1Although game theory now occupies a central role in the toolkit of economic theorists, a remarkable feature of its history is that in the 1950s, 1960s, and 1970s, this approach struggled to enter the economics mainstream. However, in a discipline striving to develop a formal, truly scientific, and possibly unified methodological canon, such as the 1950s political science, the kind of formal theory initially proposed by John von Neumann and Oskar Morgenstern was immediately perceived by some scholars as the ideal toolbox of methods, notions, and techniques. This aspect also points to another remarkable feature of game theory. Namely, it was a tool capable of being exploited across different disciplinary domains other than economics. This article shows that in the 1950s and 1960s, game theory occupied a central place in a definite intellectual agenda, and this was not part of economics but political science instead.

2Such a push for the adoption of game theory outside economics had its roots in some reviews of von Neumann and Morgenstern’s opus (von Neumann and Morgenstern, [1944] 2007) like Herbert Simon’s one (Simon, 1945). For what concerns political science, the 1950s saw some early results obtained through the so-called “cooperative game theory,” like those by the future Nobelist Lloyd Shapley and fellow economist Martin Shubik (Shapley and Shubik, 1954). These must be added to the well-known attempts to use the theory of games in international relations (Kaplan, 1957; Schelling, 1980). However, it was thanks to the commitment of a political scientist, William H. Riker, that game theory became the primary tool of the attempt to develop a truly scientific political science. As Riker wrote in the first chapter of his most ambitious theoretical work, The Theory of Political Coalitions (1962), “the main hope for a genuine science of politics lies in the discovery and use of an adequate model of political behavior” (Riker, 1962, 9). Such a model to him was eminently game-theoretical.

4Riker’s story fills different narratives, to which this article aims to contribute. The first is the history of game theory and, more generally, postwar mathematical economics, following the trail blazed by the works of Weintraub, Giocoli, and Leonard, among others (see Weintraub, 1992; 2002; Giocoli, 2003; Leonard, 2010). To these works must be added the reconstructions of the development of the postwar American Social Sciences and the notion of “cold-war” social sciences (see Amadae, 2003; Erickson, 2015; Erickson et al., 2015; Hauptmann, 1996). Finally, the development of American political science has been explored in many historical works. Indeed, the dramatic changes that occurred in the discipline in the postwar years (both in terms of its institutionalization and theoretical developments) framed Riker’s intellectual enterprise. Then, in the 1950s, a young generation of political scientists, like David Easton, Robert Dahl, and David Truman, among others, challenged the traditional approaches to political studies (history and law), advancing a plea for more empirical and quantitative analysis. Such a movement is known as the “behavioral revolution” in political sciences (Dahl, 1961; Somit and Tanenhaus, 1967; Adcock and Bevir, 2010; Adcock, 2009).

5Riker’s story fits all these narratives since he was a political scientist doing political theory when such “behavioral revolution” occurred. Riker indeed joined the “protest” against traditional political science, but not the revolution as a whole, focusing mainly on some tenets like the “plea” for objectivity in political theory. In doing so, he explicitly saw economics as a role model and adopted game theory. Therefore, this article also aims to contribute to the ongoing literature about the various attempts to extend the economics toolkit outside its traditional boundaries, closely following other works (see, for example, Medema, 2000; Medema, 2013; Fleury, 2010). We intend to show that Riker’s case was not a simple transfer of tools from one domain to another. The American political scientist indeed stressed those aspects of economic theory that fit his scientific, political science idea. However, he interpreted economics, especially its methodology, differently from what postwar mathematical economics was becoming.

6Riker’s use of game theory and formal analysis was strictly influenced by his being a political scientist working within the political scientist community. Then, whereas the development of game theory deeply affected the way postwar economists used to address theoretical problems, both in terms of mathematical sophistication and how they interpreted economic knowledge, Riker saw game theory differently. To him, this tool enhanced a strong predictive power, and his employment of it is justified on the basis of a robust positivistic attitude, which resembles Milton Friedman’s case for “positive economics” but also the “nomological-deductive” approach. However, it is well known that such positions were far from being the main force that fuelled economics’ radical postwar mathematization. This, in our eyes, represents a sort of “dilemma” that, as it will become apparent, Riker was not really able to solve. This work explores why Riker chose such a methodological point of view and how this affected his use of game theory or the immediate suitability of his model. In a nutshell, our thesis is that Riker presented to political scientists a relatively less sophisticated image of economics than what economics was becoming in the postwar years, and we try to advance some explanations for this.

7Section 1 and 2 describe Riker’s education and intellectual life until the late 1950s and how he became acquainted with game theory. Section 3 presents Riker’s main arguments in The Theory of Political Coalitions, focusing on his working through game theory to produce a suitable model of political coalition-building. Riker’s argument in this work was neither mathematical nor axiomatic. Thus, it is very different from the high theoretical game theory development in the 1950s (think of Princeton and RAND theorists). Consequently, it does not occupy a central place in the history of the development of game theory qua theory. However, it had an important role in how game theoretical ideas crossed domains different from economics. Section 4 discusses Riker’s relations with economic theory and outlines his methodological “dilemma.” Finally, Section 5 offers concluding remarks.

1. William H. Riker’s Education and Early Works

9Young Riker’s Harvard experience is extremely interesting to properly understanding the state of political science in the late 1940s and 1950s. In particular, it can be seen as a proxy of the problematic relationship between younger and innovative scholars within the unsatisfactory framework of a consolidated discipline. He arrived at Harvard before the period of intense methodological development and commitment to the quantitative method he would later define as “the ferment of the 1950s,” which coincided mainly with the “behavioral revolution” in political science and the development of new quantitative and qualitative analyses (Riker, 1997). At Harvard, in the 1940s, instead, the approach followed even by scholars more committed to the scientific method like Herring was mainly that of case studies, with a particular focus on public administration. Otherwise, the other important strand of research was the history of political ideas. Whereas Riker dismissed the earlier as “simply artistic investigations of events” (Riker, 1979, 39), the latter instead embodied what David Easton, at the time Riker’s fellow graduate student at Harvard, defined as the “historicist attitude in modern political theory,” equally opposed to empirical and theoretical analysis (Easton, 1951). In Riker’s own words, such a historicist attitude was defined as follows: “The idea was to have a clever interpretation of some event or a clever interpretation of some historical development and not to have a scientific approach to politics.” (Riker, 1979, 45) To his eyes, its main representative at Harvard was the famous German scholar Carl J. Friedrich, about whom he spent some harsh words in the interview with Shepsle (Riker, 1979, 41). In reality, in the pre-behavioral era, Friedrich was among the few scholars interested in setting empirical research within an original theoretical framework by establishing a theory of power. Consequently, he was pretty dismissive, as Riker was, of simplistic empirical analysis. But to Riker, Friedrich’s work, equally hostile toward any general description of political events, was without any usefulness in establishing a science of politics.

11The main tenets of the “behavioral revolution” entailed the emphasis on prediction and the explanation of political issues. These were based on observation and data collection, the development of interdisciplinary and “self-conscious criticism” about its methods and results. But also on pure research, leaving aside any normative aspiration to establish the “truth or falsity of values” like democracy, freedom, or equality, which are not amenable to scientific validation. Theoretical development occupied an important role in orienting and directing research (Somit and Tanenhaus, 1967). But this did not represent an explicit unified paradigm or set of theories. Instead, in the words of Robert Dahl, “those who were sometimes called ‘behavioralist’ … shared a mood: a mood of skepticism about the current intellectual attainments of political science, a mood of sympathy toward ‘scientific’ modes of investigation and analysis, a mood of optimism about the possibilities of improving the study of politics” (Dahl, 1961, 255). Up to conclude that “‘the behavioral approach’ might better be called the ‘behavioral mood’ or perhaps even the ‘scientific outlook’” (Dahl, 1961, 258). Besides, according to Riker, an important point was also occupied by reformist goals and practical interest in public affairs, which animated the young political scientists (Riker, 1997).

12Riker certainly shared such a mood but focused his attention more on the theoretical aspects rather than on the empirical analyses carried forward by behavioralists like Dahl or David Truman. Indeed, despite resting on more sophisticated methods than before, especially about statistical estimations (although far less advanced than incipient econometrics), the methodology of political theory was, to him, still grounded on flawed and unspecified ways of reasoning. These flaws became apparent to him after he published his textbook on the American political system, Democracy in the United States (Riker, 1953), primarily based on his teaching course in American politics at Lawrence College (WI), where he worked between 1949 and 1961 (Riker, 1979, 50). In his vivid account, working on this book led him to rethink the foundations of political science. In fact, after having published it, he started to realize that “it would be hard to say that any sentence in it was true” (Riker, 1979, 60); “I began to think that once you raise the question of what can you do to bring a particular moral position into some sort of effective institutional operation, why you also raise the question of whether or not institutions accomplish what they are intended to accomplish” (Riker, 1979, 2). Therefore, entailing an answer to these questions needed more than a normative stance and more than a plain description of how institutions work.

13In Riker’s mind, the issue at stake became that of ascertaining what political science is and if it does utter or not true sentences. Therefore, in his case, the strongest incentive to develop his intellectual agenda was the perceived need for a rigorous foundation of the methodological premises of the discipline. To pursue this ambitious aim, Riker started reading the philosophy of science and logic. But he soon realized that logic bore more on the validity of argument than its truth content. So, he paralleled these studies with more applied mathematical courses (Linear Algebra and Calculus) before discovering von Neumann’s and Morgenstern’s Theory of Games and Economic Behavior around the mid-1950s (Riker, 1979, 5 et ss).

2. The “Ferment of the 1950s”: Riker Meets Game Theory

14Riker recalled that “von Neumann’s book was the one that really turned me on because it seemed to me that there were some generalizations there that ... one could look at in nature and see if those generalizations turned out to be true.” (Riker, 1979, 5) Clearly, it was an intimidating book, especially for a political scientist with little math training. However, Riker felt confident to grasp the most important results from it, and, as we will show in the following section, he developed his theory of political coalitions entirely out of von Neumann and Morgenstern and not on other results of cooperative game theory.

15Riker quickly became “something of a publicist” for game theory in political science. For example, he insisted that the political theory panel at the “Midwest Conference of Political Scientists” at the University of Michigan, Ann Arbor (April 1958) was devoted to game theory, paralleling more traditional issues (Harry Davis to Riker, January 10, 1958). On that occasion, Riker presented a brief working paper that exposed some game theory principles for political analysis to fellow political scientists. (“Contribution of Game Theory to Political Theory”; Riker, 1958) He started by addressing some difficulties applying game theory in political science, commencing with political scientists’ lack of mathematical training. Nevertheless, he stated, the game-theoretical approach had much relevance to politics since

the category of zero-sum, two-person games is clearly a model for those political situations in which two persons are each trying to do the other in. ... The n-person game is clearly a model of the contemporary nation-state system of the free market of classical economy or of legislatures with undisciplined parties. (Riker, 1958, 2-3)

18In the cooperative case, the fundamental issue is that of choosing which coalition to join, given each player’s expectations regarding the payoffs, what he will obtain by selecting a coalition over another (through “side payments”), and finally, which partition of the game represents the solution to it. Besides, in this case, there are multiple notions of solutions, each with axiomatic and substantive properties that make them acceptable, both from a mathematical and rational point of view. To von Neumann and Morgenstern, for n-person zero-sum games, each coalition’s worth can be represented by a “Characteristic Function,” and what each coalition gives its members by a vector, defined as “imputation.” Due to their vectorial nature, each imputation can be related to another, using the notion of “dominance.” Then, a solution for a n-person game is offered by the set of all imputations that do not dominate each other and dominate all the imputations outside this set (this was called the “Stable Set”). However, this was not the only solution for such games. Other ideas came out, stressing one property or another of the definition of cooperative games (as the “Shapley Value,” discussed below).

20They defined power as the chance, represented by a “Power Index,” each committee member has of being critical to the success of a winning coalition (Shapley and Shubik, 1954, 787). The authors conceived their method as a first step to addressing such problems as designing the size and type of legislative bodies, protecting minority interests, and even finding a criterion for “fair representation.” Their analysis does not consider any sociological or political superstructure in a legislature; nevertheless, they argued, it could help set up norms or standards, “the departure from which will serve as a measure of, for example, political solidarity or regional or sociological factionalism in an assembly” (Shapley and Shubik, 1954, 791). This index represents the a priori chance for each committee member to be pivotal for a minimal winning coalition.

21Then, one can interpret Shapley and Shubik’s power index as a “technical definition of power” compared to the popular analysis of power, namely, the ownership and use of resources or the act of domination or influence of some individuals over others.

23In a late reminiscence, Riker attributed to Shapley and Shubik’s article a pivotal role in catalyzing his interest in game theory. Then, he summed up the importance of their result:

Most persons who have tried to analyze power have interpreted it as the ability of one person to make another person do something the other would not otherwise do. While I have deep reservations about this (and most other definitions of Power [Riker, 1962]), it is clear that Shapley’s definition is quite different. It involves not the ability to control persons but the ability to control outcomes through being the pivot or the marginal person between winning and losing coalitions: the last added member of a minimal winning coalition. (Riker, 1992, 212)

25From Shapley and Shubik’s power index, a vast literature emerged that applied this and other similar indices to legislatures, committee decisions, or even to the analysis of fairness criterion (Straffin, 1994). However, when Riker made his ambitious attempt to provide a full-breadth game-theoretical analysis of political coalitions, he took from Shapley and Shubik only the notion of a “minimum winning coalition.” Instead, he rested on the original analysis of von Neumann and Morgenstern. Moreover, he explicitly rejected any definition of rationality in terms of “maximization of power.”

27Despite the time spent at the CASBS, there are no clues that Riker was much in touch with the community of game theorists in the 1950s. In general, with very few exceptions, the intellectual communities of economists, political scientists, and game theorists remained disjoint. The game theorists’ community was made up, in the 1950s, of young mathematicians interested in the most abstract developments more than in practical employment. In places like RAND, the emphasis was allegedly put on the applied strand of game theory, e.g., its use in strategic and international political issues, but pure theoretical research was easily funded even there. In that community, not surprisingly, Riker was an outsider, lacking the necessary advanced mathematical capabilities needed to produce new mathematical theoretical developments. Furthermore, political scientists at RAND were anyway much interested in issues like nuclear deterrence or, in general, strategic analysis (the most notable case was that of Albert Wohlstetter, but also Thomas Schelling spent research time at RAND: Amadae, 2003). Riker’s focus on a well-defined issue, coalition formation in politics, and within a well-defined framework, namely “cooperative game theory,” may explain his distance from game theorists and, more generally, from those dealing with international politics.

28But the most crucial reason for his being an outsider was perhaps that Riker was advancing his theoretical agenda by advocating game theory. This agenda differed considerably from traditional approaches in political science as well as from the most recent “behavioral revolution.” Meanwhile, it was not easy to be integrated into the actual developments of game theory due to Riker’s mathematical difficulties.

29In the aforementioned interview with Shepsle, when asked if he ever sent any of his ideas to contemporary game theorists, Riker remembered only Duncan MacRae, whose response filled with detailed criticisms is not, unfortunately, among Riker’s papers stored at Rochester (Riker, 1979, 14). Another equally interesting proof of his being an outsider among the community of game theorists can be found in Oskar Morgenstern’s papers at Duke University. Riker completed The Theory of Political Coalitions in 1961 and sent the manuscript to Princeton University Press and Yale University Press. At Princeton, Morgenstern was extremely critical, rejecting its publication (Martin Shubik Papers, Box 8). Indeed, in a letter sent to Gordon Hubel (who was press editor at Princeton University Press), Morgenstern wrote: “The basic attempt is very laudable, and nobody doubts that Game Theory will influence Political Science vary considerably, but the execution leaves much to be desired.” (Morgenstern to Hubel, August 16, 1961) He continued: “Even the outline of Game Theory itself is full of misunderstandings and gaps. A reader not acquainted with Game Theory would not understand the exposition, and one already familiar with it would quickly spot the error” (ibid.). Morgenstern attributed the poor mathematical quality of Riker’s manuscript to his having worked by himself and advanced the suggestion to establish some cooperation with a real game theorist or spend some time obtaining a specific education in it. In fact, before writing his comment, he tried to detect who Riker was and what were his education, capabilities, and scientific research, but without obtaining any meaningful information. Finally, to remark on his point, he stated that “I am sure that anyone else who is at home in Game Theory and who would see this manuscript, perhaps given to him by some other publisher, would come to the same conclusion.” (Morgenstern to Hubel, August 16, 1961, Oskar Morgenstern Papers, Box 83)

31Shubik began his report praising Riker’s manuscript: “This manuscript is well worth publishing. It will make a rather controversial book containing several imaginative ideas.” Moreover, “its worth depends upon an imaginative insight concerning the application of the methodology of game theory to the subject matter of political science.” (Shubik, 1961, 1) This, in his own eyes, can prevent the “unfair criticism” that political scientists and game theorists would have likely levied on technical grounds.

32This point is interesting and deserves attention: Shubik’s appraisal of Riker’s work and his defense of “unfair criticism” rests more upon methodological aspects, that is, the employment of game theory in political science, than on technical grounds. In fact, he judged Riker’s argument about minimum winning coalition “too verbal for one part of his audience and probably may not be sufficiently verbal for the other part.” Besides, it is not clear, Shubik stated, to which extent Riker’s resting upon previous literature (like the work of Raiffa and the work of Vickrey about coalitions) suited political theory.

33Focusing on the detailed comments on manuscripts, the only substantial analysis advanced by Shubik is about what seems to him too much emphasis on the zero-sum model. To his eyes, much of Riker’s analysis would also hold in a non-zero-sum game, mainly because the most crucial feature of his game-theoretic analysis is the indeterminate temporal length. In contrast, zero-sum is well-defined only for a small finite part of the game. Instead, the main feature is the opposition of interest, which is a prerogative of a zero-sum (and constant sum) game and in a “more or less strictly competitive non-constant sum game” (Shubik, 1961, 2). Other comments are less substantial, although still interesting, like contesting that “side payments” has an underlying reference to money, as stated by Riker (although Shubik admitted that this is a common misconception of game theory). Still related to this is the remark that “to include threats as a form of side payments leads to a rather poor modeling of human affairs.” Because “the result of a threat may be a rather low personal payoff to an individual. However, the threat itself is more properly a part of a strategy” (Shubik, 1961, 4).

34Shubik recommended Riker’s manuscript for publishing, even with only editing corrections. Interestingly, he also advanced some forecasts about this work’s reception: “The odds are that it will receive very mixed reviews, including several very favorable and several highly unfavorable comments. It is certainly not going to make any ‘best seller’ list. However, it should make a worthwile (sic) contribution to the development of political science.” (Shubik, 1961, 4)

37Thus, whereas Princeton, the place where game theory was initially created and where there was a small but enthusiastic community of game theorists, rejected Riker’s manuscript, Yale instead accepted it, and The Theory of Political Coalitions was finally published in 1962.

3. Riker’s The Theory of Political Coalitions (1962)

38Riker’s The Theory of Political Coalitions represented the most significant accomplishment of the author’s intense commitment to game theory and formal analysis. He published other such general works only in the 1980s, although his focus shifted from game theory to social choice analysis, political theory, and American History (see, for example, Riker, 1982). This effort was an extraordinarily ambitious enterprise that aimed to construct, using an “existing general theory of coalitions (the theory of n-person games),” a theory of coalitions useful in studying politics and that rested on exact and verifiable assumptions (Riker, 1962, vii).

44The bulk of Riker’s analysis is centered around the “size principle,” namely “the fundamental principle concerning the size of coalitions,” that goes as follows: “In n-person zero-sum game, where side-payments are permitted, where players are rational, and where they have perfect information, only minimum winning coalitions occur.” (Riker, 1962, 32, italics in the text) A descriptive statement (or “sociological law”) is related to this principle: “In social situations similar to n-person, zero-sum games with side-payments, participants create coalitions just as large as they believe will ensure winning and no larger.” (Riker, 1962, 32-33)

46As seen, Riker aimed to discuss political coalitions, namely coalitions involving winners and losers. Then, the framework of his analysis is cooperative and not competitive since it involves coalitions and, therefore, communication and agreements among players. Unfortunately, as he rightly noted, no unique solution exists for such games (contrary to the latter type, where a solution is a Nash Equilibrium). In his view, the cause is that too much emphasis has been put by game theorists on the properties of coalitions, like their existence, reasonableness, or fairness, overlooking instead the possibility of delimiting coalition structures directly. Since among the different solutions that followed von Neumann and Morgenstern’s, none appeared to him significantly preferable to the latter, neither in terms of empirical testing nor generality, Riker based his analysis directly on the original solution concept developed by the creators of game theory (von Neumann and Morgenstern, [1944] 2007).

49Riker restated von Neumann and Morgenstern’s original model, in a more straightforward and less mathematically sophisticated way, to describe in a statical way the coalitional structure of a political situation modeled as a n-person game. However, he also interpreted such a structure in terms of equilibrium and disequilibrium. Each v(S) can assume a range of values, which is a function of its size, and the size of the opponent blocking or losing coalition. Riker’s definition of equilibrium and disequilibrium directly reflects each agent’s strategy and rational decisions in the coalitions. In particular, he defined the notion of “equilibrium” in terms of each coalition’s realizability or not. Then:

• 26 Unfortunately, Riker was not sufficiently precise about what the criterion of realizability refers (...)

[i]f there are some values of v(S) so unnecessarily disadvantageous for S as a whole that rational players reject S in favor of an immediately available alternative T, then these values of v(S) will be said to be in disequilibrium and S will be said to be unrealizable. Conversely, those values of v(S) which are not disadvantageous in comparison with an immediately available alternative will be said to be in equilibrium, and S will be said to be realizable. (Riker, 1962, 262, italics in the text)26

50He outlined three different types of winning coalitions:

• those whose value decreases monotonically with the growth of their size;

• those that gain by adding new members, at least until a certain point. After that point, the value decreases;

• • 27 Again, Riker’s analysis is quite involute. He adopted a notion in von Neumann and Morgenstern’s The (...)

  those whose values are indifferent to their size.27

51Intuitively, the first states that the value of the coalition decreases with the growth of its size. The second case relates instead to a coalition that gains by adding new members, at least until a certain point. Finally, there are coalitions whose values are indifferent to their size. So then, the puzzle is the following: if having reached a majority a coalition deems its own size disadvantageous and prefers to leave out some members, then this is not an equilibrium. Riker showed that, in the first type, the only equilibrium, that is, the only coalition that is realizable is represented by a minimum winning size. In the same way, in the second case, coalitions are realizable only until the peaked point is reached. Finally, the only equilibrium size in the third case is m, the arbitrarily chosen size (Riker, 1962, 245 et ss).

52Riker was looking to develop a theory that could be used to make predictions and to be tested against the reality of political facts through the formal structure of his assumptions. As he wrote: “whether or not the just-stated conclusion is of any scientific value depends on whether or not an analogous statement about real-world can be verified.” (Riker, 1962, 47) The “analogous statement” is the “size principle,” which states that in social situations similar to n-person zero-sum game, only coalitions no larger than the minimum size occur.

I do not suggest, of course, that these nineteenth-century statesmen appreciated this principle as a law of rational behavior. What I do insist, however, is that it describes their behavior, even though they probably perceived their problems thus: With our overwhelming majority, there are so many and so conflicting interests in the party that none can be satisfied. As long as two conflicting interests remain in the party, neither can be satisfied [which, I add, is why a grand coalition is valueless]. For the sake of action for the interest we approve, we shall therefore decide to satisfy one interest, and if others are offended, they may leave the coalition. (Riker, 1962, 65-66).

54In a similar spirit, he integrated the role of information in his model by outlining a relationship between the level of information of each player in a coalition and the size of the winning coalitions. Namely, the greater the degree of incompleteness of information, the larger the size of coalitions. This rule, which Riker named “the information effect,” could explain why minimal winning coalitions are often not found in the real world. But, also, why some elections in US history have been “critical.” The American political scientist V. O. Key developed the notion of “critical election” to define those elections where the voters’ involvement is high and new electoral groupings are created (Riker, 1962, 90 et ss). But, Riker stated, one could interpret this notion as a period where the amount of information in the system declined and the uncertainty grew about the size of the winning coalition.

55Riker also elaborated upon some statements from Anthony Downs’ economic analysis of democracy. According to the latter, in a 2-parties model, where voters want to maximize their utility and parties want to maximize their share of votes, it could be convenient for both parties to be as ambiguous as possible. However, this would contradict the assumptions about voters’ utility maximization because this makes it more difficult to vote rationally for each citizen, thereby encouraging voters to make their decision on some different basis from issues (viz, the candidates’ personality). This paradox represented a blow to any attempt to use rationality to define voters’ and parties’ behavior. However, Riker was convinced that his model offered a getaway from this situation. If parties seek to maximize the share of votes only up to the size needed to become a minimum winning coalition, therefore, it is not any more convenient for them to becloud their positions in any situation, but only about those issues that are of concern to voters about whom they have imperfect information. So the principle that parties and voters are rational (i.e., utility maximizers) is preserved.

56The “size principle” represented an ideal standard to which any reasonable attempt to form a coalition should conform. In this sense, although resting on von Neumann and Morgenstern’s solution for n-persons games, it was not a solution for such games but a “sociological principle.” In the second part of his work, Riker investigated how political leaders set forth coalition-building and reached a stable arrangement if any. This analysis aimed to fully exploit what the author later recalled as the main feature of game theory, namely the choice of strategies (Riker, 1992).

57In a nutshell, Riker discussed how coalitions are formed, maintain their structure, or add new members across a multi-stage game whose last stage represents the outcome of the process. For example, in voting, where a weighted majority is required, different coalitions are present (or “proto-coalitions” in Riker’s terminology). Then, the leader of each proto-coalition tries to add new members, if necessary, by offering side payments. If, in the final stage, the coalition structure is such that a minimum winning coalition occurs, then this represents an equilibrium outcome.

58Riker outlined his model as follows: assume a decision-making body, I, made up of n-members (i.e., a n-person zero-sum game with side payments). In this body, there are different roles, but each member can assume any role. Each member’s power (i.e., the weight) is assumed to vary. The decision rule is that a coalition with weight m, where m is greater than half the sum of the weight of each player, can act as a whole. The ZSC imposes a limit; no decision can be taken, so losers would prefer to resign from the body rather than acquiesce. In this model, coalition building begins when a leader that is a member of the decision-making body undertakes the task of forming a coalition on a particular issue. To this aim, the leader needs to attract followers among the other participants of the decision-making body. Given the focus on the dynamic process, Riker distinguished between coalitions and “proto-coalitions.” In brief, the first are end products of coalition-building and can be “winning,” “losing,” or “blocking.” Followers join instead in a “proto-coalition,” a subset of I when this has at least three subsets, and none has weight m. These proto-coalitions change their size due to moves made by each member of I, and each move has the effect of changing the body’s internal structure. Thus, in the first stage of such a game, there are n-single member coalitions. In the second stage, there are (n - 1)-single-member proto-coalitions, one 2-member proto-coalition, and so on, up to the last stage, where either a winning coalition or different blocking coalitions exist.

59Since any attempts to build a coalition generate opposition, the effect of the leader’s first step toward building a proto-coalition is that others follow him and try to build their coalitions. The growth of proto-coalitions depends on the leaders’ ability to attract followers by offering side payments (Riker, 1962, 122). These side payments can vary, but Riker listed some examples. These are payments in promises on particular policies, or subsequent decisions, up to the threat of reprisal. Besides, these side payments also have costs, which the coalition leader pays, and must consider (Riker, 1962, 109-120). Most importantly, Riker assumed that side payments were scarce and finite, subject to considerations regarding their economic value.

60The study of dynamic coalition building is important because it involves strategic considerations about the behavior of political actors and the equilibrium outcomes and, therefore, their inner stability. To discuss these features, Riker introduced a notion “in some respect stronger, and in some weaker” than von Neumann and Morgenstern’s set-valued solution because the latter did not specify if some coalition in the V-set was winning. He proposed the notion of a “uniquely preferable winning coalition,” which involves the specification of a determined winning coalition. A uniquely preferable winning coalition is a coalition that has a greater value than any other one possible and in which all the participants can satisfy their initial expectations. An “initial expectation” for a proto-coalition equals the best it can do in joining alternative non-minimal winning coalitions.

61From these considerations, any proto-coalition has some advantages (and disadvantages) in different stages of the game. An equilibrium solution is such that when a “uniquely preferred winning coalition” occurs, none of the other proto-coalitions can neither join it or form a new winning coalition. Since this entails the “size principle,” then an equilibrium corresponds to the presence of a minimum winning coalition.

62However, the most crucial problem with this kind of analysis is that the equilibrium in coalition-building cannot be maintained (i.e., it is not stable), but it seems to depend on the size and the relative strength of the minimum winning coalition (Riker, 1962, 147). The effects of this lacking of equilibrium for political analysis could be very serious: “equilibrium in society is a kind of stability despite the change. And to say that this model lacks equilibrium is to say that the social processes it purports to describe are so unstable that the political society itself is in fact unstable.” (Riker, 1962, 147-148) Therefore, the last three chapters of The Theory of Political Coalitions contained a purely verbal discussion about the components of this disequilibrium and its consequences.

63Once more, Riker rested on History to assess this theory. In particular, the event he tried to explain was the so-called “corrupt bargain of 1825,” when Andrew Jackson won a majority in the electoral college but lost the vote at the House in favor of John Quincy Adams, who became the sixth President of the United States (Riker, 1962, 149-159).

65Then, the historical argument again serves Riker to show the explaining power of his model and provide the basis for a new understanding of historical and contemporary political facts. Again, furthermore, Riker stressed the fact that his example did not show that Adams, Clay, or Jackson were employing game theory or rational choice, but that their behavior can be explained as if they did.

4. Political Science and Economic Modeling: Riker’s Unsolvable Dilemma?

66Riker’s work was reviewed in the American Political Science Review and other social sciences journals (Fagen, 1963; Matthews, 1963; Hotz, 1962; Kaplan,1963; Flanagan, 1965). All the reviewers highlighted Riker’s methodological originality and the importance of his non-trivial generalizations about politics (although with some reservations about the notion of rationality). Yet, none stressed its formal features. Indeed, none of the reviewers was a real expert in game theory. As to economics, the book went completely unnoticed in economic journals.

67As Riker lamented in Shepsle’s interview, not many people had a sense of his work’s theoretical features (Riker, 1979, 24). Political scientists indeed focused only on some aspects of his model, especially the last three verbal chapters. Furthermore, as it is apparent from many reviews, Riker’s idea came to be framed and discussed mainly in international politics. Riker’s last chapter, where he tried to detect some considerations about the developing rivalry between the United States and the Soviet Union, caught the readers’ attention more than the formal characteristics of the model. Besides, Riker’s adoption of von Neumann and Morgenstern’s solution went mainly unnoticed by game theorists. Consequently, the importance of Riker’s work on political coalitions rests upon its being the first attempt to elaborate a model of political behavior explicitly based on a game-theoretical approach, even if this was far from reaching the levels of contemporary formal analyses in economics. Although Riker’s work did not offer anything new to the development of game theory, it still represented, in the light of what formal political theory became from the 1960s onwards, the first step of one of the most successful translations of theoretical ideas from one domain to another.

68A further episode can make apparent how economists and political scientists remained disjointed communities in those years. In a review of a comprehensive collection of essays about the different approaches to the study of politics, Riker complained about the lack of an economic approach (Riker, 1959). We believe that this complaint can be paralleled with the publication of a strictly formalized volume about the use of mathematics in the social sciences, with several highly mathematical essays about economics, management, and psychology, but no reference to political science (Arrow et al., 1959). Unsurprisingly this volume went unnoticed in political science journals. Indeed, only one reviewer (the future Nobelist Reinhard Selten) noticed, in Econometrica, the absence of an essay on political science (Selten, 1962).

69His theoretical shortcomings notwithstanding, The Theory of Political Coalitions, alongside other works, like that of Buchanan and Tullock, Anthony Downs and Duncan Black has marked the birth of a formal political theory (Ordeshook, 1986; Persson and Tabellini, 2002). Besides, among these authors, Riker was the only one who used game theory extensively and, overall, was a political scientist with a definite theoretical agenda.

70In the remnant part of this section, we discuss Riker’s use of economic theory concerning his agenda of transforming political theory and the development of postwar mathematical economics. In particular, Riker showed a sheer interest in some methodological issues, which can be confirmed by two philosophical papers, the first chapter of his work on political coalitions, and other works we will briefly address (Riker, 1957; Riker, 1958; Riker, 1962; Riker, 1977). In the meanwhile, however, he did not adopt deep methodological arguments. So, the main feature of his philosophy of science is represented by the robust faith in the idea of science as a positive discipline. In order to be a “genuine science,” a theory must display those elements that make it possible to explain the phenomena and predict their outcomes, eventually by discovering laws that relate different pieces of reality under a single theory. Riker’s approach is “nomological-deductive.” However, he paralleled such a view with a position entailing a more instrumentalist approach. Here lies what can be defined as “Riker’s dilemma.” He advocated the development of positive political science, resting heavily on formal assumptions, but the tools and the kind of analyses he was trying to adopt were far from being able to fulfil his aspirations.

71Following E. Roy Weintraub’s pivotal studies, historians of economics have interpreted the development of economics as a mathematical discipline in relation to the parallel development of mathematics as a formalist program. In this sense, postwar mathematical economics was not limited to employing math but mirrored the changes that occurred in this discipline, that is, “the changed standards for accepting proofs, changed ideas about rigor, and changed ideas about the nature of the mathematical enterprise” (Weintraub, 2002, 2). Similarly, Giocoli summed up the radical transformations in economics between the 1930s and the 1950s as two distinct visions of economics (Giocoli, 2003). The first is the idea of economics as a “system of forces,” which entails the idea that its main subject is the analysis of the processes generated by market and non-market forces, including—but not exclusively—the processes leading the system to an equilibrium. Economists paralleled this idea and replaced it with economics as a “system of relations.” According to the latter, “economics is a discipline whose main subject is the investigation of the existence and properties of economic equilibria in terms of the validation and mutual consistency of given formal conditions, but that has little if anything to say about the meaningfulness of these equilibria for the analysis of real economic systems.” (Giocoli, 2009, 24)

72Such a transformation was far from being accepted without resistance among economists and gave new fuel to the everlasting debates concerning the philosophy and methodology of economics. In particular, the spirit of new axiomatic economics challenged the most traditional views of the scientific enterprise as an explanation and, to a certain extent, a prediction of phenomena. For instance, it is pretty obvious that a mathematical model such as the “General Economic Equilibrium” model lacks both explanatory and predictive power. Indeed, it is explanatory only in the sense that a mathematical theorem explains something, and it is predictive in the same way. Then, as Pierluigi Barrotta rightly put it, Gerard Debreu’s statement, at the very beginning of his The Theory of Value, according to which his theory explains how the prices are determined from agents’ private ownership through markets and their role in an optimal state of an economy, could be seen as meaningless if one assumes that to explain something one has to find general laws relating different phenomena and their appearance (Barrotta and Raffaelli, 46; Debreu, 1959). This does not mean that economists are no longer trying to explain phenomena or advance their predictions about possible outcomes, but new languages and practices have been developed to fulfil this aim.

Given social situations within certain kinds of decision-making institutions (of which parlor games, the market, elections, and warfare are notable examples) and in which exist two alternative courses of action with differing outcomes in money or power or success, some participants will choose the alternative leading to the larger payoff. Such choice is rational behavior and it will be accepted as definitive while the behavior of participants who do not so choose will not necessarily be so accepted. (Riker, 1962, 23, italics in the text).

76Furthermore, Riker also stated that not all behavior needs to be rational, but rational behavior is crucial for managing any economic or political institution. Thus, like the markets are controlled by those economic agents who adopt a maximizing behavior, the same holds for the working of political institutions that “select and reward with success behavior which is apparently motivated by the intention to maximize power” (Riker, 1962, 21).

77One can find even more strong references to a sort of instrumentalist position in the pages where Riker attempted to assess his “size principle” historically (Riker, 1962, 65-66). Then, as seen above, what matters to him is not that politicians closely employ game theory but that the model offers an accurate explanation of their behavior, thereby making possible a fuller understanding of it.

78Further details, although not developed systematically, concerning the nature and the scope he attributed to social sciences can be found in a review essay significantly titled The Future of a Science of Politics (Riker, 1977). Riker again rejected the particularistic study of political events, proper of the more traditional approaches of political studies, emphasizing instead a “positivistic view of science” whose central tenets are sets of scientific laws, i.e., “well-verified generalizations.” Besides, by scientific laws, Riker defined not only those discovered by observation but also theorems derived from axioms. He seemingly attributed the same scientific status and explanatory power to both:

Law and axioms thus reinforce each other. The necessity of the inference makes the law seem reasonable, and the empirical validity of the law makes the axioms seem true. Thus, with a theory, there is a much stronger reason than mere observation to accept a scientific law. (Riker, 1977, 15)

[price theory] contains all the elements in our previous description of science. It starts with an empirical law, which is presumably universal when properly restricted. This law is then imbedded [sic] in a theory of choice. In turn, this initial theory is elegantly elaborated to produce a nonobvious and far from trivial inference about market clearing, which is in turn strongly supported by empirical evidence. (Riker, 1977, 21-22)

80If in this work, Riker’s position shows a “nomological-deductive” approach, assuming the importance, for the science, of discovering general laws in order to explain phenomena, in another paper, he returned to the issue of predictability (Riker, 1980). There, he explicitly stated that economics is a theory that admits predictions of an equilibrium. Furthermore, its prestige among other social sciences is due to the “actual occurrence of numerous predicted equilibria” (Riker, 1980, 434). Note that Riker generally refers to economic theory and not to a part of it (like, say, game theory).

81However, his close identification between equilibrium and predictions raises several problems for political theory. Riker linked the main advantage of equilibrium analysis to its ruling out interpretive and psychological motives behind people’s actions. As he wrote about one of the most important results of the theory of voting:

ideological extremists who vote eagerly for the party closest to themselves certainly intend to bring about extreme results; yet one social consequence, as McKelvey (1975) has elegantly shown, is that they drive parties to converge at the ideological center. No amount of sympathetic interpretation of individuals’ motives and actions can explain this unanticipated social result. ... Even when individuals accomplish exactly what they intend, social outcomes are not explained by interpreting motives. (Riker, 1977, 28)

82The failure to produce general results concerning the theory of voting (the most significant example in economics of such a general result being the General Economic Equilibrium), and, consequently, the flowering of many “impossibility results” (see especially those discovered by Richard McKelvey and Norman Schofield) scattered Riker’s faith in his positivistic idea of science linking equilibrium, individual rationality, and predictions so that he famously argued that not economics but

politics is the dismal science because we have learned from it that there are no fundamental equilibria to predict. In the absence of such equilibria, we cannot know much about the future at all, whether it is likely to be palatable or unpalatable, and in that sense, our future is subject to the tricks and accidents of the way in which questions are posed and alternatives are offered and eliminated. (Riker, 1980, 443, italics in the text)

83Therefore Riker, although not rejecting his positivistic program in toto, spent the remnant part of his career (he died in 1993) investigating further the institutional arrangements surrounding the persistence of disequilibrium and the occurrence of many, very fragile, temporary equilibria in choice settings.

85Ordeshook claimed that Riker attributed too much significance to the idea of equilibrium as stability and, therefore, to the idea that price theory itself referred to market stability. As it turned out, “the presumed stability of markets is an abstract fiction that most economists recognize as a a theoretical impossibility” (Ordeshook, 1980, 447, italics in the text). It was something existing in the formal model but not necessarily in reality. The same holds for the theory’s predictive power: abstract descriptions of markets might predict how a change in the general settings of the model affected prices and consumption but could not anticipate these changes. For instance, in a market with one seller and two buyers, the value of the coalition of buyers is zero. The core (i.e., the set of all undominated imputations) comprises only those imputations that attribute value to the seller and nothing to the buyers. Namely, the single seller is a monopolist and will extract all the added value from any exchange. Nonetheless, it could be reasonable to assume that buyers could form a cartel and negotiate as a team, and a new equilibrium would arise. For example, this now becomes a bargaining problem, where the monopolist tries to obtain a distribution as advantageous as possible on the Pareto frontier. However, the core now consists of all the points in the Pareto frontier, and therefore, the existence of equilibria is not a sufficient condition for predicting outcomes (Ordeshook, 1980, 448).

86Ordeshook’s central point is thus that equilibria are elements of the formal model and therefore display features like existence, uniqueness, and stability but do not necessarily entail predictive power. This argument does not exhaust the question of the impossibility of collective choices but instead points to new ways of analyzing the problem. In particular, he called for political scientists’ genuine contribution to developing new formal models and not only to employ notions and ideas taken away from economics.

87Looking at the differences between Riker’s argument and Ordeshook’s allows a final appraisal of how Riker used game theory and economic theory and how this differed from postwar neoclassical economics and other attempts to extend economic reasoning across domains different from economics. Returning to Giocoli’s distinction between “economics as a system of forces” and “economics as a system of relations,” Riker’s analysis looks closer to the former vision. Indeed, to him, equilibrium is not an analytical framework within which formal analysis can be conducted (and neither the solution of a game) but instead a relationship of forces. Take, for instance, how, in his work on political coalitions, Riker defined this notion: “[T]he notion of equilibrium is that of a relationship of forces arranged so that the deviation from some point of balance results in a (possibly automatic) correction back to balance.” (Riker, 1962, 147) Only in this way, equilibrium can be related to prediction. Besides, this can also explain why he was so concerned with the issue of disequilibrium. Indeed, in a “system of forces” framework, disequilibrium, and equilibrium have the same importance. Since it is clear that reality, especially social reality, hardly shows anything similar to “physical” equilibrium, disequilibrium sometimes has a stronger appeal to the researcher. On the contrary, in a purely axiomatic model and within the notion of equilibrium widely employed in game theory (that is, Nash Equilibrium), equilibrium is simply the necessary outcome of the model, i.e., the solution of a problem modeled like a mathematical problem. Naturally, then, the main issue in such models is the existence or non-existence of equilibrium itself (and, possibly, its multiplicity).

88The point is that in economics, game theory was conceived within the “system of relations” framework. This simple historical fact shows how the entry of game theory into political science differed substantially from the way it entered economics. It also makes it apparent how the task Riker tried to accomplish, especially in his analysis of political coalitions, was arduous to achieve: not only because Riker lacked the advanced game-theoretic skills that could have made his research more mathematically robust, but also because he considered game theory from a viewpoint that was too different from his actual development in mathematics and, later, in economics.

89Finally, some hypotheses can be advanced for explaining Riker’s resting on the old idea of “economics as a system of forces.” Riker was an outsider among the community of game theorists and economists as well, so the most immediate hypothesis is that he simply lacked adequate knowledge of economics to fully assess its most recent developments. True as it could be, such an explanation is not sufficient. A suitable answer lies, in our view, in the fact that Riker was trying to make sense of the idea of political theory based on rational choice for political scientists, an audience much different from economists. In this sense, one could explain, for instance, his rejection of a preferences-based tautological argument regarding rationality (Riker, 1962).

91Compare Riker’s idea with von Neumann’s theory characterizing rational behavior with prudence. Indeed, in his 1928 paper and his 1944 work, rational behavior is represented by the “security payoff” given by the minimax strategy. Namely, a player does not need to know what his opponent’s plan will be in reality, but if he plays the minimax strategy, he will maximize his expected payoff in the worst possible case. (von Neumann, 1928; Giocoli, 2003b) This idea solves the paradox of perfect knowledge discussed in the 1930s by authors like Morgenstern and Friedrich von Hayek, albeit in different forms (Morgenstern, 1935; Hayek, 1937; see also Giocoli, 2003). Like von Neumann, Riker focuses only on one feature of human behavior: the preference for winning outcomes. Avoiding a too narrow idea of rationality (i.e., that “individuals’ scales of utility ... are isomorphic with the scale of some objective measure such as money or even power”), he expected that “rationality as winning” could establish the foundation of a theory of political coalitions based on von Neumann and Morgenstern’s formal analysis. If one interprets Riker’s argument that way, it could be possible to understand why he chose it. Nevertheless, there is no contradiction between a formal argument and an idea of rationality that encapsulates concrete human behavior features. Von Neumann’s solution was criticized for equalizing rationality and prudence. However, it was not this aspect that undermined its acceptance, but the mathematical difficulty in proving a similar result for those situations (non-cooperative and cooperative) different from 2-person zero-sum game (a problem that the newborn idea of Nash Equilibrium overcame).

92To conclude, one could explain Riker as resting on an old idea of economic analysis as a “system of forces” that, attractive as it might be, was increasingly being displaced in the very area of economic analysis that he had selected as his theoretical reference (i.e., game theory) by new ideas concerning axiomatization through a view of economics as a “system of relations.” An area, it should be added, that until very recently has always been the most distant from the possibility of empirical validation. This, in a nutshell, was Riker’s unsolvable dilemma.

Conclusion

93This article showed how game theory entered political science and what was the role of William H. Riker.

94I focused on how Riker’s analysis differed from economics and formal game theory, primarily for what concerns the structure of the argument and the different scope pursued. I showed that Riker’s relationship with economics and game theory was, in a certain sense, fuzzy. He referred to economics as a role model, but his idea of economic theory was distant from that of economists at his time. His treatment of rationality lacks the generality for establishing a full-breadth theory and, indeed, will be discarded when “Positive Political Theory” aligns itself with economics. Besides, he understood what was missing in game theory but was an outcast in the community of game theorists.

95Riker certainly had a limited influence on the development of game theory qua theory. Instead, emphasizing the consistency of his theory with the explanation of real-world (or even historical) political phenomena served better his task of showing how functional game theory could be in political analysis. To this aim, more than a mathematical sophistication that few political scientists were barely able to grasp, he showed how political behavior was inherently game-theoretical and, therefore how fertile game theory was for allowing “political science to rise above the level of wisdom literature and indeed to join economics and psychology in the creation of a genuine science of human behavior” (Riker, 1962, viii).

96With the passing of the years, the difference between formal political science and economic theory narrowed, up to the point that important contributions were also published in economic journals like Econometrica or The Journal of Economic Theory. This process paralleled and was the effect of establishing a community of scholars entirely devoted to the formal analysis of political issues. At the same time, it opened a new stream of methodological issues, namely the attempts to reconcile positive aspirations with the ambition to develop a genuinely mathematical analysis (Austen-Smith and Banks, 1999). In the end, this was Riker’s most significant legacy. Such a story, which starts with Riker’s creation of the Political Science Graduate Program at Rochester University, is the necessary complement to this article.

I want to acknowledge Professor Giocoli, who supervised my Ph.D. dissertation; Professor Lapidus and Arena, who read a previous version of this work at the 2021 ESHET Summer School in Paris, providing useful insights; Catherine Herfeld, who similarly read a previous version of this work; and the participants to the STOREP Conference (2020), ESHET (2021) and HES (2021), who read and commented the previous versions of this article. Finally, special thanks to all the professors, the staff, and the fellows at the Center for the History of Political Economy at Duke, with which I had a lot of valuable exchanges in the eight months I spent there. I also want to acknowledge the staff of the Rare Collection at Rubinstein Library for having assisted my research, and finally, the Staff at the Rochester University Library.