Crime News and Racialized Beliefs: Understanding the Relationship

Group Decision and Negotiation, 1994, Vol. 3, No. 2, (237-261).

Decision Making and Decision Aiding: Defining the Process, Its Representations, and Support ‡

Gregory E. Kersten * and Stan Szpakowicz ** * DAL, School of Business, Carleton University

** Department of Computer Science, University of Ottawa

Abstract

We present a formalized account of decision making as a multi-step process that involves several classes of participating entities. A series of increasingly formal representations of the decision problem are developed, from a mental model conceived by the decision maker to a knowledge base that may be used in a decision support system.

1. Motivation

We have been working on the development of decision problem representations to support decision making agents. We have now reached the conclusion that the commonly used definitions of decision making are not adequate. They do not encompass all the relevant elements of the process and its stages.

In this paper, we attempt a definition of the decision problem and the decision making process, and discuss the implications of the new definition for the field of decision representation, analysis, and support. We would like to lay the foundations for various methods of representing decision making processes within the world of the agent. The world boundaries may be differently delineated, and its entities variously differentiated or amalgamated. Each particular choice means a new perspective of the same decision.

The long-term purpose of the work reported in this paper is the creation of a complete theoretical basis for the Negoplan project. This is a project in decision analysis and support that may, in

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specific circumstances, be extended toward hybrid (human-machine) decision making and ultimately toward autonomous decision making.

2. Nine Steps in Decision Making

2.1. Four Steps

People make and implement decisions because they want to achieve goals and to prepare for future decisions. Decision making is, therefore, an evolutionary, causally motivated reasoning process. It comprises four steps (Simon, 1960; Fredrikson, 1971; Witte, 1972)

1. recognize the problem or realize that a decision must be made, 2. evaluate the agent’s objectives and preferences, 3. analyze the decision problem and its constraints, and develop alternatives, 4. choose among alternative decisions.

For example, consider the decision to purchase a house: (1) an agent realizes that she needs a new house, (2) she considers such objectives as price, size and neighbourhood, (3) gathers information about available houses, financing options, determines trade-offs and compares different models, and (4) selects a house. Obviously, the agent may loop between consecutive steps or return to any previous step whenever new information becomes available.

2.2. Two perspectives

The last of four decision making steps listed in the previous section is only part of the decision making process. It is not sufficient to select the best alternative. “Effective decision makers devise plans to carry out their decisions. They anticipate the likely setbacks and are ready with countermeasures” (Wheeler and Janis, 1980, p. 9). This is often a strategic aspect because the agent needs to consider actions and reactions caused by the chosen decision.

The house purchase decision may be strategic insofar as it changes the agent’s life-style or status, influences the children’s education, and so forth. Strategic decisions usually lead to other decisions. This introduces an additional complexity to the process. Alternative houses are then evaluated from a dual perspective.

One perspective is determined by the goals that the agent expects to achieve with the purchase of the new house, that is, by direct decision outcomes (such as more living space, comfort, prestige). The second perspective is established by the goals that the agent wishes to reach in her subsequent decisions. These will be made in the circumstances created by the implementation of

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the frst decision. For example, she may want to buy new furniture, have to find a better paid job to pay the mortgage, or become interested in gardening.

The two perspectives are present when decisions “are … better seen as strategic first-move interventions in a dynamic internal system than a choice in a classical sense” (March, 1988, p. 41). The perspectives may conflict. The agent’s current objectives and preferences may be at odds with her evolving (and not always fully determined) future objectives and preferences.

Important decisions are often analyzed for their ability to change the situation beyond the direct goals and outcomes. For example, an agent may decide to continue college education and choose a particular discipline because this can lead to an interesting job which will provide satisfaction and funds for opening a business, which in turn will increase personal wealth. Strategic decisions set the stage for other decisions; these may be strategic decisions, too, and so on.

To see how a decision influences the subsequent decisions, it is necessary to analyze the results of the implemented decision. We therefore recognize two more steps in the decision process:

5. implement the decision, 6. determine and evaluate the impact of the implemented decision on the agent and her

situation.

2.3. Individuals

Levin (1936) theorized that individual behaviour may be understood in terms of interaction between the environment and the agent. Without a clear analysis of the two and their interactions in any particular situation, one cannot understand the meaning of an indvidual’s behaviour.

Levin’s environment is rarely uniform. A decision process often involves participants other than the agent. For example, the agent’s friends, spouse, a real-estate broker may be involved in the purchase of a house. Such individuals may influence the decision process and may be affected by the decision outcomes. They ought to be introduced into the decision process as separate entities. The complexity of the process increases again. More individuals must be accounted for in the decision process, more elements represented, and more mental effort expended to reach a decision.

We must determine how the individuals react to the decision, how its implementation influences them and how subsequent decisions may be affected. We add two steps to the decision process:

7. represent individuals other than the agent, 8. determine their actions and reactions.

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The introduction of multiple participants extends individual decision making with interactions between the agent and the other individuals and among the others. Such interactions may take on an additional meaning of negotiation and group decision making. Concepts and paradigms such as conflict resolution, concession, consensus and strategic interaction become applicable and useful.

2.4. Environment

Decisions are made in a given setting or situation. The “agent’s world divides up into a collection, or succession, of situations: situations encountered, situations referred to, situations about which information is retrieved, and so on” (Devlin, 1991, p. 30). A situation explicitly represents entities at a given time. The agent individuates other participants because they are closely involved in the process, can be clearly identified, and individually represented.

A decision situation also consists of numerous other entities that must be taken into account because they influence the implementation of the decision and its outcomes, but need not be identified and separately considered. For example, different agencies, institutions, and markets need not be individually represented, but their outcomes such as interests rates, mortgage conditions, or government housing programs must be considered in a house purchase decision.

The numerous individually unidentified entities constitute the decision environment which changes spontaneously, and also because of the agent’s decision. The environment, a broader context in which the agent makes decisions, is characterized by information about its past, present and possible future states but not about its structure. The individuals are separately considered entities, whereas the environment is a group of entities that the agent does not see as distinct.

To consider the environment, we add one final step to the decision process: 9. develop the state of the environment during and after decision implementation.

If no participants other than the agent must be distinguished in the process, the individuals’ needs and requirements may be “folded” into the environment. More things are observed within the environment than would be if we insisted on keeping some entities separate. In a simple, routine decision, the behaviour of the individuals may be considered constant. That is, they do not change their behaviour when the decision is chosen and implemented. In such a case they may be treated as if they were part of the environment. Their requirements and goals would be added to description of the decision problem.

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The structuring of the situation (the distinction between the agent, the other individuals, and the environment) depends on the agent’s cognitive ability to separate entities, and on her perceived need to consider individuals in isolation from the environment.

The nine-step organization means that replicating the decision making process in a formal way is complex and often time-consuming. Moreover, it is a process whose intellectual and computational complexity increases with the number of participants, the size of the environment, the number of future decisions which are considered, and interactions between the participants.

3. Representations of Decision Processes

3.1. The World and Its Elements

In discussing the decision making process we introduced three classes of real, distinct, interacting entities. These classes are:

• the agent who makes decisions (A), • the other individuals (Ij, j = 1, …, n), and

• the environment (E).

Three types of entities are drawn from these classes at any given time. The agent is always the same, and the environment is treated as a super-entity (its elements are not differentiated). The other individuals vary in time (they come and go, or become irrelevant, or inactive).

The agent, the other individuals and the environment constitute the world:

W = (A, {Ij}j = 1, …, n, E, R), (1)

where R is a set of all possible relations between entities.

W is assumed to be closed in the sense that no information from outside of W can be obtained to make and implement decisions. W is also assumed to be complete; the agent does not need anything more than given in W. Each entity in the world has its own place and it may have its own internal structure. W can be viewed as a schema of the world and provide a point of reference for particular situations and for the development of representations of situations.

Entities are involved in situations. A situation comprises information about each entity, its relationship with other entities, and possibly its structure, needs, restrictions and expectations. This information is collected by the agent and used to solve the decision problem.

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Situation theory encompasses the world in a given state, or the maximal situation, and the situations of individuals and entities which comprise the world (Devlin, 1991, pp. 49-85). The situation of an entity is both its state at a given time and relationship with other entities. For example, when an agent wants to purchase a house, she becomes a house-buyer with specific goals and specific purchasing abilities. If she considers a real-estate broker as a participant, she enters a broker-client relationship. The broker becomes an individual in this situation.

Formula (1) describes the general structure of the world. At any time t the world is described by:

Wt = (At, {Itj}j = it1, …, itnt, Et, Ht). (2)

At represents the same agent as always. We use the superscript to express the fact that the agent’s perception or situation may be different at different times. {Itj}j = it1, …, itnt, (nt ≤ n) is a set of

individuals Ij at time t which is selected from the set of all {Ij}j = 1, …, n. Et is a selection from E,

and Ht is the history of the world, which contains elements and relationships from previous worlds Wt-1, Wt-2, …

The descriptions A, {Ij}j = 1, …, n, E, R are unilateral: we are interested in capturing the

ontological structure of the world. The descriptions At, {Itj}, Et and Ht of entities at time t are

bilateral: they include specifics of entities, as well as relevant relations in which these entities are involved. The elements of R relevant to the situation at time t are, then, distributed throughout the description of the world.

The world description Wt contains the entities and relations from W that the agent individuates and describes at time t. Using Yu’s terminology, Wt is the agent’s habitual domain which she can access (Yu, 1985). For example, if the agent is about to decide to buy a house, the world may contain her family, houses that she had seen previously, her financial situation and her preferences. At time t this world will not contain real-estate brokers if the agent does not know or contact any.

Wt describes a specific situation which the agent can perceive and in which the entities may find themselves. What elements of W enter Wt, how specific is their structure, what is the level of detail of their description and which elements of R are actually present in Wt depends on the expertise and cognitive abilities of the agent and the others who help her make a decision.

Note that we also allow the number of individuals to vary. Not all Ij go into a situation Wt. We

may focus on any of them, maybe none. We may select entities from the environment and consider them as separate individuals. Continuing our example of an agent purchasing a house,

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this may be illustrated by the agent initially not considering banks and trust agencies but only mortgage rates. When she decides to buy a house, she may need to negotiate the terms of payments with a particular bank, which then becomes an individual.

Situation theory makes it possible to consider the passage of time as a sequence of situations. If we assume discrete time, the length of time periods is subjective and depends on the agent’s perception of the situations. The agent moves from one period to another when the situation of at least one element of Wt changes. Such a treatment of time enables us to measure time by cycles of the agent’s cognitive process, moves of an inference engine, or steps of an algorithm. We omit the time/situation index only when we consider a one-shot decision and the decision outcomes are not viewed as part of the world but as a separate entity.

3.2. Representations

Wt is the agent’s perception and understanding of the world at time t. When the agent recognizes the need make a decision, Wt is reconstructed and turned into a representation useful for solving a decision problem. We consider a representation Wt of the world Wt. The representation is a set of mental images and constructs—the effect of the agent’s conscious and purposeful effort. The images and constructs describe the world and its elements in a given situation for the specific purpose of solving the decision problem. Insofar as we stay at the level of mental models (as opposed to formal or computerized representations and inference procedures), this is the real world, although reduced to the relevant entities.

The purpose of the progression from W and Wt to Wt is to develop a representation necessary to make a decision. The progression reflects the agent’s evolving understanding of the overall situation at time t, and of elements of this situation relevant to decision making. This involves five principal actions:

1. choose elements and their structures from Wt to be represented in Wt, 2. isolate elements and relations between elements of At and {Itj} that describe the

agent’s preferences, assumptions and expectations, 3. isolate elements and relations between elements of At, {Itj} and Et that describe their

resources, restrictions and abilities directly influencing the choice of decision, 4. isolate the history Ht, 5. isolate the dynamic aspects of world Wt which are used to compare, analyze, reason,

and make calculations—and package them separately from Wt.

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The first action is to decide what elements are relevant and how they should be represented. This usually involves simplification; it makes the elements of Wt that correspond to A, {Ij} and E less

rich than what is found in Wt. At contains the agent’s goals, preferences, assumptions and expectations about herself. These are separated in order to develop the agent’s representation At. That is, At is a description of the agent’s goals, etc. as well as relationships between these elements. Similarly, the preferences, assumptions and expectations of the individuals are also separated and used to develop representations {Itj} which later can be used to determine the actions and reactions of the individuals. The construction of At and Itj is the second of five

actions.

The remaining characteristics of the agent, the other individuals and the environment are examined in the third action. They do not describe the behaviour of the entities—reactions to the agent’s choices and independent actions have already been taken into account in the second action. The third action is to consider elements and relationships which describe the present conditions of decision making. For example, the list of houses for sale belongs to the environment, but the agent needs to separate them from it in order to develop a list of houses that she can purchase at time t..

The conditions of decision making include resources, restrictions and abilities of the agent, the other individuals and the environment. The agent needs to take all that into account to determine a feasible set of alternative decisions. Therefore, these interrelated elements are separated into a description of a decision problem Pt. For example, the resources of a home buyer, such as the available down-payment for the house, the monthly income, or the spouse’s income are elements taken from At and introduced into Pt. Information from a bank about the available mortgage may also become part of Pt.

We need a criterion for deciding what becomes a part of Pt and what constitues the representations At, {Ijt} and Et. Such a criterion should reflect the distinction between elements

necessary to determine an alternative without considering the effects of its implementation and elements required to determine the reactions and behaviour of the agent, the other individuals and the environment if this alternative is chosen and implemented. In effect, Pt is created in order to determine a set of feasible alternatives. At, {Ijt}, and Et serve to evaluate and analyze possible

actions and reactions.

At and Pt are built from the agent’s knowledge of W, and from information available at time t. They can be viewed as specific constructs, in the sense that the entities and their elements are now in a particular and known relationship and that they were selected for a particular purpose. W

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is a set of all possible constructs and relationships that, according to the agent’s knowledge, can describe the world. Wt consists of entities and relationships of which the agent is aware at time t. Wt contains elements chosen to make, evaluate and implement a decision and determine its outcomes.

The agent’s knowledge of the history is isolated in the representation Wt because it is used to verify the appropriateness of Wt and to determine elements of future representations Wu, u > t. For example, the agent may use the history of her monthly income to estimate her monthly income in future. Ht denotes the elements of the history Ht that the agent has separated in the fourth action for the purpose of making a decision at time t.

The representation Wt is transformed and manipulated in such a way that a decision can be determined and evaluated. Reasoning, computation and other operations in Wt need to be identified, and their roles and applicability established. The fifth step of the construction of Wt identifies such operations. They do not go into representation Wt because they operate on it and its elements, and because they may be enhanced with other mechanisms external to the agent. The agent’s reasoning, computation and other dynamic aspects are grouped in set TA (see the next section). Note that elements of TA do not change in time. They are either the agent’s own

reasoning mechanisms, or mechanisms available to her and extending her reasoning and computational capabilities such as computer-based support systems.

We have introduced three levels of conceptualization of the world. The agent is obviously the key, and it is important to recognize the differences between A, At, and At. Generic categories, constructs and mechanisms the agent can use to describe the world and reason about it are grouped in A. The difference between A and At is that between constructs and mechanisms which may exist, and constructs and mechanisms available to the agent at time t.

At only partially represents the agent. It describes the agent’s biases, preferences, subjective probabilities, goals and objectives. In the decision making literature it corresponds to the subjective and real agent At, whose rational and idealistic model was developed by von Neumann and Morgerstern (1944). In the decision support literature At is often the user who interacts with a support system.

All in all, we have:

Wt = (At, {Itj}j = it1, …, itnt, Et, Pt, Ht ) (3)

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Formula (3) provides a rich description of the world from which representations of the agent and the problem may be constructed. The distinction between the agent and the decision problem is a cornerstone of the decision theory which distinguishes between the model decision maker and the model decision problem (French, 1986, p. 343). It is also a basis for decision support which often is concerned with the problem while the agent is an entity external to a decision support system.

The specific constructs derived from the reformulations of the world W, its situations Wt (t = 1, 2, …) and its descriptions show that although a decision problem Pt does not belong materially to the world, it is a product of the analysis and reformulations of the world’s descriptions. Pt is the product of the agent’s thought processes based on her perception, reflecting her needs to make a decision.

At is the description of the agent which, with the help of decision theory, may be transformed into a model decision maker. Pt can be transformed into a model decision problem. The remaining elements of the world description Wt constitute the decision problem context which the agent has to take into account for the decision to be implemented and its outcomes evaluated. Two super-entities emerge from this discussion of the development of the representations required to choose a decision alternative and to make and implement a decision. The agent and the decision problem constitute the world description in a narrow sense (we indicate this by adding the subscript N):

WNt = ( At, Pt ), (4)

and the remaining entities make up the decision context:

({Itj}j = it1, …, itnt, Et, Ht ). (5)

If the decision context is absent, formula (4) denotes the amalgamation of all entities but the agent. It is a typical decision-theoretic problem description that views decision making as the development of one problem structure. The only active entity is the agent who analyzes, manipulates and solves the problem. The solution encompasses only the direct outcomes of the decision (see section 2).

One of two basically different approaches to decision making limits decision-making to formula (4). The second approach emphasizes the fact that the entities A, Ij (j = 1, …, n) and E are active

and, therefore, includes formula (5). These entities act, interact, make decisions, respond and react. Therefore, they must be separately described, and their structure and interrelations determined. The decision making process manifests itself in connections between the active entities.

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3.3. Transformations and Control

The world Wt+1 results from decisions, actions and reactions of the entities in world Wt, which also change themselves. We can denote this transformation by T, and stipulate the existence of a corresponding transformation T between Wt and Wt+1. Note that Wt (t = 1, 2,…) are representations, so that T produces representation which the agent uses to make decisions in world Wt+1. To do so the agent uses description Wt.

Wt arose from the analysis of Wt. Similarly, Wt+1 corresponds to Wt+1. To establish this correspondence, we distinguish three types of transformation mechanisms:

1. mechanisms TA are under control of the agent, 2. mechanisms TI are under control of the individuals, and 3. mechanisms TE govern changes and transformations of the environment.

The basis for decision making is the existence of choice. Traditionally it is assumed that the agent has choice from among the alternative decisions. This choice implies that, for a given description Wt, the agent can choose among competitive transformation mechanisms from TA, and control

their application. Let C denote whatever choice and control devices the agent can use. We assume that these devices, like the transformation mechanisms, do not change in time.

We can represent T as a structure:

T = ( TA, TI, TE) (6)

The process that leads to the determination of a decision δt at time t can be summarized as follows:

(C, TA)

( At, Pt, Ht ) —> δt. (7)

When decision δt has been implemented, the other individuals and the environment react to it. The agent can assess these and other repercussions of the decision for the descriptions and transformations that she had developed. The situation of the individuals and the environment at time t+1 arises from transformations TI, TE applied to Wt:

TI

({Itj}j = it1, …, itnt, Ht, δt ) —> {It+1j}j = it+11, …, it+1nt+1, (8)

and

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TE

( Et, Ht, δt ) —> Et+1. (9)

Decision δt and the new situations determined for the individuals and the environment directly influence the realization of the agent’s goals, objectives and preferences at time t+1. At time t they were described by At. Their realization is given by At+1, obtained by applying the choice and transformation mechanisms under the agent’s control:

(C, TA)

( At, δt, {It+1j}j = it+11, …, it+1nt+1, Et+1, Ht ) —> At+1. (10)

Note that in formula (10) we have the same set of mechanisms as in (7). In (7) the agent used goals, objectives and preferences to determine a decision. After the decision has been implemented, it prompts reactions of the individuals and the environment. The agent determines At+1 by taking into account these reactions as well as spontaneous actions. She can only use the transformation mechanisms under her control. If there is a choice among the available transformation mechanisms, the agent can apply the available choice mechanisms.

Formulae (7)-(10) formally represent all nine steps of the decision-making process and all the entities, and they introduce all the elements that can be involved in the process. Formulae (3) and (6) - (10) can be drawn together to express the fact that the agent can use the choice and transformation mechanisms to determine the world description at time t+1:

(C, T ) Wt —> Wt+1. (11)

The decision outcomes, as they are considered in decision theory, need not be explicitly presented. This is because decision making as described by (7), (9), (10) can be viewed as a process of choosing the transformation and control mechanisms (C, T) that lead to a new world situation (Wt+1). For given descriptions of the agent, the other individuals and the environment, the decision problem can be reduced to selecting from C, TA the choice and transformation mechanisms from C, TA. The choice of the mechanisms implies the choice of a decision. For

example, if the agent established a list of houses and their attributes, and knows her preference structure, the choice of a house depends only on the method used to compare houses.

4. Modelling

4.1. Mental Images and Structural Models

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Representations, transformation and choice mechanisms included in Wt, T, C respectively, are the agent’s internal (not externalized) insights and reasoning rather than something formal and well-defined. Wt consists of mental images constructed by the agent. The agent’s own processing capabilities and control mechanisms are represented by T and C. A mental image need not be formal, is not associated with any theory, and does not have a well defined solution procedure. An image of the real world is as the agent develops it, the development need not conform to any rules.

We distinguish between a mental image of the real world as it is perceived and internalized by the agent, and its models (formal representations) such as those used in decision theory, systems science and artificial intelligence. A model is obtained from the direct application of a theory, explicit assumptions, and the use of a rigorous method and scientific apparatus. It is a mathematical or logical representation that encapsulates some part of the world within the confines of the relationships constituting a formal system (Casti, 1989). Models are fixed in that they portray a given situation in terms of a given set of symbols, parameters, and relationships.

World W defined in (1) is the point of departure for the development of mental images, transformations and choice mechanisms. W represents the agent’s knowledge about herself and the world, and it provides a framework for determining Wt and Wt which are defined by observables. Models are built in formal systems such as symbolic logic. Apart from the usual purely formal operations on symbols, domain-specific axioms may be required to build a theory of a domain. For example, one could include the axioms underlying rational behaviour in decision making, formulated by von Neumann and Morgerstern (1944).

The formal system we propose to use is first order logic (FOL). In it, we may build declarative models which are formal representations of the mental images from Wt. They describe the structure of mental images with explicit relationships between elements. These models are qualitative and structural. They identify the significant elements in a representation, and determine their place in the situation. A structural model at of the representation At of the agent at time t can be a FOL formula. Similarly, FOL formulae derived from the respective mental images Itj, Et would represent the other individuals (ijt, j= 1, …, nt), and the environment (et). A

formal counterpart of formula (3) can be:

wt = (at, {itj}j = 1, …, nt, et, pt ) (12)

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We do not model history Ht from formula (3). Formal models describe a situation at time t. History can be used to verify the appropriateness of the models, determine parameters unobservable at time t whose past values are known, or evaluate future situations.

Structural models were traditionally of interest mainly to behavioural scientists concerned with the development of qualitative models for the interpretation of social phenomena. Systems science, cognitive science and artificial intelligence have lent the process of modelling a formalization and rigor often neglected in behavioural sciences.

The structural aspect has been long recognized within decision theory. The approach to solving a decision problem based on the decision-theoretic framework reduces the problem to three subproblems:

1. develop a set of decision alternatives and their possible outcomes, 2. determine the probabilities of possible outcomes if the competing alternatives were

actually implemented, 3. develop a preference structure and represent the utility of possible outcomes.

An important limitation of decision theory is that it neglects the first of these steps. It concentrates on choosing the best alternative from a fixed set. The most difficult part of an analysis—problem structuring which translates ill-defined mental images into models and procedures—has been often left to a decision analyst and considered more an art than a science.

In the introduction to this paper we said that we are assembling a theoretical basis for the Negoplan project which attempts to create a framework for decision support and, in specific circumstances, for autonomous decision making. An important part of the project is to develop structural and qualitative models representing the three classes of entities specified in formula (12). In Negoplan we clearly separate the interacting entities and the inference processes by which the agent determines decision alternatives, evaluates their impact on the individuals and the environment, and constructs her own representation (Kersten et al., 1991).

Negoplan is obviously not the first approach that attempts to build structural models. A number of methodologies concentrate on the development of structural and qualitative models. One of the better known is cognitive mapping introduced by psychologist Tolman (1948) to represent an individual’s internal perception in a form that can be analyzed by others. Several techniques based on cognitive mapping were developed within the operations research and systems science (Eden, 1989). Checkland (1981) developed a soft systems methodology to represent structures of

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autonomous individuals and their actions and reactions. Friend’s approach (1989) focusses on the development of structural models for incremental decision making.

Negoplan uses FOL to develop structural models of entities. These models, mentioned in (12), are sets of well-formed formulae. The use of FOL makes it possible to apply logic-based inference mechanisms to determining the properties of the models. It is possible to check a model’s validity, logical consistency, satisfiability; and to introduce causal relationships between different entities and between the same entity in different situation. While other approaches to the development of structural models often concentrate only on building the representation, the Negoplan method also includes analysis and verification (Kersten et al., 1990).

4.2. Measurement Models

Decision theory, as many other theories which use the mathematical apparatus, is concerned with measurement. One approach within the decision-theoretical framework is based on the utility theory whose key assumption is the existence of a scalar function that describes preferences of alternatives when their outcomes are uncertain. Another approach accepts that the specification of the utility function is not possible and calls for comparison of alternatives with respect to multiple objectives. These approaches assume that the set of decision alternatives is given either implicitly or explicitly. The focus is on the choice of an alternative under the assumption that there exists a measure for comparing alternative decisions. The measure can be elicited from the agent, for example using one of the decision analysis technologies, or the agent is directly involved in the choice if she can compare alternatives. The latter case is considered within the framework of multiple objective decision making.

The underlying assumption of decision theory is the ability to measure. The question of developing representation of situations, or—if we use Howard’s drama metaphor (1992)—creating scenes, is rarely considered. It is not the structure of the world that is the main concern, but rather the possibilities that a particular structure offers to the agent. Therefore, many approaches begin when the models that constitute the world wt are given; this is the case with, for example, multiple criteria decision making models or optimization models (Zeleny, 1982; Yu, 1985). Other approaches assume that the world is not modelled but the agent has created its internal representation as in (3). The agent uses the mental images and determines the set of available alternatives or options. Analytical methods are used to determine the preferred alternatives and their outcomes (Frazer and Hipel, 1984; French, 1986).

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We said that these methods are concerned with measurement, and therefore we call the models that are used to measure things measurement models. Measurement models play an important role in decision making. They enable the comparison of alternative decisions, determine the strentgh of relationships between elements of a structure, assess the probability of actions and reactions of the environment, and directly include the quantitative elements of history into decision making.

At the beginning of the Negoplan project we disregarded the quantitative aspects of the decision problems. We made this decision to determine the expressive power of logic in modelling decision problems, and its applicability to manipulating structures. We viewed the decision making process primarily as the process of manipulating structures, of determining the situation of the agent and other entities. The quantitative aspects which are determined with the measurement models were considered as secondary.

An important aspect of using logic is the ability to view the structure as primary and the quantitative aspects of a problem as secondary. The distinction between the qualitative, structural aspects of the decision problem and the quantitative aspects is an important feature of Negoplan. This is not to say that the quantitative aspects are not relevant and do not affect decisions. In fact, their unavailability can make some elements of a structural model unusable. For example, the agent may be unable to determine monthly payments for a house she want to purchase, and therefore abandon the transaction. The quantitative aspects may also cause modifications in the structural models. For example, if the interests rates increase significantly, the agent may revert her decision to buy a house, and consider renovating her present house.

The assumption of primality of the qualitative aspects allows us to introduce measures as parameters of structural models. Measures are obtained from quantitative models which are not separated from the structural model. For example, suppose that the agent has created a structural model for the house purchase problem. One of the parameters of the model is a monthly mortgage payment. The value of the payment is then calculated outside of the structural model, using an appropriate quantitative model. A quantitative model can also be used to determine the possible appreciation of the house value, another parameter of the structural model.

The two examples show how the structural models introduced in formula (12) may include numerical parameters if required. Such an approach to modelling seems natural, because representation of knowledge—formula (12) is such a representation—is assumed to be qualitative and not quantitative (Newell, 1982; Simon, 1991).

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Introduction of numerical parameters and quantitative models requires that formula (12) be replaced with:

wt = (at(Xa), {it(Xi)j}j = 1, …, nt, e(tXe), pt(Xp) ) (13)

where each Xx = [Xix] i = 1, …, nx, x = a, i, e, p, is a vector of endogenous variables computed from model Xix = ƒix(Ylix) l = 1, …, mi. Ylix is an exogenous variable that is directly observable in the

world Wt (including the history Ht). The interpretation of formula (13) is that each structural model may include one or more parameters which are values of endogenous variables computed from a model with exogenous variables. To simplify the notation we assumed that each parameter value can be obtained only from one model.

4.3. Decision

Formula (7) states that a decision arises from an application of control and transformation mechanisms to the descriptions of the agent At, decision problem Pt, and history Ht. We said in the previous section that we do not include history explicitly in the structural models. Let us replace At, Pt from formula (7) with their counterparts from formula (12). Let us also stipulate the existence of formal control mechanisms c and transformation algorithms tA that correspond to C and TA. We get the formula

(c, tA)

( at, pt ) —> dt, (14)

where dt is a formal representation of δt.

We said that we wanted to consider difficult and complex problems. They cannot be dealt with by applying a procedure, well known to the agent, that has repeatedly solved the same simple problem. Solving a complex problem requires the agent to reformulate the problem representation (Weber and Coskungulu, 1990). The agent develops a problem representation, determines a solution, analyzes it, then modifies the problem representation, obtains a new solution, and so on. This means that developing problem representations and solving problems are two interwoven processes that influence each other (Mayer, 1989, p. 49). According to Duncker (1945) solving a problem means continuous narrowing of the range of options through modifications of representations. The problem representation becomes more specific possibly to a point that there remains only one alternative to consider.

Formula (7)—and its formal counterpart (14)—may be reapplied iteratively. This would reflect the way in which people solve complex and difficult decision problems. The consequence is that

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both the mental image of the decision δt and its representation dt are hierarchical structures of interrelated elements (for example, directed acyclic graphs). Such structures contain goals that the agent does or does not realize, and elements of the decision problem relevant to a given decision alternative. In the house purchase example, a decision alternative would not be a particular house, its price and mortgage, but a graph which includes all these elements, relationships among them, the level of the agent’s satisfaction with this choice, and other goals that she may have.

Typically, decision analysis and support assume that the agent has a complete structure describing the decision problem, and the analysis and support focuses on the selected elements of this structure. These elements are the decision attributes. The reasons of their relevance to the agent, her goals and values do not enter the picture. The exchange of information between the agent and the support system is limited to a sequence of unrelated attribute values. The relationship and analysis of what a particular sequence means for the agent has to be done by the agent herself.

We can make the dependence on variables explicit and so enhance formula (14) just as we had rewritten formula (12) into (13) :

(c, tA)

( at (Xa), pt (Xp) ) —> dt (X*), (15)

X* is a vector of values of elements of Xa and Xp which were computed for the decision dt. Some elements of Xa and Xp may remain undetermined if the alternative at hand does not require their

values or if the agent is unable to secure the necessary data.

The view of a decision as a hierarchical structure is similar to that taken in the analytic hierarchy process (Saaty, 1990). The difference is that AHP uses one hierarchical structure (goal decomposition) to determine the importance (weights) of goals and subgoals. We propose to separate the goal representation from the problem representation. More importantly, the weights or preferences are secondary to the decision making process. The agent need not use them if she prefers only to modify the representations and not compare some of their elements. This enables the agent to use a holistic viewpoint. The use of logic also allows to analyze and evaluate alternatives with or without the quantitative preferences.

We distinguish between the decision as it is seen by the agent and as it is implemented. The former, given by formula (15), involves all the logical statements (possibly with parameters) that are relevant to a particular alternative. The latter contains only those statements which the agent wants to announce to the other participants, and which can be implemented. For example, a house purchase decision alternative perceived by the agent may include a description of the agent’s

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goals that this alternative satisfies, as well as the considered house, neighborhood, financing, and the market situation. The implemented decision may consist only of such elements as the house, the price the agent is willing to pay, and the value of the mortgage.

We propose, and this approach is being taken in the Negoplan project, to use many structures, each describing a different entity, and to manipulate them so that we can obtain a structure relevant to a particular alternative and determine possible reactions of all entities to this alternative (Matwin, et al, 1989). This enables us to differentiate goals and subgoals for a particular situation and use different measuring mechanisms, for example both utility and flexibility (Kersten and Szpakowicz, 1990).

The decision making process requires the establishment of the impact of a decision on future situations. This requirement was introduced in formula (11). Determining future situations introduces a possible feedback between these situations and the current decision. The agent may need to modify representations when she realizes the direct and indirect decision outcomes. In Negoplan this feedback mechanisms are modelled with logical statements that describe causal relationships between the agent and the other entities. These statements enable us to link the different steps of the process into one consistent sequence of actions and reactions. They also enable us to introduce changes in the representations caused by particular actions.

Feedback mechanisms used to relate structures describing different entities and modifying these structures when the situation changes, are conceptually similar to feedback mechanisms which link representations at (Xa), pt (Xp) and decision dt (X*) and which cause possible modifications

of the representations as discussed by Mayer (1989, p. 49). Such mechanisms can also be modelled with logical statements (Kersten et al., 1991)

5. Decision Support

5.1. Support Environments

Since the mid-1960s a considerable effort has gone into the development of computer-based decision systems, but “neither decision analysts nor knowledge engineers have been particularly successful in developing a comprehensive methodology for creating decision systems that truly assist decision-makers in all aspects of the decision making process” (Holtzman, 1989, p.7). In most instances, decision support is passive and narrowly focussed—the use of decision aids requires quantification of alternatives (Mayer, 1982, p. 24). It is used for parametric analysis, generation of alternatives, preference elicitation, or determination of chunks of knowledge that

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are relevant to a situation at hand. Although this type of support may be quite complex and useful, it adresses only the problem of choice and its quantitative implications.

There is a need for systems that can actively interact with an agent to formulate, reformulate, evaluate and apprize problem descriptions. The available technologies and formal methods enable the development of systems which provide support throughout the process as it is outlined in this paper. Such technologies may become an integral part of the agent’s processes of building representations and solving problems. Research has been initiated on this type of support, which offers an integrated support environment rather than a set of specialized tools for one aspect of the problem. The most notable example is Geoffrion’s structured modelling environment which is a hybrid information/analytical modelling system (Geoffrion, 1987, 1991).

The structured modelling environment supports model building, data processing and report generation. In contrast with other support systems, the modelling environment consists of interacting entities that perform special functions, are logically separated, and can form hierarchies which describe particular situations.

The structured modelling environment is based on the principles of information processing and quantitative modelling. It aims at providing an agent with a methodology of developing structurally connected activities required to solve a complex problem. The complexity stems from the number of variables, their interrelationships, constraints, and so on. While the Negoplan project also aims at creating a set of tools and mechanisms to develop a support environment, it builds upon the logic-based modelling principles and interaction between multiple objects in space and time. This will help represent interactions between these objects and enable the agent to “see” the roles of different objects and the causes of actions and reactions.

5.2. Levels of Support

According to our considerations in the preceding section, two distinct types of activities may be supported: developing descriptions and determining solutions. Therefore, we have two types of support: support for modelling and support for solution.

Support for representation gives assistance during the development of structures, helping the agent to clarify her mental images, determine relationships between them, and develop a formal representation of the world and its elements. The focus is on identifying the relevant entities and their components, that is, on decomposing the world into mutually related elements. The degree of decomposition is determined by the need to obtain structures sufficiently detailed to understand the decision problem, make a decision and evaluate its implications.

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We propose to further distinguish between support for mental modelling (of descriptions included in Wt), and support for formal modelling (of models included in wt).

Support for the development of mental images is relatively simple. It involves receptors which collect data and mechanisms for data processing such as data bases and data analysis tools. These mechanisms verify, sort and categorize data about Wt and help establish relationships between the data. The objective is to produce information that can be used to develop relevant description of entities, determine their behaviour, and place them in the world. The aim of support for mental modelling is to enhance and expand the agent’s ability to develop her own mental constructs and integrate them into a coherent mental structure Wt given in formula (3).

Support for formal modelling involves theories, methods and procedures which are used to choose or develop formal models and determine their parameters on the basis of the collected information. Two different classes of models are discussed in sections 4.1 and 4.2. Consequently, we distinguish support for measurement, which aims at the development of models used to supply values and aggregates, and support for representation. This is used to build, verify and analyze structures of entities and logical relationships between them.

Traditionally, the user developed a model and entered it into the support system. The model was then analyzed and solved. The focus was on support for solution. In the case of expert systems, a solution is a qualitative recommendation or diagnosis. In systems which use measurement models, a solution is one or more measures. Only recently an effort is made to provide tools for building representations (Smith, 1989). Support for problem structuring—the most difficult part of decision making (von Winterfield, 1980)—translates mental images into formal models (Pitz, 1983). Such systems are driven by substantive rather than formal problem features.

A support system may consist of several separate models and algorithms. For example, a problem a set of non-linear constraints may be described, together with probability distributions and some aggregation functions. From the point of view of the agent these models and algorithms are tightly coupled. The output from one is an input to another, and the agent has often no understanding of, and no control over, the flow of information between the separate representations. Existing support systems are rigid and opaque (Weber and Coskungulu, 1990) A system is opaque because:

• the separate representations are often integrated and presented as one large quantitative model,

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• the logic guiding the development and integration of the representations may be very different from the agent’s understanding of the problem,

• the representation of the qualitative aspects of the problem may be hidden in the quantitative representations and choice mechanisms.

The inability to relate the problem representation and problem resolution to the decision problem and the agent is compounded when:

• the agent’s reasoning is hidden in the solution algorithms and assumptions underlying the development of models a and p (as it is the case in the optimization models and their solution algorithms),

• a is tightly coupled with p (for example, both the agent and the problem may be incorporated into a multi-attribute utility function),

• developing a formal model of the agent a requires the analysis of abstract unrealistic examples (for example, to determine the preference structure and risk attitude the agent is given different lotteries to compare).

This means that, from the agent’s viewpoint, the representation is closed—also because decision theory is used to develop quantitative models and apply numerical procedures which rarely can be decomposed into logically interrelated elements. The agent, then, uses a system which can be evaluated on the basis of its input and output, and not on the basis of its functioning. This makes it difficult to compare the agent’s mental image of the problem with its formal representation. Also, it is not possible to support modifications of problem representations.

As Winograd and Flores (1987) point out, “every representation is an interpretation”. With respect to computer-based decision support, there are several levels of representation (physical machine, logical machine, abstract machine, programming language, data bases, formal models) and therefore several levels of interpretation. While all levels of representation are important for the analysts, designers and developers, a decision-maker treats the level at which the system communicates with her as important.

To sum up, we can distinguish the following three levels of support: 1. support for representation • mental images • formal models • structural models • measurement models 2. support for solution

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• reasoning (consistency, consequences, inferencing) • numerical algorithms 3. support for communication

5.3. What Computers Can Do

Within the artificial intelligence community, there is an ongoing discussion on what computers can/cannot do (Dreyfus, 1992; Simon, 1991; Winograd and Flores, 1987). While we do not attempt to address the question of what computers cannot do, we think hat they can support decision makers to a much greater extent than they do now. Three directions of research are critical:

1. developing tools for the structuring and restructuring of problem representation, 2. incorporating the agent’s time-independent control and reasoning mechanisms, 3. integrating decision analysis into structural modelling.

Other relevant areas of research can facilitate the development of active and cooperating systems: for example, agent-system communication, case-based reasoning and computer-based learning.

A computer system cannot replace the agent, cannot develop representations on its own. It can, however, build them from prefabricated elements. If the agent describes entities and defines the mechanisms that can retrieve elements relevant to a particular situation, the system will be able to construct a sequence of representations. When the agent adds control mechanisms, such sequences will accurately reflect the agent’s own decision making processes.

6. Conclusions

We have outlined the process of disciplined development of formal representations of decision problems “from first principles”. The canvas we have painted shows areas of support never considered, yet feasible in a not very distant future. The reason why we discuss the creation and reformulation of descriptions in decision making is our ambition to define the types of decision support, delineate possible boundaries between the agent and the computer, and indicate the role which the Negoplan approach can play in the design and development of decision support systems. We have introduced three classes of active entities that contribute to choosing, implementing, and evaluating a decision. Representing such entities in a computer system makes it possible to give the agent analyses of possible future situations that are both qualitative and quantitative. Some, but not all, of their elements can be represented with numbers, others can be represented with other types of symbols. Numeric and non-numeric values must be integrated in a

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structure that describes a situation. It is simplified, and therefore it is ultimately the agent who accepts or rejects a particular situation. To get a close agent-system cooperation the system should interact with the agent in a manner not unlike her own understanding and reasoning.

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