Strategy

by Lawrence Freedman

  In 1982, Riker became president of the American Political Science Association. He could observe the dominance of “the rational choice paradigm.” Its success was “driving out all others.”8 He was now arguing against the need to add such modifiers as “positive” or “formal” as this was the only “political theory” deserving of the name because it met scientific standards.9 By the 1990s, mathematics was an essential attribute for a political science program, and rational choice articles accounted for some 40 percent of all contributions to the American Political Science Review. There were complaints that the growing influence of the paradigm was due to a strong-arm mentality as much as clarity of thought. Rather than criticism being taken seriously, it was dismissed because the critics lacked the training to master the methods and so failed to understand what was going on. Because they supported their own, it was alleged that rational choice scholars would prefer a second-rate member of their own fraternity to anyone else when it came to appointments.10

  Their theory was not a simple imposition of an economics model. The development of economics as a discipline had been served by the assumptions of self-interest, narrowly conceived, so that individuals facing the same constraints and with the same preferences would make the same choices each time. Both goals and the resources used to obtain them could be expressed in monetary terms and numerous comparable transactions could be observed in everyday economic life: the larger the sample the less important anomalous behavior and the more distinct the observable patterns and relationships. Riker was impressed by the robust market economics of the Chicago School, and this was present in his original Rochester curriculum. But he embraced game theory well before mainstream economists, and he was always careful to distinguish economics—which attributed a mechanical rationality to agents—from politics—in which rationality was deliberate and conscious, often in direct opposition to other actors. This was the basis of game theory, and on its use Riker’s school followed rather than led.

  As the theorists became more ambitious, they moved from the areas where it might be assumed to be most valuable, with large samples but few variables, into areas of small samples and many variables. This included international relations. When the available options were not naturally constrained, the approach struggled because the identification of both a clear interest and an optimum strategy were hard to discern. Even in areas where findings were expressed with high confidence—for example, election studies—quite subtle variations in underlying conditions might render these findings unreliable. The more stable the environment the more behavior within it should show regularity. The more uncertain the environment the harder for actors to discern a rational way forward. In the textbook he wrote with Peter Ordeshook, Riker observed that when the “range of alternatives is infinite and when the consequences of choosing each alternative are uncertain, it is likely that most choices involve error.”11

  If only certain sorts of solutions could be recognized, then only certain sorts of problems could be addressed. The most susceptible were likely to be the most narrow, with the model incorporating as few factors as possible. If any attempt was to be made at empirical validation, data sets were needed which involved a sufficiency of comparable instances that would occur in a measurable form. While the findings might confirm what had been deduced from the model, despite the mathematical trappings, this could rarely be considered a proof. Causation might have something to do with those factors that did not fit easily into the model or could not be readily measured. Even when goals were achieved it was not always possible to be sure whether this was the result of the actions chosen rather than chance, coincidence, or the critical intervention of an extraneous factor.

  In the natural sciences, laws could be established. As particles did not have free will, cause and effect would be predictable. This was impossible when dealing with voluntary agents. Threats or inducements that normally produced one response could on occasion produce something quite different. This might not matter when the aim was to affect numerous small and comparable transactions, as was often the case in economics. By insisting that research into politics must meet standards of formal rigor and mathematical elegance, priority could not be given to the quality of the questions asked or the value of the answers. One critic observed, “Rigor is subject to a conservation law, and the more rigor along mathematical dimensions, the less of it along other, perhaps more important, dimensions.”12 As game theorists addressed these limitations, they either had to move away from the strict confines of the theory or take it to levels of complexity that only the cognoscenti could savor or follow.

  In one of the most serious challenges to rational actor theory in political science, Donald Green and Ian Shapiro observed that despite all the effort, what had been learned about politics was “exceedingly little.”13 They addressed one standard problem for rational choice theory which suggested that it would be irrational for anyone to vote since the time invested in the process would have to be set against the minimal impact that one person could expect to have on the final result. Yet people did vote in large numbers. How could the finding be reconciled without challenging a core precept of the theory? They mocked one response which explained the outcomes by “psychic gratification,” which might be an interest, but then why that rather than other interests? And what was the source of this gratification? Was it a concern for a cause, or belief that democracy depends on voting, or the quality of the candidates? The theory offered no good answer. When an interesting finding was obtained, explanations had to be found outside the theory. Stephen Walt concluded after surveying the application of the rational actor model to international relations theory that its “growing technical complexity” had not been matched by any “corresponding increase in insight.” The complexity allowed key assumptions to be buried and made the theories difficult to evaluate.14

  One Kuhnian answer to this challenge was that “a theory cannot be rejected because of disconfirming facts.” It could “only be supplanted by a superior theory.”15 But this exaggerated the status of what were often no more than speculative hypotheses deduced from suspect models. The fact that they might be discussed mathematically did not put these theories on the same level as those in the natural sciences.

  Forming Coalitions

  The book announcing Riker’s new approach was on coalition formation. The nature of communication between players, and whether this could be incorporated within the game or involved working outside the confines of the game, was one of the most challenging issues for game theory. If the starting presumption of autonomous, rational individuals devoid of social ties and cultural references meant that there could be no presumption of empathy, cooperation would depend solely on the logic of situations rather than any natural inclinations. Von Neumann and Morgenstern had promised, without quite delivering, advice on how to form coalitions when more than one player came into the game. With three or more players (n-person games), it became harder to make simplifying assumptions. The conflicts of interest were less straightforward. With three players, two acting in concert should win. When such a coalition was formed the calculation was as simple as it would be for a two-person game with a minimax solution. The challenge was on working out whether the rational course for weak players was to gang up against a strong player (balancing) or ally themselves with a strong player (bandwagoning). As many alternative coalitions might be stable, it would be necessary to go methodically through all potential coalitions to work out an optimum strategy.

  Just before Riker published his book, William Gamson had sought to develop a formal theory of coalitions. He agreed that the problem had to be reduced to a two-person game. He defined coalitions as “temporary, means oriented, alliances among individuals or groups which differ in goals.” They were likely to come together for the pursuit of power itself, by which he meant the ability to control future decisions. This they would be able to do because their joint resources would be greater than those of other units or coalitions. Some of the
goals of the component parts would remain incompatible, but they could concentrate on those that were distinctively their own. But when it came to predicting who would join with whom, which required understanding the resources most relevant for a given decision, their distribution, and what alternative coalitions offered the parties in terms of payoffs, Gamson found that game theory produced too many solutions. His general hypothesis was that participants would expect from a coalition a proportional share of the payoff according to the resources they contributed. This, he suggested, depended on reciprocity and a step-by-step process of pairing until a decision point was reached.16

  Riker took this further and developed a strong proposition, based on a study of coalition formation in legislatures, that complete and winning coalitions were “minimal” in the sense that they were just large enough to win and no larger, with the rider that the less perfect and less complete the participants’ information the larger the winning coalition would be. He found this “sparse model” worked quite well, though it deliberately excluded ideology and tradition.17 He also concluded, however, by the end of the 1960s that “much more energy has been expended on the elaboration of the theory of coalitions than on the verification of it.”18 Once again, the limits of game theory became evident when there were too many potential inputs and many possible outcomes.

  In his book on coalitions, Riker asserted, “What the rational political man wants, I believe, is to win, a much more specific and specifiable motive than the desire for power.” This posed the issue in zero-sum terms, which for most political men might be true only in a narrow sense and suggested that attitudes toward coalition formation would at best be grudging. It also allowed him to define rationality without reference to power, giving his rational political man a definite personality: “The man who wants to win also wants to make people do things they would not otherwise do. He wants to exploit each situation to his advantage. And he wants to succeed in a given situation.”19 This reflected Riker’s own personal interest not so much in the occasional political acts of ordinary voters, to which his reflections on democracy assigned only a limited significance, but on the key players among the political elite. Arguably, just as game theory worked best in economics when looking at oligopoly, where there were few players, this form of political science worked best when looking at oligarchy.

  An important attempt to demonstrate how the theory might be applied to a wider range of situations came from Mancur Olson, who was intrigued by the implications of the logic of self-interested rationality when it came to cooperation. Whereas Marx had sought class consciousness as a way of turning a shared interest into a political force, Olson pointed to the difficulties of a large and dispersed group ever acting as a political force. This was because each individual would assess that the marginal benefit from making contributions to a public good (that is one that is shared collectively rather than held by a few alone) was normally below the marginal cost, and also that their own contributions would barely make a difference. It was therefore irrational to cooperate with others, even in great numbers, to achieve collective goals: “Unless there is coercion or some other special device to make individuals act in their common interest, rational, self-interested individuals will not act to achieve their common or group interests.” An individual’s rational self-interest was to shirk on his contributions while continuing to receive benefit from the work of others.20

  This problem of the “free rider” was one that could be recognized, for example, in a member of a military alliance who gained protection but put few resources into the pool. This point was made forcefully by Olson while working as a consultant to RAND in the 1960s. He showed how NATO’s smaller members found that they had “little or no incentive to provide additional amounts of the collective good,” and so burdens were shared in a disproportionate way.21 Even though there was a shared interest, there was no point in acting on that interest if it was likely to be achieved whether or not you acted and without you paying any price. By contrast, however, if an individual’s actions really would make a difference and the benefits would exceed the cost, then it was rational to act to secure the shared interest. In some respects, therefore, Olson offered a form of elite theory because he explained how small concentrated groups with resources could retain influence. The majority might hold a contrary interest, but so long as it was diffuse and dispersed its impact was muted.

  Part of the explanation lay in a consideration of the social costs and benefits. An individual who did not bother to vote or join a union might escape notice, whereas in a small group engaged in an active campaign this would not be the case. On this basis Olson could explain, for example, why motor manufacturers might be able to lobby together for government measures that would keep car prices up, but the more numerous consumers would not be able to act equivalently to bring prices down. Collective goods affected everyone, but they were more likely to serve the interests of those best placed to lobby for them.

  Once social pressures were admitted then the questions of where interests lay became more problematic. Questions of honor and reputation had to be socially validated. They were meaningless outside of a social context, but that also meant that they could vary with context. A theory in which interests were narrowly conceived and pursued, in the form of money and power, might remain elegant and parsimonious but not necessarily very realistic. A variety of types of interests did not in itself damage the theory, which required only that they be pursued efficiently, but it made it less elegant and parsimonious.

  The Development of Cooperation

  It was not necessarily the case that game theory could not cope with behavior other than the most egotistical. The authors of a popular account of game theory as a strategic tool noted that one difference from the first edition (1991) to the second (2008) was the “full realization of the important part that cooperation plays in strategic situations.”22 One way of providing a game-theoretic understanding of the development of social behavior was through iterated games, a point made most strongly by Robert Axelrod’s The Evolution of Cooperation. The origins of this book are intriguing. It can be traced to Anatol Rapoport, who combined intense interest in game theory with an equally intense anti-militarism. Discovering von Neumann’s support for a preemptive war with the Soviet Union while the two were discussing support for mathematical biology was said to have been a turning point in his life. In 1964, he published a polemic against what he considered to be the misuse of game theory by strategists such as Schelling.23 While at the University of Michigan (before he moved to Toronto in protest at the Vietnam War), he actively promoted experimental games as a means of exploring the validity of theoretical “solutions” to theories of rational cooperation. Among a group who continued this work at Michigan was Robert Axelrod, also with a background as an antiwar activist.

  Axelrod saw the possibilities of using computers to experiment with game theory by setting up a tournament. He invited experts to send programs for a game of prisoner’s dilemma that could be repeated up to two hundred times to see if it was possible to learn or signal in ways that produced a cooperative outcome. Not surprisingly, perhaps, the winner was a simple program submitted by Rapoport. The requirement was to play continuing games of tit-for-tat, which required that one side replicate what the other did in the previous round. The first command was “cooperate,” and a continuing cooperative outcome flowed naturally. The message was that cooperative behavior could “thrive with rules that are nice, provocable, and somewhat forgiving.”24 This made a point about the possibilities of cooperation at a time of Cold War tension, and it had the great advantage of not depending on claims about how human goodness could trump amoral rationality. Other than the somewhat critical starting assumptions, the process was then computer dependent and untouched by human hand. Compared to the egotistical presumption of the theory, Axelrod demonstrated that cooperation could be rational.

  Did this have any value for strategists? The presumption was that cooperation was a g
ood thing except when it obviously was not (such as cartels). The book was a hymn to the virtues of altruism and reciprocity. Axelrod came up with four rules to establish cooperation. First, do not be envious. Be satisfied with absolute rather than relative gains, so that if you are doing nicely, do not worry is someone is doing even better. Second, do not be the first to defect, because you need to establish the logic of cooperation. Third, if another player defects, reciprocate in order to establish confidence in your retaliation. Last, do not be too clever, as others will not be sure what you are up to. Axelrod also pointed to the importance of a long-term perspective. If you were in a relationship for a long time then it made sense to continue cooperation, even when there were occasional wobbles, but in short-term encounters there were fewer incentives to do so. Little might then be lost by defecting.