INSTITUTIONAL EFFECTS ON COMMITTEE BEHAVIOR: A GAME THEORY EXPERIMENT Richard K. Wilson Submitted to the Faculty of the Graduate School in partial fulfillment of the requirement for the degree Doctor of Philosophy in the Department of Political Science Indiana University November 1982 Accepted by the faculty of the Graduate School, Department of Political Science, Indiana University, in partial fulfillment of the requirements for the degree Doctor of Philosophy. Doctoral Committee: Elinor Ostrom, Ph.D., Chairperson Edward G. Carmines, W . D . V\ W ^ . V ith participant prefers x to y x Li y — > i is indifferent between x and y x Ri y —> x is at least as good for i as is y (but y is never better than x ) . c) Transitivity holds that an individual's connected alternatives have a consistent pattern. That is, if: xPi y and y Pi z, then x Pi z and not z Pi x. 2) Unlimited Domain. This condition simply points out that all orderings of preferences are admissible. That is, for a set of alternatives: m = {x,y,z}, there are six possible orderings that a participant might have (taking into account only strongly dominated alternatives). A participant can then have any of these orderings for preferences. 3) Independence of Irrelevant Alternatives. This condition has met with the greatest disagreement by researchers. However, the point is that if a participant has a preference ordering (x Pi y pi z) and one of the alternatives becomes infeasible (y drops out as a viable alternative), then the remaining alternatives retain their connected order (that is, x Pi z and not z pi x ) . . This seems a reasonable extension when participants maintain sincere preference orderings, and do not anticipate the preferences of others. These conditions all relate to the autonomy of the individual in arriving at a preference ordering. They are consistent with liberal democratic conceptions that only individuals are capable of making 20 decisions. Further, the ordering of preferences over various alternatives is internal to the individual. These preferences are not imposed exogenously to the individual through some other mechanism. These first conditions outline a model of individual decision making. The second set of conditions point to the structural mechanisms by which people rule. These conditions are concerned with the means by which alternatives are compared and selected. Social Conditions: 4) Positive Responsiveness. In this case, if a set of individuals have well-defined preferences over alternatives, and a single individual changes their preferences, then the social decision either remains as it is or changes in the direction of the individual's change. That is , the outcome (social decision) is dependent on the orderings that individuals have. As an example, suppose participants have the following preference orderings: a: b: c: X P In this case, z would be the outcome (both b and c have z as their first choice). Now, suppose c changes their mind and the new ordering is: a: b: c: x P z P* x P b y Now c prefers x to z (and y). The alternative x would now be the choice, since a and c both prefer it to any other alternative. Further, the change in the "social outcome" is consistent with the change by c. 5) Citizen Sovereignty. This condition very simply states that the outcome cannot be imposed. In other words, an outcome cannot occur regardless of the preference orderings held by individuals. Such a condition is quite consistent with the notion of democracy used above — that it is individuals who make decisions, and outcomes are dependent solely on those individuals. 21 6) Nondictatorship. This condition is related to citizen sovereignty in saying that no single individual can impose his will (select an outcome) irrespective of the preference orderings of all others. Those conditions build in many institutional features. First, it is the aggregate of individual preferences that decides among alternate proposals. The aggregation rule is deliberately left general. Second, no outcome can be imposed contrary to the aggregate wishes of the citizenry. Third, al l citizens have an equal say — that is , no individual's preference ordering counts for more than another's. The institution, then, is quite simple and on the surface satisfies the dictum "Rule By the People." "The People" are well-defined — they are simply some set of individuals. This could easily be all individuals, or some limited set of people. However, in the general case it includes everyone. "Rule" obtains from comparing various proposals. All alternatives are compared, with the most preferred alternative becoming the collective decision. Finally, "By" is rule by all the people. No single individual has extraordinary powers to dictate the collective decision. In some respects, this abstract model is similar to a fully democratic institution. Individual preferences are taken as givens, participants are weighted equally in their votes, and finally, no individual is entitled to impose their will on the will of others. Like all democratic institutions, the model requires that the alternative accepted by the members be most preferred to all other alternatives. In at least one important respect, this model varies from a traditional democratic institution, such as the New England Town Hall meeting sketched by Tocqueville. No provision for open 22 debate is included in the model. Debate can be important for two reasons. First, it serves as a vehicle to compromise. Where disagreements exist, debate and discussion is commonly perceived as a means for reducing disagreement and breaking deadlock. Second, debate is regarded as a means for altering preferences. Debate involves presenting arguments to convince an opposition of the untenability of their position and the soundness of one's own position. In short, the aim is to sway the preferences of others. With this model, preferences are assumed fixed. That is , each participant has well- defined preferences over al l alternatives. The aim of the model is not to understand how participants strive to change these orderings — although this is important — but rather to understand the outcomes derived from a manifestly democratic institution. Arrow's General Possibility Theorem Once general boundaries are placed on an institution, preference orderings are well-defined, and the decision procedure is established. Arrow's results are a simple exercise in logic. Rather than repeating Arrow's proof, it is only sketched here for a 3-person, 3-alternative case.10 The point by Arrow is that for certain distributions of preferences, there is no manner of selecting an outcome without violating one of the conditions outlined above. The proof relies on two features related to the conditions elaborated above. First, the proof holds that some subset of alternatives may be pareto optimal, such that: If x Pi nY for al l i members of n, then it follows that xP y (x is preferred to y by all members of the decision-making arrangement). 23 second, the proof relies on a decisive set. A decisive set contains a group of individuals V such that for two alternatives {x,y}, x Pv y.That is, x is preferred to y by the decisive set. Everyone not in the lecisive set V is in the set ~v which holds a strictly opposite preference ordering y P x (this stands to reason since the comparison is between x and y). Further, V is decisive since the number of participants in V is greater than the number in ~v. Suppose three individuals have the following preference orderings: V 1 x P a y P a z V2 z Pb x Pb y -V: y Pc z Pc x The decisive set V - {V1>V2} and the members of V prefer x to y. Meanwhile, ~v prefers y to x. Note that in this case it is impossible for the collection of the individuals in the decision-making arrangement to prefer z to y since only b has that preference ordering, and for such to be the case, b would be the dictator, violating the condition of nondictatorship. As a result, then, y R z. Further, we know that x P y, so by the condition of transitivity it follows that the members of the decision-making group prefer x to z. However, and this is the crux of the proof, this makes a single individual decisive — the dictator — in violation of the nondictatorship condition. Thus, the contradiction is established. Of course, the proof has further complexities, and here it has only been sketched for the weak case. Yet, the results are quite general. Paradoxical Democracy and Extensions A large amount of work on the General Possibility Theorem has been done.11 Much of this work turns to weakening Arrow's assumptions 24 in order to avoid those contradictions derived by Arrow. A somewhat different approach concentrates on the likelihood that a voting paradox will occur. For the relatively simple 3-person, 3-altemative case alluded to above, the probability of a voting paradox is small (p = .056). This assumes all preference orderings are equiprobable. As the number of alternatives increases, the likelihood of a voting paradox slowly increases to a limit of one. However, this rise is extremely slow. On the other hand, as the number of alternatives remains small and the number of individuals increases, the probability of a paradox rises to a limit of .09 (May, 1971). The implication, then, is that a voting cycle is relatively uncommon, and in this respect outcomes from decision-making arrangements ought to regularly appear. While this point does not counter the logical results derived by Arrow, it is optimistic in its hope for the likelihood of empirical outcomes. Vote Cycling and Multidimensional Space A reasonable supposition is that individuals generally do not confront decisions pertaining to a single alternative, but rather they face clusters of interrelated alternatives. Most policies are characterized by complexity involving a large number of varied issues. Decisions on defense spending should not be regarded separate from foreign policy, unemployment policy, or social policy. With a finite budget, money put into defense represents money that might be put into social welfare (or roads, or a multitude of other problem areas). So, individuals might be regarded as making comparisons across a wide number of dimensions for any single policy alternative. A simple 25 example may suffice. Suppose there are three individuals and they are to select an outcome. To take a traditional case, each individual is confronted with choices between guns and butter (only two ways in which money is to be allocated). They must agree on some allocation of money for both guns and butter. The comparisons that a representative individual, Mr. Alright, makes is illustrated by Figure 1-1. Mr. A has a point that he prefers the most — point A. This is Mr. A's ideal division of guns and butter. In this particular case, Mr. A prefers that " f " amount of dollars go to buy guns and " h " amount of dollars go toward buying butter. Mr. A prefers point A to all other alternatives (he believes this division is the best possible division). As alternatives move away from this ideal point, Mr. A prefers those alternatives less and less. In fact, the further the alternative from the point A (in any direction), the less Mr. A prefers i t . With three points in the two-dimensional policy space (guns and butter), m = {A,V,W}, Mr. Alright has the following preference ordering: A Pa v Pa w. Meanwhile, the circles on Figure 1-1 are representative indifference curves. That i s , any alternative lying on the same curve has the same value (utili ty) for Mr. Alright. From Figure 1-1, it is apparent that there are a large number of alternatives with which Mr. A must be concerned. Mr. A's preferences are well-defined over this space. Given the large number of alternatives available in the policy space elaborated above, we need to identify where other participants (Mr. Best and Ms. Checkered) are located. It is extremely rare when individuals have exactly the same preference orderings — especially where a large number of alternatives are possible. Therefore, it seems reasonable 26 FIGURE 1-1 A'S PREFERENCES 200 150 100 50 w 50 100 150 200 BILLIONS OF DOLLRRS GUNS 27 to represent the policy space with all three participants as in Figure 1-2. This figure repeats Figure 1-1, but now all three participants are located in the space. Each individual also has a representative set of indifference curves drawn on the figure. This figure indicates that if individuals have differences in preferences (which is a reasonable assumption), then agreement is difficult. It is quickly noted that Ms. Checkered does not prefer either Mr. Alright's ideal point nor Mr. Best's ideal point. They are both at a considerable distance from Ms. C's own ideal point. The same holds true with the other participants. However, a few points have quasi-stable properties. In Figure 1-2, these are points X, Y, and Z. They are quasi-stable in the sense that the participants hold the following preference orderings: Mr. A: X Ia z pa Y Mr. B: Y Iab x P a b Z Ms. C: Z IDC Y P D C X Further, these points all have the property that at least one of them can defeat any alternative different from that set of points.12 A problem, however, is that no single alternative is an equilibria outcome. That is, participants face an endless cycle of voting. The alternative X is an alternative that both A and B can agree on. However, C prefers either Z or Y (Ms. C is indifferent between the two). Alternative Z is one that Mr. A finds as acceptable as X. On the other hand, Mr. B prefers Y to Z, but Mr. A prefers Z much more to Y, which results in alternative Y to which both Mr. A and Ms. C can agree. However, B prefers . . . and so on. There is no single outcome to which these individuals can agree. With single-dimensional alternatives, the voting paradox appears infrequently. With 2S FIGURE 1-2 . B. C 'S PREFERENCES : 200 -) 1150 -I 100 J 150 -| o A 50 100 150 200 BILLIONS OF DOLLARS 29 multidimensional alternatives, the paradox (and accompanying Arrow results) are ubiquitous. Niemi (1969) suggests a means for examining individual choices in a multidimensional space using unfolding techniques that reduce preference orderings to a comparable scale. In doing so, he finds that as more indviduals are added to consider a small number of alternatives, the likelihood of a voting cycle decreases. However, reducing the complex array of alternatives over which individuals commonly make decisions to a single scale, may also be overly simplistic. A number of scholars have indicated that the problem of cycling endlessly in a multidimensional policy space is a very real problem. Plott (1967) is one of the first to point out that an equilibria can be located only under very rare circumstances. Extensions of this work by Kramer (1973), Sloss (1973), McKelvey and Wendall (1976), Cohen (1979), and Cohen and Matthews (1980) generalize Plott's work, showing — unlike the Arrow results where endless cycles occur in relatively rare circumstances — that cycling is ubiquitous and that an equilibrium outcome is extremely rare. With the 3-person example, an equilibria only emerges when one of the participants has an ideal point which is a median (and colinear) of the other two individuals. This is represented in Figure 1-3. Further, results by McKelvey (1976) indicate that where no equilibria exists, a single individual skilled in manipulating an agenda (or with sole control over the agenda) can always have their own ideal point chosen. The fundamental problem is that any alternative can defeat (or be defeated by) any other alternative via some agenda. 30 FIGURE 1-3 EQUILIBRIUM FOR A, B, AND C 200 150 -J 100 -I 50 50 100 150 200 BILLIONS OF DOLLflRS 31 For two alternatives s and y, it is possible to introduce another set of alternatives {t,u} to an agenda such that: s P t P u P y. But, a different set of alternatives also exists {v,x} such that: y P v P x P s. From this, two contradictory results are obtained: s P y and y P s. Obviously, this indicates that a multitude of cycles are possible. While majority rule cycles present a threat to democratic outcomes, McKelvey's findings that an agenda setter can always have their way is doubly threatening to notions of democratic rule. It appears that cycling among alternatives is a pervasive problem. Indeed, the lack of equilibrium results in a multidimensional policy space has driven Riker (1980) to declare the study of politics to be "the dismal science," dismal in the sense that precise predictions of outcomes are unlikely. This is contrary to the confidence Riker originally placed in the logical study of politics where he argued that "If we know [the mathematical solution to a game], then, if also we can assume players are rational maximizers of utility, we can predict the political future with some confidence" (1967a: 642). However, others have also turned their attention to the lack of equilibrium results, arguing that the formal results are not as serious as we are led to believe. In the next section some of these arguments are laid out. Empirical Work While the formal results found by the researchers noted above are unquestionable, some have questioned their usefulness. As Tullock 32 (1967; 1980) argues, decision mechanisms do yield decisions, individuals do not endlessly cycle, vacillating between various proposals — in short, real world institutions yield outcomes. Further, many of these outcomes are regarded and accepted as "democratic." Many different interpretations are tendered to account for such an observation. Tullock initially claims outcomes are confined to a relatively narrow subspace (1967).13 Tullock (1980) later argues that the dynamics of logrolling may contribute to very stable outcomes, when a large number of individuals are involved in making decisions across a multidimensional space. McKelvey and Ordeshook (1978) argue that cycling may occur with some frequency, but the number of alternatives is relatively small, as is the number of possible coalitions. Empirical work using laboratory experimental procedures appears to substantiate this point (McKelvey, Ordeshook, and Winer, 1978). Other laboratory experimental work by Fiorina and Plott (1978) also indicates that some mechanism is at work that results in outcomes converging to smaller subspaces. Work by Ferejohn, Fiorina, and Packel (1980) illustrates a different convergence property as participants face a decision-making situation. The empirical work indicates that where equilibria do not exist, some patterns of regularity do occur. In a way, such patterns of regularity lessen the threat posed by voting cycles. Fiorina and Shepsle (1982) provide four examples that illustrate the regularity of outcomes where no equilibria exists. The first case derives from Riker's (1962) notion that looking solely at outcomes may be misleading, and that researcher's attention should turn to the dynamics of the coalitions that form. Coalitions are regarded as 33 fundamental for the exercise of power in a democratic decision-making arrangement. Thus, understanding the composition of a coalition and the interaction among coalitions should enable an understanding of the outcomes of decision processes. Fiorina and Shepsle also point to the work by Ferejohn, Fiorina, and Packel (1980) which examines "in a systematic way the relative 'difficulty' of moving from one (typically unstable) point to another, and the constraints such relative difficulties might place on the majority decision process" (1982: 59). Third, Fiorina and Shepsle point to the work by Kramer (1977; 1978) on the minimax set, which details dynamic games, whereby any outcome is simply part of a trajectory leading to the minimax set. Further, it is thought this set is generally a small part of the set of feasible alternatives (1982: 59). Fourth, Fiorina and Shepsle point to the work by Shepsle (1979) on structure-induced equilibrium, in which institutional arrangements are viewed as constraining the decision-making process in such a way as to limit the set of feasible alternatives. In each of these examples, disequilibrium results are not seen as serious threats to democratic decision making. Instead, various constraints on the set of feasible alternatives are viewed as ways in which decision-making arrangements cope with the problems that formal work has pointed out. Structure and Outcomes The notion that institutions are designed to enable decision- making outcomes is not unusual. Liberal theorists from Hobbes to Hume regard political institutions as a means for constraining individual 34 action to prevent the anarchy feared in a state of nature. The arguments contained in The Federalist Papers are couched in similar terms — designing institutions to prevent the natural rapacity of individuals from destroying the polity. V. Ostrom (1980) points out that these thinkers view institutions as artifacts that control and are subject to control by their artifacers (members). When confronting collective choices, artifacers are quite adept at constructing mechanisms that enable them to deal with conflicts. Further, these thinkers share the view that the structure of decision- making mechanisms is important for the ways in which alternatives are put before a deliberating body, and the way decisions are made. Indeed, the reform movements of the early twentieth century turned to institutional tinkering to rid urban areas of the pernicious effects of "bossism." Practitioners of politics are fully aware of the importance of the "rules" of a decision-making body, and the important role those rules play in completing the task of deliberation. Therefore, one way to exorcize the "impossibility" results noted above may be to turn to the structure of decision-making mechanisms. This "institutional" approach is relied on extensively in the remainder of this work. Using game theoretic tools and specifying a generic decision-making arrangement, it is then possible to compare the relative costs that particular institutional structures place on participants. These formal conjectures are then subjected to empirical tests using laboratory experimental methods. 35 Conclusion This chapter raises the point that while democracy can be reduced to "Rule By the People," the make-up of the institutions that yield collective choices varies. Different rules and procedures are prescribed in order to ensure that particular normative goals are met. Further, some institutional arrangements that satisfy democratic criterion may depend on particular historical, social, economic, and political preconditions in order to survive. The framework of political institutions, then, may vary, as will the outcomes derived from those institutions. Differences between institutional arrangements are based on the costs to citizens for engaging in particular types of collective behavior. Democracy as a pattern of rules and procedures governing behavior is well accepted. The consensus is that most forms of democratic arrangements yield satisfactory outcomes and fulfill some valuable goals. However, work in social choice theory suggests that democratic institutions will not yield regular outcomes. By abstracting crucial elements of an institution that allows full "Rule By the People," and tracing the logical relationships between these elements, it is possible to show such an institution is likely to fail. Since the institution is fully compatible with most democratic criteria, the implication is that democracy is likely to fail. Either some outcome will be imposed by a single person — thereby violating a fundamental tenet of democratic theory — or else no outcome will be selected. Decisions are made in societies that approximate democracies. By and large, collective decision making is enhanced through 36 institutional rules and procedures that impose costs on different forms of behavior. As political scientists, institutions are of fundamental importance. Democratic governments are not autonomous of the citizenry, but rather the fundamental premise of democracy is that its institutions rest on the people. Further, the rules and procedures of these institutions are subject to change. This study concentrates on a limited set of institutional elements. It is argued that collective decisions do emerge — contrary to the predictions found in social choice theory — and that these decisions have identifiable patterns. The succeeding chapters develop a notion of constraints imposed by specific institutional rules and tests whether differences in these rules result in different outcomes. 37 FOOTNOTES FOR CHAPTER ONE •••Of course, this brief characterization omits questions about the way in which values or preferences are learned. However, Lockean psychology indicates people enter the world with a tabula rasa, and that their unique experiences teach them about the world. From these learned experiences comes knowledge. Likewise, with knowledge comes an understanding of the world, and an understanding of how to order alternatives in the world. Locke's Essay Concerning Human Understanding (particularly the sensationalist psychology in Book II) explicitly spells this out. Contrast this with Rousseau's position in Emile. 2For an alternative argument, see Mansbridge (1980). Mansbridge's point is that not all collective decisions are characterized by conflict. She refers to the liberal democratic position as "adversarial democracy." Instead, at some levels of society where substantial common agreement exists, alternative institutions might be possible enabling "unitary democracy," which is characterized by common interests, equal respect, consensus, and face-to-face contact. ^Aside from simply accepting the assumption that individuals have autonomous wills, there are other reasons for explicitly examining liberal democratic theory. The primary concern here is with American institutions. Duncan (1973) and Ryan (1972). Also see the excellent survey by Thompson (1976) on Mill's conception of democracy and the place of Representative Government. 5See, for instance, Pateman (1970), Dahl (1970; 1971), and Joseph (1981). "The general conditions mentioned here are related to elements of the decision situation discussed in Chapter 3. Much of my thinking on these points stems from work by V. Ostrom (1979; 1980) and Kiser and Ostrom (1982). 'Dagger's point relating to the decline of civic sense is well taken. However, his argument relating the role played by the fragmentation of a metropolis to a proposal to consolidate metropolitan areas is contradictory. For a criticism of this view of consolidation, see V. Ostrom (1973). "Aside from the original exposition by Arrow, there are numerous places where a reader can be enlightened about the GPT and the numerous extensions and developments. One of the most readable works is that by Abrams (1980). More technically oriented surveys include: Sen (1970), Fishburn (1973), Kelly (1978), and MacKay (1980). *Much of the discussion here relies extensively on Arrow (1963) and Abrams (1980). 38 reader interested in the formal proof is referred to Arrow (1963) or any subsequent commentators listed in Footnote 8. 11For surveys of this work, as well as extensions, see Sen (1970), Harsanyi (1976), Fishburn (1974), Kelly (1978), and MacKay (1980). familiar with game theory will quickly recognize that Figure 2 is a two-dimensional representation of the von Neumann- Morgenstern V-set and the Aumann and Maschler Bargaining Set. No further detail is offered on this point. Interested readers are referred to Luce and Raiffa (1957) or Rapoport (1970) for excellent surveys on these solution sets. the article by Simpson (1969) that comments on Tullock's argument. This article extends some of Tullock's results, and shows that the expected convergence of outcomes to a small subspace is unlikely except under special conditions. CHAPTER TWO THE SEARCH FOR ORDER "All mimsy were the borogoves . - Jabberwocky A bas ic t ene t of l i b e r a l democratic theory holds t h a t outcomes are a funct ion of ind iv idua l w i l l s . This implies two p o i n t s . F i r s t , c o l l e c t i v e dec i s ions must be derived from ind iv idua l s and not imposed by o t h e r s . Second, some se t of ru l e s and procedures e x i s t s whereby a defined se t of ind iv idua l s make d e c i s i o n s . If these poin ts hold, then it follows that well-defined preference orderings yield regular collective outcomes. This is precisely Arrow's point, although his finding is that regular outcomes fail to occur under some circumstances. This undermines the fundamental premise of democratic theory that decisions will be made. Yet, it is apparent that collective decisions are made, and that these decisions do not wander aimlessly in n-dimensional policy space. This turns the table, asking why, if the logic of formal democratic theory holds, do well-defined preferences and well-understood arrangements yield regular outcomes? Determining whether outcomes form patterns of regularity in democratic institutions is the primary concern in this chapter. While casual observation serves as an excellent heuristic, detailed empirical work is more convincing. Considerable empirical work examining the nature of outcomes in a collective decision-making arrangement has been conducted with much of this work concentrating on small group processes and relying on game theory as a theoretical foundation. This chapter is a survey of empirical work that indicates regular patterns of outcomes do occur. The succeeding chapters extend 40 some of this work, focusing on the effects of institutional costs on behavior and the relation of costs to outcomes. Is Regularity a Figment of Our Collective Imagination? While the formal conjecture that equilibria should be rare or vary considerably is well-established, evidence corroborating or contradicting this conjecture is not. Real-world empirical studies of outcomes in democratic decision-making arrangements are well-reviewed (see Browne, 1973; Murnighan, 1978; Hinckley, 1981). Yet, those studies do not precisely address the question of whether patterns of regularity appear. These studies have focused on various legislative systems and have generally turned toward explaining patterns of coalition formation (see particularly Leiserson, 1968; Dodd, 1976). From the way competing groups coalesce, inferences are made concerning the types of policy outcomes likely to be adopted. One of the primary concerns is with testing Riker's seminal model of coalition behavior — the minimum winning coalition. Studies generally conclude that while the model is powerful in i ts logical formulation, it is rarely satisfied in the real world. More recent work has produced other explanations of the coalition formation process, finding some support for a model that coalitions form and distribute largesse (primarily ministry seats in parliamentary systems) based on the proportional strength a party candidate contributes to a winning coalition (Browne and Frendreis, 1980). Generally, however, this work concentrates on coalition activity and not on outcomes. 41 However, political scientists are not dissuaded from the study of outcomes. A tradition of experimental research in political science provides unique opportunities for such study through including, controlling, and manipulating various influences on outcomes. Experimental research allows for ready comparisons across different decision-making contexts and allows precision in defining outcomes for those contexts. It also provides the opportunity for inexpensive testing and replication of well-specified hypotheses. In short, as Plott (1979) notes, experimental methods provide a unique opportunity for examining relationships between preferences, institutions, and outcomes. The conceptual assertion that outcomes should be rare, and the empirical observation that some regularities do occur, seems particularly susceptible to empirical evaluation within an experimental framework. Since the mid-1960s, numerous experimental studies have been conducted attempting to uncover patterns of regularity in the context of small-group decision making. Although researchers generally agree that some regularities exist, as Riker (1980) remarks, the research has been marked by a fundamental dichotomy — that between the study of values which individuals bring with them in framing decisions and the institutional rules that provide incentives or constrain the collective decisions that individuals make. This point is also noted by Hinckley (1981) who characterizes the study of values as "social-psychological" experimentation and the study of institutions as "empirical."1 However, these differences are important only for the questions they ask and the relationships with which they are interested. The aim of these different research programs is with 42 apping different components contributing to decision making. The focus on values has led social scientists to ascribe influences on outcomes to differences in the resources individuals bring with them when making decisions. The focus on institutions has turned toward understanding those external constraints on individuals that appear to "induce" regularities into decision-making outcomes.-3 In this discussion I take Riker's advice that "we cannot leave out the force of institutions" in studying decision making (1980: 432). To do so first requires the careful description and elaboration of those elements that constitute an institution. Second, it requires linking behavior to those institutional components. Game theory provides a natural tool, indirectly allowing this second step through describing strategies available to individuals within particular decision-making contexts. This is accomplished through describing a solution (or set of solutions). However, in order to uncover solutions, the decision-making context — including the structure of institutions — must be fully elaborated. Game theory provides such a tool for linking behavior to institutions. In addition, game theory is relied on since it is particularly adept at bridging the gap between conceptual and empirical work. The experimental study of group processes in political science relies extensively on game theoretic processes. By and large, the application of game theory to decision-making situations has the effect of deducing solution concepts (outcomes) from some central set of assumptions. These solution concepts, as von Neumann and Morgenstern argue, are "plausibly a set of rules for each participant which tel l him how to behave in every situation which may conceivably 42 apping different components contributing to decision making. The focus on values has led social scientists to ascribe influences on outcomes to differences in the resources individuals bring with them when making decisions. The focus on institutions has turned toward understanding those external constraints on individuals that appear to "induce" regularities into decision-making outcomes. In this discussion I take Riker's advice that "we cannot leave out the force of institutions" in studying decision making (1980: 432). To do so first requires the careful description and elaboration of those elements that constitute an institution. Second, it requires linking behavior to those institutional components. Game theory provides a natural tool, indirectly allowing this second step through describing strategies available to individuals within particular decision-making contexts. This is accomplished through describing a solution (or set of solutions). However, in order to uncover solutions, the decision-making context — including the structure of institutions — must be fully elaborated. Game theory provides such a tool for linking behavior to institutions. In addition, game theory is relied on since it is particularly adept at bridging the gap between conceptual and empirical work. The experimental study of group processes in political science relies extensively on game theoretic processes. By and large, the application of game theory to decision-making situations has the effect of deducing solution concepts (outcomes) from some central set of assumptions. These solution concepts, as von Neumann and Morgenstern argue, are "plausibly a set of rules for each participant which te l l him how to behave in every situation which may conceivably 43 arise" (1944: 31). The solution, then, is nothing more than a prescriptive rationale for individual action informing a person how to order available strategies within the context of a defined decision situation. The result of this melding of institutions and behavior is represented by an abstraction — the solution. Riker (1967a) illustrates one application of this abstraction to political science by raising two questions. 1. What is the mathematical solution to a game? 2. What are the strategies which will ensure players of achieving the solution? Riker then argues: An answer to the first question indicates what may be anticipated as the outcome of political events. If we know it, then, if also we can assume players are rational maximizers of utility, we can predict the political future with some confidence. An answer to the second question (about strategies) permits political engineers to give advice to politicians about how to behave successfully (1967a: 642). In seeking order, political scientists appear to have taken Riker's advice, using experimental studies to uncover a game theoretic solution which provides the best fit to the data. Yet, as shown below, the results of many tests are less than conclusive. Rather than a single solution concept serving to "predict the political future with some confidence," it appears a variety of solutions work. The implication of this, I suggest, is that predicted solutions vary with the specific components modeled into an institution. Equilibrium Solutions A principal result of game theoretic literature is the dominance of an equilibrium concept — the Core. As a solution concept, the 44 Core is an excellent starting point for discussing patterns of regularity. The Core requires individual preferences to be distributed such that at least one individual's preferred alternative is the median of all other individuals. Where the Core exists, no strategy by any participant can better i t .4 Experimental research indicates that where the relatively strong (and rare) conditions for an equilibria are met, outcomes occur there with some frequency. This finding is especially pronounced in the work by Berl, et a l . (1976). This experiment is discussed at length here, since many of the experiments discussed later utilize a similar format. Berl, et a l . , use a procedure that places either three or five persons into a simple majority rule committee structure. The committee is charged with reaching majority agreement on a single point in a well-defined two-dimensional policy space. Individuals introduce proposals (points) in that space until a majority of the committee votes to pass a single proposal. In i ts bare form the committee consists of five basic elements: 1. Individuals select a policy from a set of clearly defined alternatives; 2. Every participant has well-defined preferences over the set of alternatives; 3. Sidepayments are not allowed; 4. A defined aggregation rule exists for committee decisions; and 5. Deliberations are made in face-to-face discussions with all members present. The set of alternatives is contained by a simple two-dimensional Euclidian space, with axes labeled X and Y and marked off in discrete numerical units. This space is displayed on a blackboard before the 45 full committee. All points in the space are real-valued, with each individual assigned a different maximum point among the alternatives. Further, each individual is given a payoff index that duplicates the proposal space before the committee, and includes a set of indifference curves with corresponding payoffs for those curves. Payoffs are a monotonically decreasing function of distance radiating out from the maximum point. The experiment does not allow participants to discuss personal payoffs during negotiation, since, as Berl, et al., argue, "the transferable utility assumption in particular limits the social relevance of the resultant research" (1976: 454). No player is excluded from a payoff in the experiment (even if they vote against a winning proposal), although the structure eliminates the possibility of sidepayments. Proposals are voted on one at a time, and a proposal passed by a simple majority vote is the winning proposal. Finally, all discussion takes place in a face-to-face context. The only limit on this discussion is mention of payoffs. Figure 2-1 illustrates one of the proposal spaces (with individual ideal points and a set of sample indifference curves) used in the experiment. This example is that of a 5-person game with the equilibria solution at C (which is committee member 5's ideal point). Berl, et al., use this configuration of preferences and two related configurations to test the power of an equilibrium to attract and retain votes. Their results indicate that the Core, in fact, serves as a good predictor of outcomes. First, they find that the Core serves as the focal point for proposals and negotiation. While the set of proposed points tends to be scattered across the space, the 46 Y Axis Figure 2-1 Proposal Space Used in Berl, et al., Experiments X Axis Adapted from Berl, et al. (1976), Figure 1 , p. 459, 47 proposals passed are nearer the Core than other proposals (1976: 468). Roughly 65 percent of the final proposals appeared in the 95 percent confidence interval for the true mean (i.e., the Core — assuming these outcomes are bivariate normally distributed, 1976: 467). As Berl, et al., note, some participants thought it might have been possible to better their payoffs, even though they were at the Core. As they argue, the results "illustrate the power of the Core in that even when players did not understand the theoretical properties of the game they were playing, they tended to end up near it anyhow" (1976: 478). The Core, then, appears to be a good predictor — when it exists. Although Berl, et al., note that deviations away from the Core apparently are a function of "bargaining skill or intelligence" (1976: 470), this does not detract from the observation that empirical outcomes focus on this equilibrium concept, when it exists. An experiment conducted at about the same time by Fiorina and Plott (1978) also provides evidence that when an equilibrium exists, decision-making outcomes tend to focus on it. This study uses the format described by Berl, et al., with the exception that proposals are voted on according to parliamentary procedure, with a status quo proposal serving as an initial starting point. Fiorina and Plott also are concerned with specific conditions, the first being whether or not participants are able to discuss alternate proposals. In either case, there is little apparent difference (see Table 2-1). The null hypothesis that there is no difference between the mean outcomes under different communications conditions cannot be disconfirmed using two-way analysis of variance. This second concern is with the size of payoffs individuals play for. Here, they differentiate between high Communication is of Fiorina and Plott Data High Payoff Core = (39,68) Mean Outcome = (37,68) Mean Distance from Core =4.70 n = 10 = 7.28 Low Payoff Core = (39,68) Mean Outcome = (47,72) Mean Distance from Core = 10 = 14.25 = 344.49 No Communication Core = (39,68) Mean Outcome = (38,69) Mean Distance from Core = 5.76 a 2 = 34.539 n = 10 Stat i s t ics for Two-Way ANOVA: Core = (39,70) Mean Outcome = (36,70) Mean Distance from Core = 12.30 a 2 = 182.46 n = 10 HQ1: (iCommunication = uNo Communication F(1,36) = .0413 sig <.001 H 0 2 : μHigh Payoff = μLow Payoff F(1,36) = 7.373 s ig >.O25 Ho3: Interaction Effects: F(1,36) = .586 sig <.001 Data analyzed from that presented in Fiorina and Plot t (1978, Table 1: 584). 49 and low payoffs. As shown in Table 2-1, differences do occur (see H 02) . With low payoffs to participants, proposals tend to scatter, while high payoffs yield outcomes which cluster around the Core. Further, no significant interactions occur between the communication and payoff conditions. While this experiment also points to the usefulness of the Core as an equilibria solution, a second test was conducted using a series of committee games without a Core. The results obtained from these series indicate that where an equilibria is absent, proposals adopted by the committee do not wander throughout the alternative space. As Fiorina and Plott note, "the pattern of experimental findings does not explode, a fact which makes us wonder whether some unidentified theory is waiting to be discovered and used" (1978: 590). Formal examinations of equilibria concepts note that they rarely exist (Plott, 1967; Sloss, 1973). When they do exist, they must meet extremely stringent conditions as to the distribution and configuration of participant preferences. Generally, this means that the equilibria must be the median proposal for all committee members. Such a notion is extremely limiting, especially given the variety of preferences observed in the world. Uncovering regularities where no equilibria exists, then, is a fundamental concern. Nonequilibrium Solutions Since the existence of an equilibrium is a rarity, work has turned to situations where no Core exists. Since few collective decisions meet equilibrium conditions, experimental work should 50 examine such cases. The rationale behind this stems from the casual observation that collective decisions exhibit patterns of regularity. Determining what these patterns are and what drives them is of fundamental concern. However, defining solutions for nonequilibrium contexts is more problematic than contexts with an equilibrium. A large number of nonequilibrium solutions have been proposed that abstract the processes at work within group decision making. Three are dealt with here: the von Neumann-Mor gen stem V-set, the Bargaining Set, and the Competitive Set. These are discussed primarily because of the attention paid to them in experimental research. Many other solutions have been described and tested, with the limit to the number of solutions apparently confined only to imagination in changing assumptions about the decision-making context.6 The V-Set One of the earliest experimental studies of nonequilibrium solutions in political science was conducted by Riker (1967a). For this experiment, three participants were placed in a context requiring them to: 1. Form a 2-person coalition, and 2. Agree to divide a fixed amount of money. In this "divide-the-dollar" experiment, the odd person left out received nothing. Only two individuals could agree to a monetary split. Negotiations were allowed between all pairs of participants, and the experiment ended when the experimenter separately asked each participant how they wished to split the money and with whom. If two 51 participants privately agreed on a division, they were paid accordingly. If no agreement was reached, they received nothing. Riker defined the payoffs for the various coalition pairs to be: (12) = $4.00 (13) = $5.00 (23) = $6.00 Using the simple V-set as a solution, this meant that players could be expected to divide the money as follows:' Player (12) Coalition (13) (23) 1 $1.50 $1.50 $.00 2 $2.50 $.00 $2.50 3 $.00 $3.50 $3.50 Accordingly, the first division involved a split between the coalition pair (12) with player 1 receiving $1.50, player 2 receiving $2.50, and player 3 nothing. The other possible coalitions are read likewise. Riker's data indicates that players selected a division belonging to the main simple V-set 23.7 percent of the time. Players agreed on an equal split only 11.8 percent of the time. While Riker (1967a) discusses the outcomes of 93 t r ia ls , a paper coauthored with Zavoina (1970) expands this set of observations to 206 t r ia ls . No longer examining divisions that exactly matched the V-set, but taking into account how the final divisions clustered around the V-set, they report that 20 of 21 pooled observations fell within the 95 percent confidence estimate of the V-set divisions. In fact, deviations for all 21 sets of pooled observations averaged only 28 cents from the expected V-set divisions (see the data in Riker and Zavoina, 1976, Table 1: 54). Even though players were often oblivious to the V-set solutions, Riker notes that the V-set, 52 was always a severe constraint on behavior in the sense that outcomes seemed to vary randomly around i t . This fact should give po l i t i ca l s c i en t i s t s confidence tha t , when it is possible to specify the solution of a po l i t i c a l s i tua t ion , par t ic ipants are very l ikely to behave as if they are trying to achieve it or something very close to it (1967a: 655). Support for the V-set with these experiments appears to be strong. A similar simple majority rule game by Westen and Buckley (1974) supports th is conclusion. In th is experiment, Westen and Buckley tested the adequacy of the V-set for 4-person games. Testing a broader array of V-set solut ions, they found that par t ic ipants deviated from the V-set 17.5 percent of the time (see Table 2-2) . This experiment demonstrates somewhat more forcefully the u t i l i t y of the V-set in predicting so lu t ions . Table 2-2 Outcomes from Westen and Buckley (1974) Set of V-Set Solutions Outcomes Outside V-Set No Coalition Total n outcomes = 97 71 17 11 .2% .5% .3% 100.0% The Bargaining Set An a l te rnat ive solution concept that has received some a t tent ion is the Bargaining se t .? Riker (1967b), using a 3-person simple majority rule s t ruc ture , found the Bargaining set is also a good predictor. As can be noted from Table 2-3, 21.2 percent of the outcomes f e l l d i rec t ly in the Bargaining set (which coincides in th is case with the main simple V-se t ) . If the Bargaining set solutions are 53 taken as a mean, then the remaining values are scattered around this set of solutions, and a l l fal l within a 95 percent confidence interval around the mean. Using a 5 percent test of significance, then it is not possible to reject Riker's claim that these experimental results are s tat is t ical ly different from the Bargaining set . Table 2-3 Outcomes in the Bargaining Set Deviations from 0 . . . 7 the Bargaining .01 - .10 . . . 4 Set (in absolute .11 - .25 . . . 7 $ amounts) .26 - .50 . . . 1 4 n o coalition . . . 1 Bargaining set divisions [1.50, 2.50, 0; (1,2)] [1.50, 0, 3.50; (1,3)] [0, 2.50, 3.50; (2,3)] n = 33 Adapted from Riker (1967b, Table 3.2: 64). Buckley and Westen (1976) reach a similar conclusion, although they directly compare solutions outside the main simple V-set with the Bargaining set. They provide, then, a clear test of nonoverlapping solutions for 4- and 5-person simple majority rule games. Taking grouped observations, 69.1 percent to 95.2 percent (an average of 75 percent) of the outcomes for 4-person games fel l in the Bargaining set. For 5-person games, the group observation range was slightly higher, extending from 72.7 to 100 percent (an average of 86 percent) .** They conclude that the Bargaining set performs well in comparison with many of the V-set predictions, and they further speculate that as the number of players increases, the predictive power of "the bargaining set will remain the same but the best prediction made by the von Neumann and Mor gen stern stable set will decrease because the number of solutions will increase" (197 6: 494-495). 54 The Competitive Solution Yet a third solution concept has been proposed to uncover regular i t ies in outcomes. This is the Competitive solution (K-set) developed by McKelvey and Ordeshook (1978). In experimental s i tua t ions , the K-set has proven to be an embarassingly eff ic ient predictor of outcomes. The primary set of published experiments are those by McKelvey, Ordeshook, and Winer (1978), Laing and Olmsted (1978), and McKelvey and Ordeshook (1979). The f i r s t two involve spatial majority rule committee games modeled on the game described in Berl, et a l . (1976). The th i rd set of experiments confronts players with 15 different proposals ( th i s compares with the 28,000 potent ial proposals in the spa t ia l committee game). Each player is given a set of well-defined preferences over each a l te rna t ive together with a payoff schedule. A "winning" proposal is selected by a majority of the members of a committee. With the exception of l imits on the number of proposals under consideration, the process of negotiat ion, voting on a l t e rna t ives , and forming a committee is ident ical to the spatial committee game used by Berl , et a l . In a l l three groups of experiments the Competitive solution predicted outcomes quite well . McKelvey, Ordeshook, and Winer (1978) find that in only one out of eight experimental t e s t s was there a significant deviation from the Competitive solut ion. In taking the absolute sum of the differences between the p layer ' s predicted payoffs under the Competitive se t , and the p layer ' s actual payoff, outcomes from four of the experiments have a to ta l average deviation of less than $1.00. These deviations are fa i r ly small given that payoffs to each coal i t ion ranged from $20.50 to $24.75. 55 Further, McKelvey, et a l . , are encouraged by the fact all of the external coalitions predicted by the Competitive solution formed at least once. This is contrary to predictions under the Bargaining set. Also, no outcome falls in the