Journal of the Operational Research Society (2010) 61, 1761 --1776

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OR as rational choice: a decision and game theory perspective RJ Ormerod∗ University of Warwick, Coventry, UK Social science disciplines have used decision theory and game theory to provide metaphorical understanding and analytical rigour in their particular domains. The paper explores whether a similar perspective can be applied to operational research (OR) in order to provide an integrating theme for both theory and practice. It is argued that, while the methods of OR are instrumentally rational, OR interventions embrace non-instrumental aspects as well. A case study of an application of decision theory is described and analysed from a decision and game theory (DGT) perspective. The case demonstrates that although the model developed was instrumental, the structure and content of the model reflected the normative and communicative aspects of the decision context. The paper concludes that OR could use a DGT perspective as a conceptual framework for the teaching, research and practice of OR. Journal of the Operational Research Society (2010) 61, 1761 – 1776. doi:10.1057/jors.2009.146 Published online 2 December 2009 Keywords: decision theory; game theory; social science; philosophy of OR

Introduction Most operational research (OR) practitioners would claim that the advice they give to clients is underpinned by rationality, and that they help clients make rational decisions. This advice may involve drawing rational inferences from given data, or developing a model to support a rational choice given several options, or devising a participative process to address an issue. The ability of OR practitioners to provide such advice is based on the development of their three core competences: conducting analysis, designing and managing intervention processes, and understanding context (Ormerod, 2002). Figure 1 lists the main components of each competence. Rational inference, involving logical, statistical and probabilistic analysis, is the subject of another paper (Ormerod, 2009b). Rational choice is the subject of this paper. Methods designed to support rational choice, such as decision theory, sit at the centre of OR’s historical development (Morton and Phillips, 2009). Perhaps less well known in the OR world is that these same methods have come to play a prominent theoretical role in the social sciences. At the same time, social scientists criticise OR and other technical disciplines for taking too narrow a view of rationality. For instance, the philosopher and sociologist J¨urgen Habermas, who uses decision analysis in his arguments, would describe the quantitative, analytical approach of OR as applying ‘instrumental’ at the expense of ‘communicative’ rationality. One reasonable response is to point to the development of ∗ Correspondence: RJ Ormerod, 33 Normandy Hill, Plymouth, Devon, PL5 1LF, UK. E-mail: [email protected]

soft OR and problem structuring methods. However, much OR is conducted without the use of soft methods and this paper will argue that, even so, OR has traditionally taken a much more sophisticated approach to making choices than a simple description of its techniques might suggest. The approach taken in this paper is to describe OR in terms of decision and game theory (DGT) in order to provide an integrated characterisation of its approach and use of methods. Decision theory concerns itself with choosing the ‘best’ from a number of options. Game theory is concerned with choosing the best option when the outcome is also determined by the actions of others (adversaries, competitors, collaborators and so on). Decision theory is a special case of game theory where there are no players in the game other than the decision maker: the game is played against nature. Although many illustrious predecessors worked on problems that can be associated with games, it was in 1944 that the formal conception of game theory as part and parcel of economic theory was first presented in the Theory of Games and Economic Behavior by John Von Neumann and Oskar Morgenstern (1944). A second mathematical landmark was in 1950 when John Nash at the age of 22 published a paper on the ‘Nash Equilibrium’ in the Proceedings of the National Academy of Sciences (Nash, 1950). While Neumann and Morgensten had addressed noncooperative games in the case of ‘pure rivalries’ (in other words, zero-sum games), Nash turned to rivalries with mutual gain; his analysis of two-person cooperative games is referred to as the ‘Nash Bargaining Solution’. In 1951 a paper attached his name to yet another side of economics referred to as the ‘Nash Programme’; this called for the reduction of all cooperative games into a non-cooperative framework (Nash, 1951).

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Core Competences of OR

Conducting Analysis

Designing and Managing Process

Appreciating Context

Problem structuring

Intervention design

Outer context

Rational inference

Facilitation

Inner context

Rational choice

Project management

Policy analysis

Figure 1

OR competences.

In 1957 an authoritative text book, Games and Decisions by Luce and Raiffa (1957), was published. The mathematical findings of game theory initially provided insight when applied to military strategy and tactics, economics, biology and political science. Later game theory, along with decision theory, came to be used for analytical purposes in other areas of social science such as anthropology, sociology and philosophy (and in other domains such as artificial intelligence). While the use of DGT in the social sciences was often conceptual in nature, in management science OR sought to apply the ideas practically to help managers take decisions. Moore and Thomas (1976), Moore et al (1976) and Kaufman and Thomas (1977) give early examples of applications of what they refer to as decision analysis (mainly based on decision trees). Today decision theory continues to be of both academic and practical interest; in the UK developments include multiple criteria decision analysis, or MCDA (Belton et al), strategic choice analysis (Friend and Hickling, 2005), and robustness theory (Rosenhead, 2001). Within OR, the application of game theory developed as operational gaming (see, for instance, Sloman, 1977) and as metagame theory (Howard, 1971), hypergame theory (Bennett et al, 1989) and more recently drama theory (Bennett et al, 2001). This paper does not attempt to advance the subject of DGT as such. Rather, it seeks to follow the social sciences in using DGT conceptually to provide a better understanding of the nature of OR. What do we mean when we talk about helping clients to make rational choices? What should we mean? Do the answers to these questions help define OR? In the next two sections the subject of rationality and choice is introduced and brief descriptions of DGT are given. The following section reviews the use of DGT in economics, political science, sociology and philosophy. The role of rational choice theory in OR is examined in the next section. It is argued that OR methods, viewed from a decision and game perspective, are instrumentally rational. A case describing the use of decision theory in the UK National Coal Board (NCB) is introduced (drawing on the author’s experience as Deputy Director of NCB’s Central Planning Unit (CPU)). Although this case dates from the 1980s, it has been chosen because it provides a good illustration of rational choice in practice. The conclusion is reached that, despite the instrumental

rationality of the formal methods, non-instrumental aspects are reflected in the model structure and content. The final discussion section draws out more general conclusions, arguing that there are implications for the teaching, research and practice of OR.

Choosing and rationality Primitive man survived and flourished by making, more often than not reasonable and sensible, choices in the face of a risky and uncertain natural environment populated by other animals (and other humans) that do not necessarily have his or her well being at heart. Making choices has been necessary for man to evolve and survive. Faced with various options, man has to make choices on the basis of his or her beliefs about the likely outcomes in terms of safety, shelter, food, procreation and so on. Making choices is a basic human activity. The theory of rational choice or decision theory is a modern formal investigation of the ancient concept of deliberation discussed in Aristotle’s Nichomachean Ethics. Setting aside choices made under compulsion or ignorance, Aristotle argues that deliberate choices to engage in particular behaviours are ethical acts subject to moral evaluation. In some deep sense it seems likely that human actors would try to choose actions that will give the best expected result: we would expect them to act rationally and make rational choices. Aristotle formulates the deliberation that takes place before an action as a practical syllogism in which the major premise is the aim or desired outcome, and the minor premise is the belief that the action in question will achieve the desired outcome. An action that can be expected to achieve a desired outcome is deemed a rational action. To choose such an action is a rational choice. Many researchers across a wide range of disciplines take Aristotle’s formulation as a theoretical starting point for their deliberations. It might be protested that instincts, emotions, altruism and habits also play a part and that a rational choice perspective is deficient in this respect. Adherents of the rational choice perspective might accept that their perspective has its limitations, but argue that their models provide insights nevertheless; others try to show empirically that rational choice models do indeed provide explanations of actual observed behaviours, including some that at first sight might seem irrational. Those seeking a wider conception of rationality look to Kant, who claimed that reasons for action can take the form of either hypothetical or categorical imperatives. If one assigns priority to one’s personal inclinations, then hypothetical imperatives determine what it is rational to do; if one assigns priorities to one’s duties, then the categorical imperative determines what it is rational to do. Weber reflected these two types of imperative in what he called Zweckrationalit¨at and Wertrationalitit¨at; the former is broadly instrumental, whereas the latter consists of action that is directly prescribed by some transcendent set of values, which are historically determined, and symbolically transmitted and

RJ Ormerod—OR as rational choice

reproduced (for instance, the Protestant ethic). Talcott Parsons (1902–1979), the American sociologist, generalised this to argue that every organised system of instrumental action was sustained against a background of social institutions maintained through systematically non-instrumental (or nonutility-maximising) behaviour (Heath, 2003, pp 13–14). An agent’s non-instrumental behaviour conforms to rules, norms and roles within a system of shared expectations. In other words, an agent operates within a particular culture. Kant, Weber and Parsons see the non-instrumental form of action as directly incorporating publicly shared reasons for action into the agent’s deliberative process, categorical imperatives for Kant, values for Weber and norms for Parsons (Heath, 2003, p 14). Economists tend to assume that individuals making private choices are instrumentally rational when developing their economic models to explain aggregate behaviour. In contrast, sociologists focus on the role of social norms and public noninstrumental motives to explain behaviour and institutions. Most sociologists tend to assume that social values, norms and so on are not rationally based but derive from history, culture, habits and so on. Attempts to provide a rational basis for non-instrumental action has proved problematic. However, some philosophers (Davidson and Habermas, for instance) have tackled the issue head on and have attempted to provide a logical rationale. As we shall see, DGT has played a central role in these programmes.

Decision and game theory Decision theory While Aristotle first articulated the relationship between reasons, beliefs and actions, it was the enlightenment philosopher Condorcet (1743–1794) who put forward a general theory of the stages of a decision process as a way to reach agreement on the French constitution of 1793. Modern interest in the subject would seem to stem from the American pragmatist John Dewey (1858–1952) who wrote: Upon examination, each instance reveals, more or less, five logically distinct steps: (i) a felt difficulty; (ii) its location and definition; (iii) suggestion of possible solution; (iv) development by reasoning of the bearings of the suggestion [evaluation of the consequences]; (v) further observation and experiment leading to its acceptance or rejection; that is, the conclusion of belief or disbelief. (Dewey, 1910, p 72)

Within a decision process, such as that described by Dewey, the analytical problem of evaluating actions and their consequences is addressed by what we now refer to as decision theory. In decision theory, alternative actions are compared by considering what the outcomes might be, given a particular projected ‘state of nature’ (sometimes referred to as a scenario). As the state of nature is uncertain, the outcomes are considered against a number of discrete states of nature. In the mainstream theory of individual decision making, decision

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matrices (sometimes referred to as utility matrices) are the standard representation of a decision problem (see Appendix A). The preferred action is chosen by comparing the consequences (outcomes) for the different options (actions) under the different scenarios (states of nature). Decisions (choices) can be characterised as being made under certainty, risk or uncertainty. Luce and Raiffa describe these as follows: We shall say that we are in the realm of decision making under: (a) Certainty if each action is known to lead invariably to a specific outcome (the words prospect, stimulus, alternative, etc., are also used). (b) Risk if each action leads to one of a set of possible specific outcomes, each outcome occurring with a known probability. The probabilities are assumed to be known to the decision maker. For example, an action might lead to this risky outcome: a reward of $10 if a ‘fair’ coin comes up heads, and a loss of $5 if it comes up tails. Of course, certainty is a degenerate case of risk where the probabilities are 0 and 1. (c) Uncertainty if either action or both has as its consequence a set of possible specific outcomes, but where the probabilities of these outcomes are completely unknown or are not even meaningful. (Luce and Raiffa, 1957, p 13)

Under certainty, each action leads to one outcome; the action can be chosen that delivers the best outcome in terms of the highest gain or lowest loss. Under uncertainty, no probabilities can be attached to the different scenarios; the choice can be made by adopting various strategies such as maximin (maximise your minimum gain) or minimax (minimise your maximum loss). Under risk, the probability of each scenario is known and a probability distribution for the outcome of each action can be obtained. The criterion for choosing between actions has to be consistent with the decision maker’s objectives and preferences. Once obtained (revealed or expressed), these preferences are introduced into the decision model. For a decision under certainty, the decision maker’s preferences are represented by a single-attribute or multi-attribute value function that introduces ordering on the set of consequences and thus also ranks the alternatives. Decision theory for risk conditions is based on the concept of utility. The decision maker’s preferences for the mutually exclusive consequences of an alternative are described by a utility function that permits calculation of the expected utility for each alternative. The alternative with the highest expected utility is considered the most preferable. The resulting model is sometimes referred to as the utility maximising conception of practical rationality. For most practical decisions, the probabilities that can be attached to each state of nature are not known exactly, nor are they completely unknown; however, the decision maker is likely to able to provide some indication. If so, decision making under uncertainty can be converted into decision making under risk by using the decision maker’s subjective prior probabilities, in other words by taking a

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Bayesian approach. Combining the decision matrix with the decision maker’s prior estimates of probability is referred to as Bayesian decision theory. Having adopted a Bayesian approach, decision making under certainty, objective risk and uncertainty are just special cases. Decision theory itself is not concerned with defining objectives, designing the alternatives actions or assessing the consequences; it usually considers them (beliefs and values) as given from outside, or previously determined. Given a set of alternatives, a set of consequences, and a correspondence between those sets, decision theory offers conceptually simple procedures for guiding choice. Histories of the development of decision theory can be found in Zeckhauser et al (1996), Shanteau et al (1999), Raiffa (2002), and Morton and Phillips (2009).

Game theory In decision theory, the beliefs of the actors (as to how options or strategies give rise to outcomes under a given state of nature or scenario) are taken as exogenous allowing the choice options to be simply evaluated. In the case of games, the states of nature are no longer considered passive. As Von Neumann and Morgenstern put it: Every participant can determine the variables which describe his own actions, but not those of others. Nevertheless, those ‘alien’ variables cannot, from his point of view, be described by statistical assumptions. This is because the others are guided, just as he himself, by rational principles. (Von Neumann and Morgenstern, 1944, p 11)

Game theory addresses the case of the decision maker (player A) who has to make a choice in the knowledge that another actor (player B) will also be making his or her choice. Seen from this perspective, decision theory is a special case of game theory in which the game is played against nature (nature is player B). The decision problem potentially becomes tractable when it is assumed each player acts rationally and assumes the other player will do likewise. The simplest game involves two players involved in a zerosum game, each player having two options. It is assumed that each player is rational, that each assumes the other will also choose an option (a pure strategy) rationally and that the two cannot communicate. A matrix, similar to that of decision theory above, is used to summarise the payoffs to the player whose strategies are given by the rows. Some simple situations can be modelled but the scope is limited. Allowing each player several options extends the model a little. It may be possible to identify a dominant strategy or a maximin/minimax saddle point in which case the solution is stable, that is, neither player can improve on their position (a position described as Pareto efficient). More generally the preferred solution for each player is unstable (a player can improve their position by choosing another option). The game theory solution to this problem is to consider a repeated

game in which each player chooses a mixed strategy by assigning probabilities to his or her options: in a particular game a (pure) strategy is selected according to the chosen probabilities and each player assumes that the other is similarly adopting a mixed strategy. A stable solution can now be found according to the minimax theorem, which states: Minimax Theorem If mixed strategies are allowed, there always exists a value of the game. (Hillier and Lieberman, 1967, p 272).

Von Neumann was a mathematician, but Morgenstern was an economist. Their seminal joint book (1944) was therefore titled Theory of Games and Economic Behaviour. However, during the Second World War interest in game theory in the US developed at the Statistical Research Group (coordinated by the National Defense Research Committee) and the Operations Evaluation Group attached to the Navy. The first applications of the theory were by the Army Air Force and the Anti-Submarine Warfare Operations Research Group. It was the interest of the military in mathematical and statistical approaches that led to the setting up of the RAND institute after the war. Until the mid-1950s the RAND institute became the point of reference for those working on matters related to game theory at Princeton, Michigan, and military-sponsored research institutions. ‘This decade saw the ‘stabilization’ of the mathematics of games through the elaboration of its links with other areas of mathematics, with linear programming and with statistics: the theory became one strut in the framework of ideas developed under immediate postwar military patronage. The concentration on two-person games reflected its relation to military conflict as revealed during the war’ (Leonard, 1992, p 69). The theory has subsequently been extended to address many variations including n-person games, non-zero-sum games, repeated games, cooperative games and games with imperfect information (which incorporates Herbert Simon’s concept of bounded rationality). By doing so, it has been possible to apply game theory to a wider range of problems, activities and behaviours. The subject matter has proved to be of enormous importance to the development of many disparate fields from biology and sociology to economics and artificial intelligence. As a consequence, the theoretical foundations have developed in scope, complexity and subtlety. However, the above introduction should be sufficient for the following description of the use made of the theories in various disciplines. The history of the development and application of game theory can be found in Weintraub (1992).

DGT in social science Economics Game theory has emerged as a powerful challenge to the conventional approach to economics. For economists, the main purpose of game theory is to consider situations in which, instead of agents making decisions as reactions

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to exogenous prices (dead variables), their decisions are strategic reactions to other agents’ actions (live variables). An agent is faced with a set of moves he can play and will form a strategy, which he will use to guide his play, a best response to his environment. A ‘Nash Equilibrium’ will be reached when each agent’s actions results in a reaction by all the other agents, which, in turn, supports the same initial action. In other words, the best responses of all players are in accordance with each other. During the early 1960s, Robert Aumann and Martin Shubik began to apply cooperative game theory extensively throughout economics (for instance, to industrial organisation, general equilibrium and monetary theory); in the process, they invented several solutions for coalitional games. Evolutionary game theory started its development somewhat later; its objective is to apply the concepts of non-cooperative game theory to explain phenomena that are often thought to be the result of cooperation or human design, in other words ‘institutions’ and ‘conventions’ such as market formation, price mechanisms, social rules of conduct, money and credit. One of the earliest exponents of the theory of evolutionary games was Thomas Schelling (1963) who argued that apparently ‘cooperative’ social institutions are maintained by ‘threats’ of punishment and retaliation. Subsequent developments include the intriguingly named: ‘Nucleolus’ solutions for coalitional games; ‘Trembling Hand Equilibrium’ for Bayesian games; and, ‘Perfect Folk Theorems’ for infinitely repeated games. At the same time as game theory research was advancing within economics, strategy was developing as a subject in business schools. The initial emphasis was on planning. However, there were also attempts to relate strategic thinking to micro-economic theory, particularly as it related to the nature of markets and competition. In terms of impact, it was Michael Porter who managed to gain the attention of senior managers worldwide with his books Competitive Strategy (Porter, 1980) and Competitive Advantage (Porter, 1985). Based on micro-economics in general and game theory in particular, Porter examined the relationships between companies, competitors, customers and suppliers. The classic empirical study on cooperation is by Axelrod (1984). Dixit and Nalebuff (1991) did much to popularise the insights explicitly gained from game theory with their book Thinking Strategically. Kay (1993) provides a more academic account in his book Foundations of Corporate Success. In the 1990s, the game theory concepts became the bread and butter of business school research and teaching (see, for instance, Day and Reibstein, 1997).

Political science According to Riker, what passed as ‘political theory’ in the early 1950s was simply some random normative prescriptions about the good society, with hardly any mention of institutional arrangements. The difficulty was that the theory

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was almost exclusively concerned with duty (deontology), conceived and often written in the imperative mood. Political science needed testable models (built from refutable descriptive sentences) about political phenomenon (Riker, 1992, p 208). From the early days of game theory the potential for applications to politics was recognised. Using game theory, Shapley and Shubick (1954) analysed power in committees and Schelling (1956, 1963) examined bargaining and conflict. When political scientists became aware of game theory some were impressed by its rationalism, the fact that it based its analysis on what a goal-orientated rational chooser would choose (thus setting aside instinct, thoughtless habit, unconscious self-defeating desire, and metaphysical and exogenous will) (Riker, 1992, p 209). Another attractive feature for American political scientists at the time was its emphasis on free choice. Economic determinism, especially Marxism, and historical determinism of an idealistic (Hegalian) sort had been flourishing and was tending to dominate social thought. Deterministic assumptions tended to be favoured by students of politics because it guaranteed regularity of behaviour and could therefore be generalised. In contrast, generalisation did not seem possible for humanistic social scientists; free will seems to imply random behaviour. Game theory, however, allowed for the possibility of combining generalisation and free choice (Riker, 1992, p 210). Game theory was used to analyse the way that vetoes, votes and coalitions resulted in power gains or losses for participants. It offered a way of measuring the effects of constitutional provisions, the purpose of which is to prescribe a routine for making decisions. For any given set of rules, the prescribed routines give to roles (and thus to those participants fulfilling the roles) the ability to affect the outcome. Similarly, changes in the rules (such as voting weights) change the influence of the various roles. Game theory came to be applied in many international contexts; for instance, Farquharson’s Theory of Voting (1969) analysed the vote in the United States Senate on the League of Nations. However, the aspect of game theory that caught on most quickly in political science was the twoperson non-zero-sum non-cooperative game. The prisoner’s dilemma game, which had been studied by Deutsch (1958) with social-psychological applications in mind, was applied by Rapoport and Chammah (1965) to international politics, the cold war, nuclear exchanges and so on. In the 1970s and 1980s repeated prisoner’s dilemma games were analysed by Axelrod (1970, 1984), Maynard Smith (1982) and others, opening up a rich seam of analysis of cooperation and trust (Riker, 1992, p 217). Such analysis spills over into questions of morality. Is it moral in the prisoner’s dilemma game to adopt a defecting strategy in the hope that the other player cooperates?

Sociology Twentieth century sociology can be seen as a response to the foundational question (Grundfrage) for sociology suggested

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by Simmel (1910): ‘How is society possible?’ This question mirrored that posed by Kant: ‘How is nature possible?’ Sociologists are interested in explaining the behaviour of individuals within groups, institutions and societies. Among the earliest papers to cite game theory were those of Bernard. In a paper on social problems conceived as problems of decision, she argued that problems such as criminal behaviour can be conceptualised as games (Bernard, 1958). Her treatment of game theory is typical of most early applications in sociology: games are treated as metaphors or linguistic devices (O’Rand, 1992). Evidence of the dissemination of game theory in sociology includes papers by Long (1958) on community structure and Thibaut and Kelley (1959) on behaviour in small groups. However, it was not until later that game theoretic considerations developed within a school of thought in sociology referred to as ‘rational choice’. The rational choice approach, based initially on exchange theory, drew on game theory to model the way that norms, loyalty, and cohesion are established and maintained by repeated interpersonal transactions. Coleman (1966, 1973, 1986, 1990) showed that in long-term relationships cooperative behaviour develops even though players in the game remain self-interested. The longer people spend time together and the more they depend on each other, the more likely it is that they will keep their word and behave in a trustworthy fashion. Trust turns out to be the key: the placement of trust allows both parties, the trustor and the trustee, to do something that would not have been possible otherwise. Although people do not, in most cases, behave exactly like the players in the game theory models, it turns out that much of how people actually behave can be modelled as games. For instance, it can be seen that people adopt quite simple (and sensible, or rational) rules such as ‘tit for tat’. Whether or not people obey norms will depend on the rational choices facing them, what they can get away with and how much they hope to gain. As in games, in social life much depends on how one person perceives the other’s behaviour: are the offers, intentions and threats credible? The game analysis of Coleman and others suggests that group norms emerge naturally in the course of rational interaction among group members. The concept of norms is related to that of rights that are bound up with social concensus; they exist by virtue of being recognised by others. Societies reward conforming behaviour and provide sanctions against deviants and freeriders (for instance, the current disapproval of smoking and obesity). The rational choice perspective provides insights into those situations in which institutions are already assumed to exist and in circumstances where the actors are faced with clear choices (whether to go to university, get married, have children and so on). However, in many other cases emotional factors and beliefs tend to dominate purely material considerations. In sociological analysis, the insights provided by game theory have to be supplemented by psychological considerations (emotions and beliefs) and institutional structural factors (Wallace and Wolf, 2006).

Philosophy Game theory has been put to several uses in philosophy. In ethics, some authors have attempted to pursue the project, begun by Thomas Hobbes, of deriving morality from selfinterest. Games like the prisoner’s dilemma model an apparent conflict between morality and self-interest, and can be used to explain why cooperation is required by self-interest. Other authors have attempted to use evolutionary game theory in order to explain the emergence of human attitudes about morality. Of particular interest in the context of this paper is the use made of decision theory by those engaged in the philosophy of action. Analysis of action turns out to sit at the centre of what analytic philosophers consider to be the key concern of philosophy, the relationship between truth, meaning, language and action. According to Kant the world cannot be accessed directly, perceptions are always interpreted through ideas in the mind of the observer. However, analytical philosophers of the late 19th and early 20th centuries concluded that, as ideas could only be formulated and expressed in language, the nature and role of language in human affairs should be the subject of analysis; thus mainstream Anglo-American analytic philosophy took a ‘linguistic turn’ (the direction Popper fought against; see Ormerod, 2009a). The application of decision theory in this context is usually associated with Donald Davidson (1917–2003). For Davidson, the writings of the Cambridge philosopher, Frank Ramsey (1903–1930), were seminal. Ramsey had developed the theory of subjective probability (see Ormerod, 2009b) and its application to rational choice. His empirical theory of decision making showed how to fit the formal apparatus of probability calculus onto the pattern of an agent’s actions and attitudes. Ramsey introduced the idea of representing partial belief by probabilities (rather than some ill-defined intensity of feeling). By adopting the assumption that an agent acts rationally (acts consistently to maximise the likelihood of realising her desires), observations of her behaviour enable the extraction of a description of her beliefs and desires. Adopting this model, Davidson introduces empirical substance to a mathematical theory (a Tarski-style theory of truth); and like Ramsey, Davidson succeeds by using observations of people’s behaviour to infer a structure that in turn can be used to interpret their words (Joseph, 2004). Thus actions, languages, beliefs and desires are brought into focus simultaneously. The fact that economists rely on the assumption of the rational man, while sociologists concentrate on societal norms and roles, has caused a deep and continuing divide in social science. Habermas, who in the German tradition is both sociologist and philosopher, has attempted to bridge the gap with what Davidson refers to as a unified theory of meaning and action. Parsons (1937) had attempted to explain the structural properties of social order (often referred to as the problem of order). Habermas turns this problem on its head: rather than introducing a type of publicly accountable action as a

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basis for solving the problem of order, he introduces it to explain the development of language (Heath, 2003, p 18). Habermas argues that there are two basic activities, instrumental acts and speech acts (Searle, 1969). To justify the identification of these two primitive analytical types, Habermas needs rational choice theory. Johnson (1993) observes that critical theory (of Habermas and the Frankfurt School) and game theory converge in improbable but potentially productive ways. Heath says: One of the major problems that arises from Habermas’s lack of precision with respect to the instrumental model is that his theory has had little impact among those who are not already interested in finding an alternative to the instrumental view. By contrast, Davidson’s critique of decision theory, which is in many ways quite similar to Habermas’s, has had a much greater effect (Elster, 1986). This is despite the fact that Davidson’s overall action theory is in some respects much less sophisticated than Habermas’s. (. . . ). The difference is that Davidson gets the decision theory right, and so knows how to make his arguments stick. (Heath, 2003, p 4)

Heath shows how Habermas’s theory of instrumental and communicative action (with some adjustments) can be justified using DGT (Heath, 2003).

Rational choice theory and OR As we have seen, the 1950s and early 1960s proved a highly creative period for applied mathematics. However, as OR in general developed, its interest in game theory fell away. One reason was the huge success of linear programming in the oil industry, where it was found to be useful for operational scheduling in refineries and logistical coordination of the supply chain. A second factor was that decision theory was found to be easier to apply in practice. As one of the pioneers of the development of game theory, Howard Raiffa, explains: Over the years I have drifted away from classical game theory. The exclusive emphasis on joint rationality and common knowledge and the dependence on equilibria analysis seems to me to limit the applicability of the field both descriptively and prescriptively. I think of myself as a professional decision analyst: someone concerned with helping myself, or my client, make wise choices in uncertain environments and in the presence of conflicting objectives. In interactive, gamelike contexts, some uncertainties stem from the actions of others who may be thinking what you are thinking. But this interactive, reflexive thinking process rarely goes deeper than one level—except perhaps in highly simplified games—and game-theoretic equilibrium is a poor predictor of the action of others. Given this observation, the approach I favor is to assess subjective probability distributions for the actions of others based on behavioural models and then to optimize against this distribution. This approach is not in the spirit of classical game theory but the domain of applicability is far wider because it does not depend on cyclical ultrarationality and the binding constraints of common knowledge. (Raiffa, 1992)

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Textbooks of OR analytical techniques usually include a short description of game theory, but it is not central to the account given of OR. To set the scene, the authors of such textbooks generally give a brief account of the process of OR. Often they use the steps suggested by Ackoff (1956). Taha, for instance, suggests: [T]he major phases through which the OR team would proceed to effect an OR study include: 1. Definition of the problem. 2. Construction of the model. 3. Solution of the model. 4. Validation of the model. 5. Implementation of the final results. (Taha, 1992, p 9)

The emphasis is on model building, but the nature of the models is not explicitly defined (of course, the text book goes on to introduce a wide range of models). The primary explicit claim of such a process is that mathematics, logic and statistics will be used to build models to analyse rationally the not necessarily rational beliefs, desires and options of a notional decision maker. The rationality lies in the model structure, not the parameters supplied. Two secondary claims may be made. First, some help may be given with the process of articulating the parameters: the parameters will still be chosen to reflect the beliefs, desires and options of the decision makers but they may wish to examine, adapt and change their views during the intervention. Second, by organising the inquiry as an intervention (supported by a consultant or project team), any difficulties in carrying out the rational analysis or clarifying the subjective parameters can be addressed. An alternative approach favoured by some textbook authors is to emphasise the role of OR in assisting the analysis of decisions: 1. 2. 3. 4.

Definition of the problem. Identification of possible options. Define criteria for choosing between the options. Evaluate the outcomes of each option in terms of the criteria. 5. Choose the best option in terms of the criteria. 6. Implementation of the final results. This formulation is more narrowly defined, and at the same time it shifts the emphasis from what the analyst does to what the client does, from creating models to taking decisions. The primary and secondary claims are the same as those given above but it is made explicit that rationality lies not so much in the mathematics, logic and statistics but rather in the structure of decision choice: the outcomes of options are evaluated in terms of criteria (desires) based on beliefs about the relationship between options and outputs. Thus the approach clearly has an instrumental orientation; the aim is to achieve the best outcome. This second formulation is in effect suggesting that OR helps clients make rational choices in the face of uncertainty. Decision theory thus takes centre stage.

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States of Nature

Decision Theory Options

Desires Game Theory

Beliefs

Figure 2

Decision and game theory.

Do the mathematical models and techniques laid out in the text books support a decision theory orientation? As has been noted above, decision theory is a special case of a two player game with the second player being replaced by nature. Thus we can depict (see Figure 2) both decision theory and game theory in the same way with beliefs providing the relationship between options and desires in different scenarios (states of nature). We can further note that linear programming and game theory are connected (Gale et al, 1951). To illustrate the point, Appendix B shows how linear programming can be used to solve a two-player game with mixed strategies; the duality of linear programming mirrors a two player game. Thus decision theory, game theory and linear programming are intimately (mathematically) connected. We can also note that dynamic programming and decision trees are extended forms of decision theory. Queuing theory, simulation, systems dynamics and what . . . if business models inform our beliefs about the relationship between options and outcomes; similarly statistical analysis and forecasting inform our beliefs. It is thus possible to view many of the mathematical techniques of OR from a DGT perspective. In fact most of the mathematical techniques can be related to the DGT perspective in that they operationalise some or all of the elements. The less mathematical OR methods can also be related to the DGT perspective. Most obviously, scenario planning addresses the issue of depicting states of nature, drama theory (which includes megagames and hypergames) provides processes for examining a situation in terms of games, and decision theory itself uses probabilities to analyse uncertainty and risk. Also MCDA addresses decision choice head on, placing particular emphasis on the criteria (desires) and the trade-offs that might be involved. Options generation can be approached directly using, for instance, SWOT analysis, De Bono’s thinking hats (De Bono, 1985) or repertory grids (Eden and Jones, 1984). Option generation is also contained within more comprehensive approaches such as cognitive mapping (Eden, 1988) and strategic choice approach (SCA) (Friend and Hickling, 2005). Thus in the Strategic Option Development and Analysis (SODA) approach using cognitive maps, bi-polar concepts that only initiate arrows can depict strategic choices (options). The cognitive maps extend

through intermediate concepts (beliefs about the relationship between strategies and goals) to concepts that initiate no new arrows; these latter end-point concepts depict aims or goals (outcomes). In the SCA, the shaping and designing modes result in decision options. The comparing and choosing modes deal with beliefs and outcomes. In soft systems methodology (SSM), options are developed (comparing the actual with conceptual) that result in outcomes that are assessed in terms of systems desirability and cultural feasibility (desirable attributes). Thus at a conceptual level it can be seen that most (perhaps all) OR approaches can be related to a DGT perspective as depicted in Figure 2. Each technique or method addresses in part or whole the problem of rational choice interpreted as instrumentally rational choice.

Beyond instrumental rationality That OR methods can be related to a DGT perspective is hardly surprising and may well be obvious to the reader. However, it is a conclusion worth reaching because it provides a secure basis from which two questions can be addressed: if OR methods are instrumentally rational, is that all they are; and if OR methods are instrumentally rational, can OR as a whole be so described? To examine these questions, a brief case is now introduced. This particular case is chosen because details of the models used are available in the literature and because the author not only directed the modelling efforts, but as Deputy Director of the CPU he also initiated the internal planning exercise described in the case and was actively engaged in discussions with the many organisations and individuals participating in UK and international energy policy debates. At the time rapidly rising oil prices had triggered great concern about future energy supplies (Odell, 1974; Foley, 1976; Lovins, 1977, Wilson, 1977; Leach, 1979). Internationally, coal was coming to be seen as a replacement for oil (Grenon, 1979; Wilson, 1980; H¨afele, 1981; Ormerod, 1981). In the UK there was a debate about the future of the coal industry in terms of the potential economic, social and political outcomes, an issue that had been heightened by the miners’ strikes and the fall of the Heath government in the early 1970s (Hughes and Moore, 1972; Campbell, 1993). In 1980, energy models, such as those deployed in the case, were a growing area of interest for operational researchers and economists (Ormerod, 1980a; Bayraktar et al, 1981). A description of the NCB’s approach to planning can be found in a report by the Monopolies and Monopolies and Mergers Commission (1983).

Decision analysis in the UK NCB In 1980, the NCB’s CPU initiated an exercise to examine the prospects and key decisions of the NCB. The NCB was a nationalised industry responsible for coal production in the UK. It was CPU’s task to orchestrate an annual planning round that would culminate in the Board submitting a Medium

RJ Ormerod—OR as rational choice

Term Development Plan (MTDP) to the Government. Broadly speaking, the MTDP was used to make the case for investment (to be authorised by Government) in new mining capacity and research. The exercise described here was intended to provide the assumptions for the main planning round, which would involve all the major production and marketing units. The main opportunity for the coal industry was to invest in new mine capacity to take advantage of a coal exploration programme that had been started several years earlier in response to rising oil prices. The list of threats was much longer: expansion of the gas grid to bring North Sea gas to market was planned; an expansion in nuclear generation of electricity was anticipated as new nuclear power stations under construction came on line; acid rain from coal combustion was a growing concern; and a market in international steam coal was developing that could result in new competition in the UK market for coal. The gas and nuclear threats were well understood, but the development of an international market in steam coal was of particular concern (Wilson, 1980; Long, 1982). The NCB was the largest coal company in the free world (in other words, excluding Russia, Poland and China) and advised companies all over the world on coal mining technology. Board members would not easily accept that the British coal mining industry was under threat from such newly established sources. Apart from the difficulty in persuading powerful actors that they should take notice of potential coal imports, the CPU planners were faced with an analytical problem. In the past, the planning assumption had been that coal prices in the UK would reflect the need to balance supply and demand in the UK. How should the possibility of coal imports and exports be taken into account? To bring these factors together a decision analysis approach was adopted. The strategic options (the means) for the NCB were various levels of investment in new coal production capacity and closure of old unproductive mines. Several scenarios were defined involving various combinations of oil prices, international steam coal prices and levels of growth in UK economic activity. The established models of the UK energy economy (developed by the NCB’s OR Executive for CPU) were then used to calculate the outcomes of each strategy within each scenario in terms of the supply and demand for coal (Ezra, 1977; Plackett et al, 1982; Ormerod and McLeod, 1984). The CPU UK energy model included data about existing capacities (for instance, power stations), estimated price and income elasticities for each fuel in each market (domestic, industrial, transport and so on), and assumptions about the planned growth in nuclear and gas capacities. The results of a similar exercise at about the same time were published in the World Coal Study (Ormerod, 1980b). The choices that this exercise laid bare were the subject of an internal debate about investment, capacity and the loss of jobs. This led, in February 1981, to a confrontation between the coal industry management, the miners’ unions and the UK government. The dilemmas facing the NCB at this time

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are described in the report by the Monopolies and Mergers Commission (1983). The dispute about the future of the UK coal industry continued for several years culminating in the 1984 miners’ strike (Reed, 1985; Scargill, 2009).

Some aspects of the NCB case viewed from a DGT perspective The theory tells us that instrumental reasoning and action involves assessing actions in terms of outcomes that desires; the relationship between actions and outcomes is based on beliefs. The instrumental conception of rationality is essentially a private one based on a set of subjective motivational states: this type of reason is agent relative and not generalisable, it is a reason for some specific agent to perform a particular action. The only constraint imposed on an agent’s conduct by instrumental rationality, is that her actions accurately reflect her preferences over outcomes. In terms of practical rationality, wider institutional concerns and societal norms have to be taken into account. These terms are in theory generalisable rather than individually subjective (Ulrich, 1988). Decision and game theorist are in general agreement that instrumental action, sometimes referred to as strategic action, is a fundamental human requirement for success and survival in an uncertain environment. The picture is complicated when the game is played against other players who can also make choices (assumed to be rational). Game theory shows that identifying stable solutions for such games may be problematic and even allowing mixed strategies, which guarantees a solution, may not give Pareto efficiency (Pareto efficiency means that no other solution exists that is more favourable to one or both players). Further, the players may have no way of reasoning that leads them to the solution. Progress can be made by introducing staged decisions and communication between players. Following this approach it is possible to argue that language has emerged to facilitate instrumental action. This hypothesis can be explored by examining the practical use of natural language (English, for instance) or, more generally, signalling activity, to see whether it can be explained in terms of individuals seeking to achieve instrumentally their own selfish ends. One approach is to introduce commitments into the equation. However, as Hobbes famously pointed out, commitments can be broken, and a selfish agent acting rationally would do so. Game theorists generally conclude that these attempts fail and that something other than instrumental actions has to be added into the equation. This added activity has been variously characterised as performing to satisfy societal norms (Parsons); telling the truth (Quine and Davidson); and seeking mutual understanding (Habermas). These activities involve socialisation, sincerity and communicative competence, respectively (Heath, 2001). More generally, in the context of a particular set of circumstances a (dynamically changing) balance is struck between autonomy, freedom, rights and liberalism on

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the one hand, and responsibility, authority solidarity, service and community on the other. More prosaically, society functions by building institutions, adopting norms, building trust, agreeing contracts, upholding traditions and enforcing laws, all of which change over time. All these important factors can be recognised in the case. Stepping back from the coal industry planning exercise in the case, it can be seen that the UK energy economy can be characterised as an extended game involving many participants who negotiate outcomes as opposed to the unfettered result of market forces; the more so at that time because most of the (institutional) players in the UK were Governmentowned nationalised industries. The interplay between the players involved multiple channels of communication (for instance, in direct bi-lateral meetings, at fora such as Parliamentary investigations and public inquiries, and at exchanges of views facilitated by the Department of Energy), publicly available plans and annual reports (containing both assertions and commitments), and public statements (such as press releases, publications and speeches). These activities created what Habermas (1984, pp 335–337) refers to as a ‘lifeworld’ within which standards of behaviour (legal and social) and reasoning (public justification) are debated and scrutinised. Nevertheless, (institutional) players pursued their individual pragmatic aims developing their own logic in the process (Dewey, 1938). In an attempt to encourage a satisfactory economic, social and political outcome, the Government had at its disposal sanctions and incentives through its control of finance, its role in permitting infrastructure investment (for instance, new nuclear power stations or coal mines), and its appointment of senior staff. Other players had their own sanctions; for instance, miners could declare an overtime ban or go on strike. The Department of Energy and Treasury would expect any submission of an MTDP to reflect the uncertainty associated with forecasts of future UK economic activity and international oil prices. At the time oil prices were extremely volatile and, although many attempted to do so, no one could offer a definitive analysis of the game being played between oil producers (coordinated through OPEC) and the OECD countries (coordinated through the IEA); the outcome of the game, the price of oil, was uncertain. Thus different growth rates of the UK economy and levels of international oil prices were commonly combined by the various players to provide scenarios (states of nature). The decision modelling exercise for the coal industry took place in the context of its own lifeworld within the context of the wider UK energy economy. The exercise was thus specifically structured for the coal industry, bringing in certain factors and leaving others out. Two large additional uncertainties loomed large for the coal industry. The first was the projected price of internationally traded steam coal. The situation was studied intensively both within CPU and in collaboration with other interested parties (for instance, Wilson, 1980; Long, 1982); it was concluded that a somewhat competitive market (a Pareto optimal game between

suppliers and consumers) would evolve, the economics of which could be modelled using linear programming (Ormerod and McLeod, 1984, pp 44–47). As a result some speculative statements about the possible range of future international coal prices were derived, but the outcome was uncertain (these assumptions were debated at the Sizewell B inquiry; Ormerod, 1997a). International coal prices were therefore included as a scenario parameter along with economic growth and oil prices (Monopolies and Monopolies and Mergers Commission, 1983, p 66). The second coal industry specific uncertainty was the outcome of the game being played between three primary players, namely the coal industry, the Government and the miners’ unions; the key issue was the level of pit closures (of course, there were other relevant players such as the electricity and steel industry customers, independent commentators, the media and so on). The situation was complex: in simple terms each set of players in the game could be said to contain hawks and doves, thus there were in effect six primary players rather than three (under the stresses of the 1984 strike further divisions within each of the three primary players became apparent); none of those involved could be certain of the moves that the others would make, nor of the outcome of any confrontation. Threats and promises were being made but not necessarily believed. Planners in other industries were able to stand back and include the outcome of this game in their scenario variables (or they could have attempted to provide a game theoretic analysis of the outcome) but for the coal industry pit closures were actions and therefore various levels of closures were treated as potential strategies in the decision choice exercise. One of the projected outcomes of such strategies was improved economic performance of the coal industry and hence Government finances, another was the loss of mining jobs. Whether one deems a particular set of outcomes as desirable or not, depends on one’s point of view; the norms of society dictate that economic performance (the NCB operated under the Coal Industry Nationalisation Act, 1946) has to be balanced by social effects. The Government of the day believed that the financial results needed to be improved; the miners argued that retaining jobs was the priority (Scargill, 2009). To work out the consequences of the coal strategies within each scenario, the actions of other major players had to be depicted. British Gas (the monopoly distributer and retailer of gas in the UK) was undertaking a large infrastructure investment programme to distribute North Sea gas across the country. It was assumed that this expansion would continue along the lines published by British Gas and supported by the Department of Energy. In other words, the assertions (plans) of British gas were believed and it was assumed that the programme would continue whatever strategies were adopted by other players. Similar assumptions were made about the nuclear power station building programme, which had in the past suffered delays. Both gas and nuclear assumptions could therefore be built into the model of the UK energy economy

RJ Ormerod—OR as rational choice

(representing our beliefs about the relationship between strategies and outcomes within given scenarios). The model also assumed that relevant Government policies would continue to apply (the assertions of Government were believed). The most important of these from the coal industry’s perspective were (i) the treatment of North Sea oil as part of global supply available at global market prices rather than as a dedicated UK supply available at the cost of production (this policy still holds today); (ii) the prohibition on the use of gas for electricity production thus retaining gas for ‘premium’ domestic use (this policy has since been dropped). For each assumption, the future behaviour of the various parties had to be based on an interpretation of the preferences, expressed or revealed by past actions, and a practical assessment of likely outcomes. By making various assumptions, by putting the strategies of some players into scenarios, by assuming some as plans that would be adhered to (in game parlance, the players would not re-optimise), by retaining some strategies as options for the coal industry, by assuming Government policies would continue to obtain, the problem was made analysable in decision theoretic terms. None of these assumptions were immutable, but the building of explicit models and decision structures allowed the impact of any changes (actual or under consideration) to be explored in ‘what . . . if’ mode. The models therefore did not optimise according to some instrumentally formulated depiction of reality. Rather, they helped planners bring together their factual and social understanding of strategic issues in a way that can be communicated and debated in their relevant lifeworld (Rosenhead, 1980; Yewlett, 2001). The models thus informed the NCB’s advocacy within the energy debate and made the coal industry’s assertions more believable, though not always believed (Ormerod, 1997a). It is not suggested that the decision modelling described in the case is typical, but it does illustrate the relationship between the problem context, the OR modelling process and the resulting model. The resulting model in the case is arguably rational. The model itself is formulated in an instrumentally rational form but it clearly includes many normative non-instrumental assumptions. The norms are societal norms in the form of laws, policies and expected standards of behaviour (for instance, the way that employees are treated, health and safety and so on). In addition, there are the norms of the UK energy economy (the lifeworld of UK coal industry strategy development), including expectations in terms of transparency of plans and intentions, balancing of short- and long-term aims, interchanges of information, Government energy policy, and the accountability of the leaders of the various industries. In addition, there are the norms of public life in terms of adherence to truth, respect for factual analysis and engagement in rational argument. The case demonstrates that despite the objective being instrumentally orientated (the aim being to achieve a successful outcome for the coal industry), the strategy exercise had many normative components. The decision theoretic

Decision Context

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States of Nature

Decision Theory Options

Desires Game Theory

Beliefs Rational Intervention Process

Figure 3

Rational choice.

model, while in itself instrumental, is structured, formulated and implemented in the light of the decision context and societal norms, and the pragmatic aims, interests and beliefs of the players. The outputs examined were socially determined goods and bads such as financial performance, loss of jobs, environmental impact and the cost of energy. But the normative, and what Habermas would call the communicative, aspects of the modelling went well beyond the choice of outputs; they affected how the future actions of the various players were depicted as strategic choices, or as scenario variables, or as part of the UK energy model (reflecting beliefs). The modelling process involved substantial communicative action and the resulting model itself reflected the communicative activity of the coal industry planning process and all the interactions with the other players that this involved. The OR approach is thus characterised by the process of intervention as well as its models. Hence the importance to OR practitioners of complementing their core competence in deploying analytical skills with the two additional core competences (i) in managing the intervention process and (ii) in gaining an understanding of the context (as depicted in Figure 1). The process ensures that instrumentally rational models are formulated and built to reflect norm-performative and communicative considerations and ensures relevant people are involved or consulted (Ulrich, 1983, 1987). Thus OR aspires to help their clients make rational choices by designing and implementing rational interventions. Figure 3 illustrates the point: it is the overall process of intervention (or engagement) and its engagement with the context that is rational.

Discussion The paper has described how social sciences, such as economics, politics, philosophy and sociology, use DGT to develop the foundations for their respective disciplines and it has been noted that the social scientists have concluded that to lay claim to rationality it is necessary to include normative and communicative as well as instrumental considerations. It then argued that most (perhaps all) hard and soft OR methods

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can be related to a DGT perspective. Further, the case was introduced to demonstrate that even when an essentially instrumental ‘hard’ OR approach is taken, the models are formulated to reflect economic, political and social aspects: their claim to rationality can therefore be defended. In the light of this it will now be argued that (i) by placing DGT more formally at the centre of OR thinking, by taking a DGT perspective, OR will be better able to make good on its claim to rationality; (ii) there are practical gains to be made by adopting this approach. Social scientist have concluded from their analysis of language, action, competition and cooperation that instrumental action is not enough to account for individual human behaviour. We can see from the case that the same can be said about the groups and institutions that provide the context for OR interventions. The modelling process and the models that result are replete with the results of normative and communicative action; the structure, shape, boundaries, content and use of the instrumentally rational model reflect non-instrumental rationality. The craft of the modeller is not to concentrate on those aspects that can be quantified and analysed in an instrumental way; rather it is explore the decisions and their context to find ways of helping the decision maker(s) make sense of instrumental, normative and communicative aspects. The balance of attention given to the three aspects will vary from case to case. Consider three OR intervention archetypes: (i) ‘smart bits’ (the quantitative modelling and algorithmic activities of OR: forecasting, scheduling and what. . . if modelling, for instance); (ii) ‘helpful ways’ (general problem solving and intervention process activities: cognitive mapping, MCDA and scenario planning, for instance); and (iii) ‘things that matter’ (activities that address important social issues such as health, housing or transport policy, issues that affect citizens: policy analysis, policy advocacy and information dissemination, for instance) (Ormerod, 1997b). In general, we might expect that those interventions concerned with developing ‘smart bits’ would be primarily orientated towards instrumental action; those concerned with providing ‘helpful ways’ are likely to be orientated towards communicative rationality; interventions concerned with ‘things that matter’ are likely to be orientated towards norm-performance (see Figure 4). However, pragmatic considerations will always strongly affect the orientation of any particular intervention. Actual interventions can be positioned on the same diagram. Figure 5 shows a subjective plot of five cases: the NCB case described above; the Javeriana case (C´ordoba and Midgley, 2006); the Sainsbury’s case (Ormerod, 1995); the Severn Trent Water case (Ormerod, 2005); and the Baosteel case (Tang et al, 2008). As can be seen, each intervention can be characterised as having a different emphasis. For instance, in the Sainsbury’s case the emphasis was on engaging senior management in developing a systems strategy to gain competitive advantage. By contrast, in the Javeriana case the aim was to engage a wider set of people and encourage

Norm-performative aspects

Things that matter

Smart bits

Helpful ways

Instrumentally rational aspects

Figure 4

Communicative aspects

Aspects of rationality.

Norm-performative aspects

Javeriana

NCB Baosteel

Severn Trent Sainsbury’s

Instrumentally rational aspects

Figure 5

Communicative aspects

Cases of rationality.

them to discuss a wider set of issues than would be standard practice in an information systems planning exercise. In the Baosteel case, the aims were to improve operations in the iron and steel industry. It should be noted that it is cases that are plotted not methods: no attempt should be made to plot methods themselves on the diagram as the methods used do not determine the orientation adopted; for instance, hard methods can be used to explore personal viewpoints and soft methods can used with a strong instrumental orientation (Ormerod, 1997c). The relative weight given to instrumental, normative and communicative action varies from case to case, but in all cases the modelling would be strengthened by more explicit recognition of the choices being made. For practitioners, the decision and game theoretic perspective provides a framework for thinking about the type of intervention that would be appropriate in a particular set of circumstances. What balance is the client seeking to strike between attention to the instrumental, normative, and communicative aspects? How

RJ Ormerod—OR as rational choice

do clients normally balance these aspects? Where can the intervention add value? Practitioners may well feel that such decisions are already well informed, and this may well be the case (particularly those in in-house OR groups who are immersed in the context). However, client, and in some cases public, accountability is increasingly a requirement. The first advantage of adopting a DGT perspective is therefore the gain in modelling quality by making the argumentation behind the model formulation explicit and transparent. Even if in a particular case this does not result in quality gains as such, the modeller will still be in a better position to defend the model’s rationality. The second advantage lies in providing a window into the social sciences. For practitioners, the insights of social science can provide both a source of ideas, insights to be included in their analysis, and a different perspective from which to reflect on the OR approach. When a scheduling problem is being addressed, an efficient solution is sought, a circumscribed problem and a limited aim can be considered. However, if an economic choice is to be made the analysis has to range more widely because economic rationality is a relative concept: can better use be made of the same resources (means) elsewhere? Concepts such as coercion and power in political science are also relative notions. Thus both economic and political considerations involve multiple choices and actions; systems of choices and actions and the relationships between them have to be considered. Sociology can be understood as addressing the residual elements after the technical, economic and political dimensions have been taken into account; it examines the glue that holds society together despite the destructive drives of technical, economic and political activity. An alternative view is that sociology provides an overarching view of all sciences, social and natural. Sociology particularly draws our attention to the role of non-rational factors in decision choice, aspects of decisions that are not related directly to self-interest. Thus, sociologists note that some choices and therefore actions are symbolic, resulting in meaning rather than utility (Parsons, 1937). Non-rational factors find a place in ultimate aims and also act as constraints on the means; these non-rational factors are institutionalised as norms and provide societal stability and continuity. The third advantage for practitioners is that the content of undergraduate and MSc courses could be better aligned with their practice: with an understanding of the application of the DGT perspective to intervention contexts, students would be better prepared to contribute to the judgements needed to make, explain and defend crucial modelling choices. New recruits would thereby become productive more quickly. The implications for the teaching of OR are (i) decision theory with its game theoretic foundations should be adopted as an integrative theme on OR undergraduate or masters courses. This may already be the orientation of some courses, but if not, the suggestion is that course designers should consider whether a move in this direction could be beneficial; and (ii) the DGT perspective could also be used to introduce

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students to the social sciences to give them a better understanding of the role of values, interests and intentionality in decision choice. It is not realistic to expect that OR students on an MSc course, who usually have a quantitative background, could gain a proper understanding of economics, sociology and political science from the ground up within an already full curriculum. However, as we have seen decision and game theories are widely applied in these subject areas; they could thus provide students with a point of entry using familiar OR concepts. Rather than helping students to develop what can only be a shallow knowledge of economic, social and political issues, it is suggested that students are taught how to understand social and strategic issues using the conceptually powerful DGT concepts. Similarly there could be benefits for practitioners from new academic research directions. Currently OR academic research in support of mathematical modelling is a mature and productive area of research (see, for instance, Fildes et al, 2008; Potts and Strusevich, 2009; Smith et al, 2009; Taylor et al, 2009; Worthington, 2009). Research into soft OR, including problem structuring methods, is progressing (see, for instance, the two special issues of JORS Vol. 57, No. 7 and Vol. 58, No. 5); although take up of soft methods in OR practice has been slow (Munro and Mingers, 2004), few would deny their influence on both practitioners (see, for instance Ormerod, 1995) and hard OR researchers (see, for instance, Robinson, 2001). Thus in relation to the core competences of conducting analysis and designing and managing of process, research programmes are well established. The third competence, the understanding of context (see Figure 1), has little existing support in OR research. For those researchers who adopt a sociological or philosophical approach in their OR research, there would seem to be an opportunity to exploit the analytical potential of DGT to build bridges between their favoured theoretical frameworks and the context of OR practice.

Conclusions OR practitioners like to think of themselves as helping clients make rational choices. In the paper, the methods and practices of OR have been examined to see in what sense OR does, in fact, support rational choice. The conclusion is drawn that the methods of OR can be related to a framework of DGT; they therefore provide models that support instrumentally rational decisions, the making of instrumentally rational choices. However, social scientists using DGT have concluded that human behaviour (strategic and speech acts) cannot be explained by instrumental behaviour alone. The analysis they use to come to this conclusion is based on the behaviour of individuals; instrumental action is defined as actions to advance the selfish interests of individuals. The social scientists have variously characterised the noninstrumental behaviour as consisting of norm performing, truth seeking and communicative actions. Using a case

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study, the paper has argued that the behaviour of groups and institutions, the context of OR interventions, can be similarly characterised as combining both instrumental and non-instrumental activity. OR interventions thus take place within a particular technical, normative, and communicative context; putative advisors respond to this unique context in deciding with their clients what to investigate, what to model, what to treat as options or states of nature or beliefs, and who to involve. The OR models themselves may be orientated towards instrumental rationality but the OR intervention, taken as a whole, combines both instrumental and non-instrumental aspects. The aim of OR can therefore be reasonably described as to support rational choice. The paper proposes that the decision and game theoretic perspective should be explicitly recognised as the foundational core of OR. Decision making is already the focus of OR methods, but the paper suggests that we should go further and use a decision and gaming perspective as a conceptual framework for teaching, research and practice. Of course, an emphasis on decision making is hardly a new direction for OR and does not require a dramatic shift in orientation; it is more a question of clarity and focus. In particular, such an emphasis could support a long-held ambition of OR to be a multi-disciplinary discipline. OR has not been particularly successful at attracting those outside the mathematical and scientific disciplines, nor is it realistic to expect OR practitioners to become expert economists, sociologists and political scientists. However, it is plausible that OR practitioners and researchers could develop an understanding of the social sciences through the lens of their own discipline, namely DGT. The fact that DGT has already been applied with good effect within the social sciences provides both an intellectual resource and an assurance that such a perspective is not a blinkered or distorted view. The potential prize is a genuinely OR perspective on a broad range of societal issues. The shift advocated here is a subtle one. By taking a DGT perspective to reflect on the nature and context of our interventions and our models, we can achieve a more cohesive understanding of OR that would benefit teaching, research and practice. Such benefits are not easily won and changes in perspective are never undertaken lightly. However, the fact that only a modest change is being proposed, and for some it involves no change at all, makes such an aspiration feasible and realistic.

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Appendix B. Solution of (M × N) games by linear programming (Taha, 1992, pp 437–438) For an M × N game A’s optimum mixed strategies satisfy   m  m m    ai1 xi , ai2 xi , . . . , ain xi max min xi

i=1

x1 + x2 + · · · + xm = 1 xi  0,

a1 a2 .. . an

2

···

m

(a1 , 1 ) (a2 , 1 ) .. .

(a1 , 2 ) (a2 , 2 ) .. .

··· ··· .. .

(a1 , m ) (a2 , m ) .. .

(an , 1 )

(an , 2 )

···

(an , m )

i = 1, 2, . . . , m

This problem can be put in the linear programming form as follows. Let   m m m    ai1 xi , ai2 xi , . . . , ain xi v = min i=1

i=1

i=1

Then the problem becomes Maximise z = v Subject to m 

ai j xi  v,

j = 1, 2, . . . , n

i=1

Appendix A. Matric form of decision theory

1

i=1

Subject to the constraints

m 

If ai represents the ith action (i = 1, 2, . . . , m) and  j represents the jth future state ( j =1, 2, . . . , n) then v(ai ,  j ) represents the associated outcome. Under discrete conditions, this can be arranged in matrix form thus:

i=1

xi = 1

i=1

xi  0,

for all i

where v represents the value of the game in this case. The linear programming formulation can be simplified by dividing all (n+1) constraints by v, reversing the inequality constraints if v < 0. Similarly B’s problem can be formulated as a linear programme with B’s problem being the dual of A’s problem. Received August 2008; accepted September 2009 after two revisions