is a shaping factor for this utility function. The vector ₂ will formally contain the hyper-parameters of his prior 'belief' density and likelihood together with any data available at the time the course of action is chosen.

In most military settings a decision-maker will be acting within a C2 structure and will be held accountable for his chosen course of action d. It is therefore reasonable to expect that the specific nature of the mission objectives and the previously absorbed general training will be reflected in the weights and .

At each level in the C2 structure, the mission statements, orders and rules of engagement must be interpreted by the commander and accommodated into his subjective utility attributes, with criteria weights which hopefully represent C2 priorities, at least approximately. We can simplify the missions described in this paper to just two levels of attributes (ie m=2), but the general theory is not limited to two levels. As already indicated, the first attribute, x₁, measures the local outcome of the mission in terms of shorter-term, lower-order considerations (such as local own-force casualties). The second attribute, x₂, measures longer-term and more global concerns related to higher-order considerations (eg integrity of the NATO campaign).

Formally, the command decision, as modelled, is a course of action d^*D that maximizes expected utility U(d, ₁, ₂) where d^*()=sup_d|U(d, ₁, ₂)| is his Bayes decision.

In this paper, it is sufficient to consider only examples where a mission's objectives can be described and formulated in terms of two attributes (ie m=2). In this case

The parameter vector =(₁, ₂) contains shape parameters ₂ of the decision-maker's probability density over his attributes and parameters ₁ of his marginal utility functions U₁ and U₂ (expressing his subjective assessment of the importance of deterioration of the situation with respect to a particular component). The decision-maker's task is equivalent to finding a d^*() such that d^*()=sup_d|U(d, ₁, ₂)|.

The space of decisions dD will typically be very complex and will be constrained by, for example, the available resources and the rules of engagement of the mission. However we contend that, at least to a good order of approximation, for a wide class of scenarios we will be able to express most types of course of action decision in the form d=(d₀, d₁, d₂).

The first component d₀ of the decision d will describe those aspects of a course of action that have an effect on both the political success of the overall campaign and the immediate success of the current mission. Henceforth, we implicitly assume that these aspects will oppose each other: a positive enhancement of the mission success being reflected in a negative effect on political implications and vice versa. A typical example might set d₀ to measure the degree of force used in a particular course of action. Low values of d₀ will embody the complementary ideas of discretion and negotiation. This idea is summed up in the assumptions below.

The two marginal utilities U₁ and U₂ depend only on the arguments d₀, d₁ and d₀, d₂, respectively, so that U_i(d, _i (₁), ₂)=U_i(d₀, d_i, _i (₁), ₂), where we assume that d₀D₀, which is a subset of the real line.

Note that the coordinates d₁ and d₂ of the decision vector d index the precise way that the degree of force is employed and will typically be qualitative (although it could be sometimes quantified in terms of number of armoured units overtly deployed, for example). Usually d₁ will encode tactical level effects and the choices will not affect U₂. It is common, at least in the UK (Dodd and Storr Maj, 2001), for the precise nature of this level of the decision to be delegated to the tactical commander. The decision d₂ represents the higher-level operational effects more concerned with strategic goals, whose choice will not impact on the unfolding of the immediate situation as scored by U₁. Again, a large component of this may need to be made by the commander in the field in real time and in response to the developing situation.

For each tactical choice d₁, the U₁(d₀, d₁, ₁(₁), ₂) is an assessment of the local mission outcome. The commander's training and experience will affect the choice of d through the components d₀ and d₁ tending to maximize U₁(d₀, d₁, ₁(₁), ₂). We note that the discontinuities in the decision process (Smith et al, 1981; Moffat, 2002) focus on the geometry of this function and explain C2 hysteresis (leading to command paralysis).

Similarly, for each pair, d₀, d₂, the function, U₂(d₀, d₂, ₂(₁), ₂), measures the commander's assessment of the consequences of d with respect to the longer-term and more global aims of the campaign (eg in terms of political impact of casualties and the integrity of the UN). Training and experience in politically sensitive combat scenarios would refine the commander's judgements and should, for a given value of d₀, affect the tactical decision, d₂, such that U₂(d₀, d₂, ₂(₁), ₂) is as high as possible.

In this paper we focus on the issue of how a decision-maker should balance his options and choose an appropriate value of d₀, given his own assessment of what he can achieve under these two objectives. To act rationally, a decision-maker must, at least implicitly, evaluate the effectiveness of his most appropriate course of action d_i for each of his goals, which, by definition, maximizes U_i(d₀, d_i, _i (₁), ₂) i=1, 2, respectively. For each goal, this represents the tactic that maximizes the effectiveness of his given mission combined with the best way of achieving this efficaciously. The problem then is how to balance these two potentially conflicting goals. He must then choose d₀ so as to maximize

where, for i=1, 2

Note, however, that now _i⁰() may depend on the parameters ₂ associated with the decision-maker's uncertainty of outcome, as well as the shaping parameters ₁ of his utility function.

We can now represent a rational decision-maker's choice of action as the value d₀, which he believes will balance the two conflicting goals most successfully (ie which maximizes the real-valued V(d₀|) given above). This function will typically be a mixture of a function V₁ in d₀ increasing (not necessarily strictly) from zero to one and another function V₂ in d₀ decreasing (not necessarily strictly) from one to zero, as shown in Figure 4. There has been considerable study of such mixtures (Smith, 1979) and thus it is possible to model how a decision-maker will qualitatively respond to various environments (generally characterized according to their criticality, controllability and predictability).

Figure 4.

Utility values for two levels of command.

Full figure and legend (12K)

It is perhaps helpful to interpret what the two components and their weights represent in this study.

• The functions V_j (j=1, 2) represent what the decision-maker expects to score on his marginal utility U_j on attribute j by choosing CoA d₀ relative to the score he would expect to get if he chose d₀ to maximize his expected marginal utility U_j. Thus, if he is very uncertain, he will not be able to discriminate between the efficacy of broad ranges of d₀, and so the function V_j will be flat. If on the other hand he can identify that certain options are significantly more promising for a component V_j, then V_j will tend to be steeply changing on certain parts of the graph. Remember, however, that this is his own subjective assessment.
• The _j⁰ will take a low value if both the associated scored effectiveness U_j for any given d₀ is low and if the original importance _j is also low. The _j⁰ will take a high value when both the associated scored effectiveness U_j for a given d₀ is relatively large (ie close to unity) and if the original importance _j is also high. Note that for U_j to be close to unity it is usually required that the decision-maker is confident he can obtain close to the best possible outcome for the jth attribute (j=1, 2). Of course, this confidence may be unfounded. Moderate values of these weights are obtained when the conditions (as described above) are mixed.

By describing the geometry of V and leaving the other, more context-specific aspects of the maximization implicit, we can focus on those aspects of the decision process that entail the balancing of the more globally compliant option against the more locally forceful option. Such aspects are the decision-maker's experience (ie the assessment of his competence to choose appropriate tactics) and confidence in his ability to recognize the need to revert to a forceful option should the situation demand. Figures 4, 5 and 6 use the range of decisions from the peace-support scenario to illustrate the geometry of V.

Figure 5.

Compromise solution for V where V₁ and V₂ coincide.

Full figure and legend (10K)

Figure 6.

The split solution when the values of V₁ and V₂ are in conflict.

Full figure and legend (15K)

As we can see, in Figure 5, there is no conflict between the local and global goals and thus there is an area where compromise is possible. This is due to the fact that the level of force deployment to satisfy local goals is not in conflict with the force deployment to satisfy more global goals. As the difference between these increases, Figure 6 shows that there comes a point where these deployment levels are in conflict. In Figure 6, in order to maximize V, the decision-maker is split between two possible values of the decision d₀^*, both giving maximum utility, but where values in-between have relatively low utility. This implies a possible 'catastrophic' switch in decision. This process is brought together in Figure 7, which shows the discontinuous effect of a smooth increase in the separation of these local and global best force deployments, and the resultant switch.

Figure 7.

The effect of increasing separation of the locally best options.

Full figure and legend (7K)

In a separate paper (Smith et al, 2005) the mathematics of these 'bifurcation' effects is laid out in complete detail.

Discussion and conclusions

The rapid planning process, based on Bayesian dynamic linear modelling (DLM), and the use of RPD-based pattern matching to determine a CoA, is the foundation for our current modelling of military C2. The original extension of the DLM provided a means to incorporate discontinuities in decision outcome through subjective loss and belief functions set within a context of two (superior and subordinate) command levels. The initial modelling work showed that a minimization of the decision-maker's expected loss results in two minima that relate directly to the mission objectives of the two command levels. The main criticism regarding the practicality of the initial model lay in the elicitation of a subjective loss function.

The analysis of the decision-making experiment results has helped us to see that the subjective utility (or loss) function is essentially composed of two (or more) functions that represent assessments of the situation in terms of the decision-maker's local, short-term appreciation and a more global, longer-term appreciation of the potential consequences. When these functions coincide, there is one solution (or even a range of decision options) that, given the decision-maker's set of situational attributes, appears to satisfy his own goal and that of his superior commander. When there is tension between the two goals (ie when the functions do not coincide), the decision-maker must assign importance weights to each of the goals. He may also re-adjust his set of attributes in order to make his situation assessment consistent with these importance weights (some situation attributes may even be totally disregarded.) The way in which a decision-maker has been trained will have a bearing on his choice of weighting factors (and attributes). His operational experience will give him confidence in his choice of weighting factors and will help him to appreciate what changes in situational discriminators would make it appropriate for him to re-adjust the weights. Personality and emotional history will also affect the choice of weighting factor but will tend to be more enduring and would emerge probably as bias factors if we were able to gather enough data on the same individuals across many decision scenarios.

The results of the RPD experimental games show that subjective differences in participants' deliberate use (or non-use) of attributes to classify and assess (in terms of evaluated outcomes) their positions (and projections) in decision space appear to be an important driver in the selection of course of action. It is these subjective differences in the pattern-matching process that must be captured in future C2 models.

Non-linear utility theory offers a formal framework for defining the constraints, subjective utility functions and projection mechanisms for the determination of course of action based on resolving the tension between local and more global considerations by the decision-maker. This analysis takes a first step in bringing together the naturalistic, subjective and human aspects of the RPD pattern-matching process and the quantitative aspects of non-linear utility theory. The analysis of the experimental data has extended the previous theory and draws together the rapid-planning process and RPD.

The aim of the non-linear utility analysis is to provide a quantitative formulation for explaining the decision responses in terms of the situation assessment attributes, their probability densities (including the situation projections) and the subjective utility functions. The inter-relationships between these elements make decomposition difficult, but, if we are to inform defence investment decisions regarding the balance between personnel selection, training and CIS decision support, it is essential that we are able to understand their contribution within the contexts of the operational drivers.

Consequently, this theory begins to explain the ways in which information, situation priors and pattern matching, learnt comfort zones, fears and beliefs about the projected situation, training, local and global values all have an impact on decision outcome. It is still difficult to separate the proportional impact that each one of these has on the decision process in terms of variability of outcome. It is also not yet possible to provide a parameterization of the decision-maker, the situational attributes and the consequential utility values so that these can be fed into the model to produce a predicted decision outcome. However, the model does provide a means of representing C2 decision-making for constructive simulations of military operations that will improve the current class of C2 agents. The theory also allows us to model hysteresis more naturally. It should improve understanding, and hence measurement of, the relative impact of command information, training and selection with the additional benefit of informing design of CIS to suit the staff, processes and organizational structures given the specific nature of the operational situation.

In summary, the approach can be used to develop a form of the rapid planning process which captures the subjective elements of command in closed form simulation models of conflict (where it is appropriate to do so). This will allow us to explore the emergent properties of interactions between C2 agents within different types of network structures where they are sharing not only situational information but also values and beliefs.

References

1. Dodd L and Moffat J (2001). Discontinuities in command decision-making: minimising expected loss results in a catastrophe. Proceeding of the ICCRTS, Annapolis, June 2001.
2. Dodd L and Storr Maj J (2001). Command modelling using the catastrophe fold: some military examples DERA unpublished report.
3. Dodd L, Moffat J and Richardson SB (2002). Defining new landscapes for control and influence to determine the value of information. Proceeding of the 19 ISMOR, August 2002, Eynsham Hall, Oxford, UK.
4. Glimcher PW (2004). Decisions, Uncertainty and the Brain; The Science of Neuroeconomics. The MIT Press: Cambridge, MA, USA and London, UK.
5. Keeny RL and Raiffa H (1976). Decisions with Multiple Objectives. Wiley: New York.
6. Klein G (1997). The recognition-primed decision (RPD) model: looking back, looking forward. In: Zsambok CE and Klein G (eds). Naturalistic Decision Making. Lawrence Erlbaum Associates: Mahwah.
7. Mathieson GL (2001). The impact of information on decision making. In: Proceeding of the International Symposium on Military Operational Research, Defence Science and Technology Laboratory, DSTL/JA02207.
8. Moffat J (2000). Representing the command and control process in simulation models of combat. J Opl Res Soc 51: 431–439. | Article |
9. Moffat J (2002). Command and Control in the Information Age; Representing its Impact. The Stationery Office: London, UK.
10. Moffat J and Dodd L (2000). Bayesian decision making and catastrophes DERA unpublished report, August.
11. Moffat J and Witty S (2002). Bayesian decision making and military command and control. J Opl Res Soc 53: 709–718. | Article |
12. Moffat J, Campbell I and Glover P (2004). Validation of the mission based approach to representing command and control in simulation models of conflict. J Opl Res Soc 55: 340–349. | Article |
13. Perry W and Moffat J (2004). Information Sharing among Military Headquarters; The Effects on Decision Making MG-226-UK, The RAND Corporation, Santa Monica, CA, USA.
14. Saunders MJ and Miles J (2004). How can network enabled capability contribute to better command and control? Proceeding of the 9th ICCRTS (www.dodccrp.org), Copenhagen, September.
15. Smith JQ (1979). Mixture catastrophes and Bayes decision theory. Mathe Proc Cambridge Philos Soc 86: 91–101.
16. Smith JQ and Harrison PJ (1979). Discontinuity, decision and conflict from Bayesian statistics. In: Proceedings of the First International Meeting. Valencia, Spain, 28 May–2 June.
17. Smith JQ, Harrison PJ and Zeeman EC (1981). The analysis of some discontinuous decision processes. Eur J Opl Res 7: 30–43. | Article |
18. Smith JQ, Dodd L and Moffat J (2005). A Bayesian Reconciliation of Conflicting Objectives in Command and Control. To be published, QinetiQ Malvern.
19. West W and Harrison PJ (1997). Bayesian Forecasting and Dynamic Models. Springer: Berlin.

Acknowledgements

The experimental results in this paper are drawn from an experiment designed and run by Graham Mathieson of Dstl and Paddy Turner of QinetiQ to whom we express our sincere gratitude. The peace-keeping scenario was devised by our military Intelligence Officer Jon Lee and we received further expert military support and guidance from Lt Col Merfyn Lloyd, Maj Harry Duncan, Maj Andy Parsons, Maj Charles Cooper and Gen Sir Rupert Smith. We also thank the 24 military officers who were the willing participants. Finally, thanks to our technical reviewers Dr David Marsay and Dr Brian Bramson with technical support from Sean Richardson, Robin Poulter and Dr Andy Belyavin, and last but not least, to our MoD sponsors and advisors DG(S&A).