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Rational Actors, Political Argument, and Democratic Deliberation
August 1998
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Randall Calvert Department of Political Science University of Rochester Rochester, New York 14627
[email protected]
James Johnson Department of Political Science University of Rochester Rochester, New York 14627
[email protected]
Paper prepared for presentation at the 1998 annual meeting of the American Political Science Association.
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Rational Actors, Political Argument, and Democratic Deliberation by Randall Calvert and James Johnson
Introduction We are concerned in this paper with political argument - specifically, with the way rational actors use argument in political decision making. We understand political decision making to be a central activity in not only formal institutions such as legislatures, but also secondary associations and social movements, and even the unorganized, politically relevant actions of citizens in society. Our goal is to specify and model causal mechanisms that account for the force of argument in politics. The sort of argument we have in mind is a key feature political deliberation, to which democratic theorists have devoted substantial and increasing attention. Those theorists focus principally on normative issues, especially on the ways, and the conditions under which, reasoned public debate among free and equal participants confers legitimacy on political processes and justifies political decisions.1 Defenses of democratic deliberation have in turn, and with some warrant, elicited skeptical responses of various sorts.2 Waldron (1996, 2188), for instance, derides advocates of deliberative democracy as “dewy-eyed” because they fail adequately to acknowledge that, even under auspicious circumstances, political conflict will be pervasive and persistent.3 We, for the most part, sidestep these theoretical disagreements. We do so for two reasons. First, regardless of the disposition of recent theoretical controversies, deliberation has been, for at least two centuries, a central component in defenses of representative government.4 Indeed, it is precisely because constituents of large, complex polities unavoidably advance conflicting material interests, advocate competing ethical judgements, and articulate disparate cultural attachments that the importance of subjecting collective decisions to public debate remains among the animating principles of representative government (Manin 1997, 6,183-87). Second, “deliberation,” as used in contemporary debates, tends not to refer to political debate or public discussion per se. It refers instead to political debate that occurs under particular normative constraints meant to insure that, because participants are free and equal, only what is called “the force of the better argument” will be brought to bear on collective decisions, and that, consequently, the outcomes that those decisions generate are normatively defensible. Critics complain that advocates of democratic deliberation 1
See, for example, Bohman (1996), Bohman & Rehg, eds. (1997), Cohen (1989), Manin (1987), Elster, ed. (1998), Gutmann & Thompson (1996), Knight and Johnson (1994), and Warren (1996). 2
See, for example, Austen Smith (1995), Gardner (1996), Johnson (1998), Phillips (1995), Przeworski (1998), Sanders (1997), Stokes (1998). 3
For clear exceptions to his complaint see Knight & Johnson (1994) and Gutmann & Thompson (1996).
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For representative examples see Madison (1961 [1787]), Mill (1991 [1861]), and Schmidt (1985 [1923]).
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do not adequately define or defend those normative constraints (e.g., Phillips, 1995, 154; Johnson 1998).5 One implication of our argument is that that task may be more daunting than either advocates or critics of democratic deliberation realize. That said, however, we focus on a set of analytically prior questions. In particular, we ask: How does such argument work? What sort of “force” does it carry? These questions and the way we pursue answers to them carry us firmly onto the terrain of positive political theory. Among the tacit themes of this paper is that, on this question and others, normative and positive theory are interwoven in subtle ways that those who practice either sort of theory rarely recognize. In the present case, before we can decide whether collective decisions reached through argument or debate are in normative terms more or less attractive than decisions reached by other means, we must have a clearer understanding of how political argument works. And we can only reach such a clearer understanding against a broader sketch of how we understand politics. Our conception of politics focuses on coordination and its vicissitudes in ongoing interactions. We start from the view that politics generally, and democratic politics in particular, is continually susceptible to indeterminacy that derives from three principal sources. First, there always are multiple ways to coordinate social and political interaction. There always are multiple sets of norms, practices, and institutions that relevant actors might adopt to govern their ongoing interactions. Second, the multiple ways that actors might coordinate social and political interaction are not, as a rule, equivalent or neutral in distributional terms. They consequently give rise to continual disagreement and conflict. Here we mean both that institutional arrangements emerge from social and political conflict and that they generate the resources and constraints that inform subsequent conflict. Finally, even once actors settle on some one of the available ways to coordinate their ongoing interactions they invariably encounter events and circumstances that they had not anticipated or that they perhaps could not have anticipated. And in such cases their established norms, practices or institutions typically afford insufficient guidance about how to proceed. This conception of politics as coordination that is only ever precariously achieved and sustained offers a background against which we can ask how political argument works.6 We suggest that when political actors engage in the sorts of political argument that constitute deliberation, the task they face is less to change preferences or to pool information than to guide coordination by influencing the expectations of other actors. Specifically, we explore how parties to political argument invoke principle or cite precedent in hopes of resolving strategic uncertainty to their own advantage. If accepted, principles and precedents not only imply a particular, partial way to define and subsequently resolve current group decision problems. They have implications for the resolution of future problems as well. 5
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But see Knight and Johnson (1997) and Cohen (1998).
In this sense our conception of politics mirrors in both substance and function what Waldron (1996, 2197-2204) terms the “circumstances of politics.” Substantively these circumstances obtain just where some population confronts the need for “a common framework, decision or course of action on some matter, even in the face of disagreement about what that framework, decision, or action should be.” Functionally he rightly observes recognition of the circumstances of politics is “indispensable for our understanding of procedural decision making rules like majority rule, and the concomitant ideas of authority, obligation and respect” (Waldron 1996, 2198).
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We model the process of political argument and decision as a coordination game that may produce equilibria supporting outcomes with various normative features and empirical characteristics. This analysis, in turn, can usefully inform the way we assess processes of deliberative democracy. Briefly, our view is that political argument may improve democratic outcomes over what otherwise would result from processes of legislation and enforcement animated solely by selfish material interests. Nevertheless, deliberation in no way insures such normatively attractive outcomes and, indeed, the circumstances under which it may do so are quite narrow. The remainder of the paper consists of four sections. In the next section we offer a view of political argument not standard in rational choice accounts. We defend the view that the reasons invoked in political argument play a coordinating role. In the process we distance our view from two more common claims, namely that argument serves to transform preferences or that its primary role is to transmit information. In section three we turn our attention to the context in which political argument is applied. Here we attempt to motivate our conception of political life as a series of incompletely anticipated coordination problems. In section four we specify a particular game of political argument and choice. We offer this model to show in a precise way how the normative quality of outcomes depends upon the aggregation of strategically selected arguments. In the final section we speculate first about possible extensions of our model of political argument, and then about the implications that our analysis holds for both positive and normative political theory.
The Content of Political Argument The model we develop in the remainder of the paper builds on a body of research that explores the effects of a particular mode of communication, namely “cheap talk,” on strategic interaction.7 On the standard view, cheap talk “consists of costless, non-binding, non-verifiable messages that may affect the listener’s beliefs” (Farrell and Rabin 1996, 116). We hope to identify a plausible mechanism that will explain that effect.8 There seem to be three possibilities. Communication in debate or argument might transform the preferences of participants, it might transmit information that would remain otherwise unavailable, or it might work to coordinate expectations. We consider each of these possibilities in turn. Before we do so, however, we must address a possible objection. Why do we model political argument as cheap talk at all? Standard accounts of deliberation differentiate it from “bargaining” as commonly understood (Barber 1984: 154, 174; Cohen 1998: 193). Elster captures this in the analytical distinction that he draws between “arguing” and “bargaining” (Elster 1995). On his account, 7
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See Crawford (1990), Austen-Smith (1992), and Farrell and Rabin (1996) for surveys of this research.
This topic is neglected by much of the literature in democratic theory, but see Warren (1992), Bohman (1996) and Fearon (1998). Among game theorists, the situation is little better. Generally, game theorists find it “hard to accept that behavior depends on things which are payoff irrelevant.” More specifically, “although language plays a crucial role in resolving conflicts, game theory has so far been unable to capture this role” (Rubinstein 1991, 914,921). See also Johnson (1993).
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parties to an argument engage in sincere exchange of impartial reasons and valid principles with the aim of persuading one another. By contrast, Elster defines bargaining by reference to standard game theoretic models where players make binding proposals based solely on assertions of private interest. Bargaining proposals, just because they must be binding, are not “cheap talk” in the technical sense. Modeling argument as cheap talk allows us to assume the burden of proof in two ways. First, it distances argument from bargaining in just the ways that advocates of deliberation seem to want. Second, it allows us to explain rather than, as in standard accounts of deliberation, to assume how impartial reason has force in political interaction (Johnson 1993, 1998). We see political argument as animated by a single, persistent strategic problem, namely the need to achieve and sustain coordination in circumstances of conflict and disagreement.9 We now are in a position to assess three mechanisms that might account for the force of argument in social and political interaction. We will dismiss the first, suggest that the second is incomplete, and endorse the third. The Preference Transformation View Political theorists regularly claim that deliberation works because political argument or debate transforms preferences and, in this way, induces agreement or consensus.10 There are, we think, good, mutually supportive methodological, empirical, and normative reasons for skepticism about such claims. We consider these in turn. First, from a methodological perspective, concern for tractability recommends that we hold preferences constant. Consequently, we differentiate between an actor’s underlying or primitive preferences over outcomes and her derived or induced preference over policies or strategies designed to reach those outcomes. While we concede that argument might alter an actor’s induced preferences, we resist for methodological reasons the claim that it alters her underlying preferences. By itself, this methodological stance might not seem persuasive to those not already committed to the modeling approach we adopt here. We believe, however, that it is supported by the following empirical and normative concerns. Second, it seems clear empirically that political argument rarely issues in substantive agreement. Even following argument or debate, participants continue not only to endorse diverse positions, but continue to do so with vigor and conviction. Indeed, plausible defenses of democratic deliberation concede that it need not issue in consensus or agreement (Cohen 1989: 23). We suggest that once we fully appreciate that democratic polities are characterized by pluralism and resulting disagreement, the claim that argument or debate will generate substantive consensus by transforming preferences appears increasingly unsupportable. 9
For several reasons we consider the distinction between arguing and bargaining to be too stark even for analytical purposes. First, as Elster readily admits, political actors regularly rationalize narrowly self-interested proposals in purportedly impartial term. Second, on the other hand, interests can and often do serve as “reasons” (Johnson 1998). Members of previously excluded groups, for instance, typically and justifiably demand full admission to relevant decision-making arenas on grounds that, just so long as they are denied full admission, their interests will not adequately be considered. Finally, bargaining problems are best understood in technical terms precisely as incompletely structured coordination problems. On our account argument serves just to address such problems. We thus disagree with Elster to the extent that he sees arguing and bargaining as informed by distinct phenomena and so depicts the “strategic uses of argument” as contingent on the intentions of particular actors. 10
See, for example, Manin (1987: 352) and Cohen (1989: 23-26, 29; 1998: 199). For a criticism of this view see Knight and Johnson (1994).
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Finally, democracy is an attractive ideal in large measure because it does not privilege any particular participant or view in advance and therefore affords considerable latitude for political disagreement and discord. In normative terms, then, those who defend political argument because it can transform preferences must at a minimum offer some account of why in a large, pluralistic society consensus over values or preferences is normatively attractive (Knight and Johnson 1994).11 Were it to obtain, such consensus would largely obviate the need for democratic practices. In combination with the methodological and empirical considerations noted above, this normative concern deflates the claim that political argument works to transform preferences. We will not consider it any further and will concentrate instead on the remaining two possibilities. The Information Transmission View Perhaps the most systematic analysis of political argument focuses on legislative debate (Gilligan and Krehbiel, 1987; Austen-Smith 1990a,b). Here legislative decision making is modeled as a three-stage process where voting is preceded first by a round of debate modeled as cheap talk, and then by an agenda setting round during which, by contrast to the debate round, signals are costly. In these models the explanatory mechanism is simple and straightforward. Participants in political debate or argument transmit information in one or both of two ways.12 First a speaker might reveal private information regarding her own preferences or capacities.13 Second, she might reveal some private “technical” information regarding the consequences of adopting some policy or pursuing some course of action. In either case, debate reveals private information that, in turn, affects the induced preferences of legislators by prompting them to revise their beliefs regarding the likely consequences that a given piece of legislation might generate. Debate clearly can reveal information. That said, models of political argument that focus narrowly on information transmission are incomplete.14 Observationally, political argument often seems to have effects on outcomes that can be attributed to information transmission only with great strain. A classic example of this was the 1970 episode, in which Senator Warren Magnuson re-framed a debate over the shipment of nerve gas (from Okinawa to the U.S. for purposes of storage or deactivation) into a constitutional argument over the prerogative of the Senate to ratify treaties (Riker 1986, 106-13). A much more recent example is the way that, in the spring of 1998, industry lobbyists defeated tobacco legislation by re-framing the debate as being about taxation rather than the public health or the exploitation (via cigarette 11
For a recent disagreement on this issue see Sunstein (1991) and Ferejohn (1993).
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For a more general survey of this research see Austen-Smith (1992). For a critical view of this work and of its implications for democratic theory see Mackie (1998). 13
This is the basic mechanism at work in signaling models and in some cheap talk models such as those described in Crawford (1990) and Farrell and Rabin (1996). 14
In fairness, Austen-Smith acknowledges as much. He concedes that “legislative debate can fulfill other roles: from the purely symbolic to the testing of arguments with which to defend representatives’ voting decisions come election time to heresthetic.” He simply admits that his model “can say little about such roles” (Austen-Smith 1990a, 144).
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advertisements) of children. Magnuson managed to fashion victory out of what appeared to be certain defeat, while the tobacco lobbyists have (at least temporarily) managed to stall impending, seemingly overwhelming defeat. In neither case, however, did the protagonists reveal any private information. Instead, they not only called attention to what all parties to the debate already knew, but they did so publicly. The “reasons” that actors like Magnuson and the tobacco lobbyists adduce in support of positions they endorse consist in an array of speech acts. They invoke principle, identify precedent, issue warnings, and so on. So advocates of the information transmission approach confront a difficult task. They must explain how the observed diversity of actual reasons that actors advanced in argument amounts to “incidental detail” insofar as argument all is animated by the same causal mechanism, namely information transmission. We, of course, face an analogous problem. Debate as Coordinating Expectations We agree that political argument can convey information and that, under some circumstances, it does so. We suspect, for the reasons that we have just given, that that is not all political argument does. Rather we think it contributes in a specific way to what in game theoretic terms we call the process of equilibrium selection. It accomplishes this by allowing actors to publicly focus or divert the attention of relevant others in a quite specific way. When advocates of one alternative in a political choice problem offer reasons for their preferred alternative, they are trying to establish the similarity of their current problem to some past or anticipated future problem whose analogous resolution might command more widespread support. We briefly indicate how participants in political argument do this when they establish precedent, refer to principle, or alter the dimensions of the issue. Citing Precedent. Schelling famously argues that when they confront the ambiguity and conflict that a coordination problem embodies, rational players not only do, but should, take advantage of whatever “incidental details” might stabilize their reciprocal expectations. The “fundamental” task actors face in such situations is to marshal available resources in what he calls “the creation of traditions” (Schelling 1960, 106-8). An actor engaged in this creative process basically endeavors to portray the current coordination problem that she and others confront as being the same as or similar to some problem that they previously have resolved. In that sense, she attempts to identify a precedent. As in legal contexts, following precedent here consists in “the doctrine that decisions of earlier cases sufficiently like the new case should be repeated in the new case” (Dworkin 1986, 24).15 The trick for speakers, in politics as in law, is to establish similarity or analogy in ways that relevant others might see and accept given that those others, for various reasons, may disagree about whether the current problem is “sufficiently like” the past case or cases being cited as precedent. Invoking Principle. In the course of debate or argument political actors frequently also invoke principles of various sorts. Here too they seek to establish relations of similarity. 15
Dworkin (1986, 99) insists that any plausible conception of law must, among other things, account for the force of precedent. And he criticizes various brands of legal theory and their attendant conceptions of law for, among other things, failing on this score. For our present purposes his larger argument is beside the point.
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Deciding based on principle requires that actors first attempt “to fit (most or almost all) precedents and a range of hypothetical cases” under some general rubric, “and then use this principle to decide the current case.” This requires that the cases thus fit are “viewed or treated in the same way” (Nozick 1993, 3).16 When political actors cite precedent they seek to establish similarity retrospectively. When they announce principles, by contrast, they also seek to do so prospectively. In this sense, principles “license a subjunctive inference to a new case that steps beyond the indicative instances that happen already to have fallen under it” (Nozick 1993, 5).17 Principles, then, not only enable actors to address eventualities that they did not or could not have anticipated, they allow actors to do two further things. First, they allow actors to acknowledge that such “unforeseen contingencies” are a pervasive feature of social and political interaction (Kreps 1990).18 Second, they allow an individual or organization to establish an “identity” as the type of actor who will act resolutely in the face of unforeseen contingencies (Kreps 1990, 126; Nozick 1993, 12-14). This holds whether the principle indicates in a constructive way how to proceed or whether it operates as a filter to exclude some range of alternatives. Doing Strategic Things with Principle and Precedent. Principle and precedent, as we depict them, both work to establish similarity. It is important to underscore here that, on our view, a speaker inhabits a strategic environment where others may not only find the reasons – the principle or precedent – that she adduces in support of her position unpersuasive, but may, in response, advance some competing account of similarity. In short, political argument is a dynamic, conflictual process in which contending speakers seek not only to establish similarity but to subvert competing views. Speakers try, in effect, to convince others that the current situation is in important ways not like that (or at least not just like that) at all. 19 Here again Riker’s Magnuson affords offers an illuminating example. Magnuson did not attempt to rearrange dimensions, in Riker’s sense, simply by invoking the interests of other Senators. In fact, on a vote based solely on interests he appeared to be doomed to defeat. He invoked principle (the constitutional prerogatives of the Senate) and clearly was concerned to highlight how the disposition of a current, seemingly inconsequential issue might establish precedent that might well prove disadvantageous for the Senate in future inter-branch interactions. He hoped to 16
We obviously are indebted to Nozick’s discussion of “how to do things with principles.” That said, we do not subscribe to his further claim that actors derive “symbolic utility” from principles (Nozick 1993, 26-28). And, for present purposes, we remain agnostic about his conception of principles as “teleological devices” in the sense that the human capacity to act from principle is a functional response to evolutionary pressures (Nozick 1993, 35-40). 17
Principles have several features that facilitate this process: they are general, qualitative and universal and, as a result, they abstract from particular individuals, events, objects and locations (Nozick 1993, 5). Compare Schelling (1960, 78) on the effectiveness of qualitative principles as focal points. 18
Such contingencies also are a troubling issue for game theorists insofar as their models assume that players inhabit a “closed universe” in the sense that they can exhaustively identify, label and trace the consequences of “all possibilities” (Binmore 1990, 117-20). See also Rubinstein (1991). 19
Here our approach differs from Kreps (1990, 91,125,127) who repeatedly portrays the use of principles as efficiency enhancing. That focus may be appropriate in the context of business enterprise that Kreps addresses, but it seems strained in analysis of politics. This point is important not just to differentiate ourselves from Kreps, but relative to the model we present in part five where we use efficiency solely to illustrate the sorts of normative criteria that actors might argue about in politics.
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show that this (the shipment of nerve gas) was not an inconsequential policy decision, but a constitutional issue of enduring importance. Magnuson, then, exercised leadership just by coordinating the expectations of his fellow Senators, getting them properly (from his perspective) to understand the nature of their problem (Calvert 1992). Our aim in this section has not been to offer a comprehensive taxonomy of argumentative strategies or resources. Neither, obviously, have we aimed to analyze exhaustively any of the strategies that we do identify. We hope, more modestly, to have shown two things. First, actors engaged in political argument advance reasons aimed at mitigating (or at purposely exacerbating) the sort of strategic uncertainty embodied in coordination problems. Second, there is a plausible common mechanism underlying a variety of argumentative strategies. In the process, we have suggested, if for reasons that Elster will likely not embrace, why “the strategic uses of argument” are a ubiquitous and unavoidable feature of social and political interaction. Two tasks remain. We first elaborate on the conception of politics as ongoing, if precarious, coordination that provides the necessary background to the way we characterize political argument. We then model in a much more precise way how political argument coordinates expectations.
The Context of Political Argument We turn now from the content of political argument to the context in which such arguments are offered, with the ultimate goal of specifying a theory of how arguments, without transforming preferences and aside from transmitting information, influence participants’ choice of actions. Two important aspects of context are important: (1) the individual social and political setting in which choices are made and actions chosen, and (2) the cultural and historical setting in which choices are embedded. After spelling out a view of both aspects of the context of political argument, we offer a model that captures some, but not all, of its central features. The Political Choice Situation The traditional rational choice approach to the effect of argument on political choice would be to depict voting or other form of political choice as being preceded by communication stages. Our approach can indeed be applied to this traditional model, showing how political argument that precedes political actions can affect those actions and determine the properties of the resulting outcomes. However, this would not capture the entire range of effects that political argument might have: in addition to coordinating the actions of voters or legislators in casting their votes (as in Cox 1997), argument may create legitimacy, inculcate solidarity, induce generosity, or produce an impression of fairness. In short, it may lead to expectations that lead to actions in accordance with government wishes.20 We want to capture some aspects of these functions of political argument by allowing for the endogenous determination of citizens' and officials' behavior following a political decision. So, for example, officials may fail to enforce a law, or use appropriated funds corruptly; or citizens may ignore a law so massively that the authorities cannot enforce it. In other words, some states of the world may be infeasible for political authorities to attain through their official decision processes. 20
Alternatively but similarly, of course, political argument could through the same mechanisms undermine government wishes or just create confusion.
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On this view, the formal proposal of laws, voting, etc., become acts of communication that may or may not lead participants thereafter to behave accordingly. Instead of portraying formal political processes as the central game being played, on this view these formal processes are simply a ritualized version of political argument taking place at a formally specified place and time, in which a small number of alternatives at stake are delineated, and the set of possible “messages” that can affect subsequent behavior are restricted to a small list of formalities: the parliamentary motion, the vote, the veto. When members of a legislature vote on a bill, they are communicating their support for or opposition to the bill in a carefully specified and formalized setting in which citizens expect subsequent government actions to correspond to the number of votes cast for and against the bill. Each vote is an act of communication, as is the parliamentary rigamarole that accompanies the convening of an official meeting of the legislature. More generally, then, we portray political life as a series of situations. In each situation, citizens, including officials, take actions that, together, determine an outcome about which they have preferences. We intend this action-choosing process to represent all the social interactions relevant to a given political situation in which people’s actions have a direct physical or economic impact on other people. It includes opportunities to provide or produce public goods, to act in concert with others, to obtain and supply information, to steal, to commit violence, and to take or not take any actions that might be the subject of political decisions or might affect public welfare. We intend these action choices to include, in particular, the activities of government officials in carrying out programs, enforcing laws, and otherwise using any powers or resources designated to their offices. Like the actions of citizens, the actions of officials may be consistent with the laws and wishes of the polity or the government, or they may violate those rules. Officials charged with enforcing or executing laws may face the temptation to shirk or to engage in corruption. To counteract this temptation, there may be other enforcement applied by other actors, and so on, ad infinitum. 21 These action choices are the ultimate target of political argument, which in turn is the focus of our analysis. We posit that, prior to choosing actions in each situation in the series, participants engage in a process of pre-play communication.22 Thus each situation in the series consists of a communication phase followed by an action phase.23 During the communication phase, a participant may simply propose an outcome to her liking, or she may advance reasons, 21
Fortunately for real-world government, these endless layers of incentives do not necessarily require endless levels of laws and enforcement; instead, the “chain” of enforcement can be circular. This is the whole point of republican democracy: consider the incentives among members of a town council who hire and fire a police chief, who in turn supervises a police department, whose officers enforce town laws upon the citizenry, who in turn elect the town council. In other instances, a rule of behavior can be mutually enforced by the people subject to it, in the manner demonstrated in the theory of repeated games.
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We differentiate between “action” and “communication” only as a terminological convenience. On our view, argument or debate is a form of action in which people “do things with words” in Austin’s (1962) sense. Moreover, in our game theoretic model below, instances of communication and action in the sense used here are both just choice of “actions” in the game theoretic sense. 23
Each phase, in turn, may consist of a whole sequence of choices of actions or communications by the participants. In the formal model below, we refer to the successive opportunities to act within either phase as different “stages” of that phase.
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based on principle or precedent, why others should accept a particular outcome or a particular kind of outcome. This communication is meant to reflect real-life phenomena of political speeches, debates, advertisements, discussions, and the like.24 The arguments given by participants in the communication phase may affect what actions they and others choose in the action phase. We assume people have expectations about the kinds of outcomes others find appealing and the kinds of arguments they find compelling. Moreover, they have expectations about how various combinations of arguments made by different speakers will interact to produce behavioral results. By this mechanism, an individual’s choice of actions will depend not only upon her own desires, habits, and understandings, but also upon her expectations of others’ actions. Our main problem is to specify such a process formally so as to leave room for participants to use argument rationally and strategically – to try to bring about desired outcomes through argument, in the sense of Elster. Embedding the Choice Situation So far we have talked about particular choice situations in which there is communication as though the situations were discrete. Obviously, however, any particular choice situation takes place against a broader cultural and historical background.25 In the broader conception of political argument and choice we wish to advance, this background is itself produced by the series of past political interactions, including arguments and actions. Culturally, we assume that parties to political argument share a natural language.26 We assume, that is, that players draw upon a reasonably stable stock of meanings, that by and large they understand one another.27 Further, they share some expectations about how people will act after hearing particular communications. Historically, any particular choice situation is part of an ongoing series of other choices and interactions. These two factors raise several related issues. First, the outcome (in terms both of communication and choice) of any single situation may have consequences for future choices and interactions. For example, holding constant whatever is said in political argument, my neighbor’s contribution to public goods today may influence my willingness to contribute tomorrow. Accordingly, the usual approach to repeated 24
If an official government decision is possible in this situation, the process of making those decisions can be portrayed either as a formalized step in the later stages of the communication phase, as a set of available action choices near the beginning of the next, “action,” phase (or some combination of the two). 25
For background on the view of politics we sketch here see Calvert (1992; 1995a,b; 1998) and Knight (1992; 1995). 26
This assumption means that the meanings conveyed in any particular act of communication derive from a larger set of conventions. Here we follow both other game-theoretic models of communication (Myerson 1989) and many prominent approaches to the philosophy of language (e.g. Austin 1962). 27
We understand the conventions establishing meaning to be the products of ongoing social interactions that in principle can be modeled in game-theoretic terms. Speakers of a natural language obviously can improvise, but they can only do so against this conventional background. The apparent contradiction between improvisation and convention has created a certain amount of consternation among both game theorists and philosophers (Farrell 1993; Davidson 1986), which a more nuanced understanding of the open-ended nature of ongoing coordination problems could go a considerable distance toward alleviating.
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game theory is to analyze equilibria of strategies for play across the whole series of games, assuming that players can specify unambiguously in advance a strategy for play in all subsequent interactions. Second, on the other hand, this traditional game-theoretic approach presumes that the connections between current and future choices and interactions will be obvious. However, it is not likely that any future situation will be unambiguously identical to one class of past situations and not to any other. This amounts to a problem of unforeseen contingencies (Kreps 1990). Actors then are faced precisely with the problem of establishing relations of similarity. In other words, it is difficult for participants to establish a repeated game strategy that they can apply to an agreed-upon, distinct set of future interactions; they constantly confront the problem of establishing whether a given situation is part of any “repeated game”, and if so which one (Calvert 1992). In fact, we believe unforeseen contingencies, the partial newness of every political situation, is precisely what gives scope and force to political argument. We continually face situations of political choice in which existing precedents and principles provide only an imperfect guide. In a court case, opposing lawyers are able to choose equally appealing lines of precedent to motivate diametrically opposed conclusions. Politicians contending over policy alternatives are able to cite principles having broad appeal in service of opposing sides of an issue. Often, one precedent or the other, one principle or the other, finally wins out and the court is able to make a decision, the government to implement a policy, with a sufficient degree of acquiescence from the losing side. All agree that a decision has been arrived at, and subsequent behavior allows it to go forward: the police free the accused person, bureaucrats carry out a new program. Once there is sufficient agreement of expectations about what is going to be done by others and what one therefore will do oneself, behavior consistent with the “winning” decision or position constitutes an equilibrium. A third issue raised by the importance of cultural and historical background is that of distributional conflict. On our view political argument aims to establish similarities in the ways sketched above. It hopefully is clear that any similarity relation that a speaker manages to get acccepted generally will not be neutral in distributive terms. There is thus a problem here not only of coordinating expectations, but also of settling disagreements over interests. This is the familiar concern that game theorists address through mixed-motive coordination games such as the “battle of the sexes.” Thus we focus in this paper on how strategic actors use political argument to solve new problems of equilibrium selection or coordination in a polity, with an eye toward distributional advantage. Political argument, we believe, is how people both create and assess each others’ willingness to accept their roles in carrying out a political decision. Beyond the mutual understanding people have about the meaning and appeal of various principles and precedents, we argue that the impact of argument is primarily a phenomenon that takes place within a given political situation or problem. That said, we also believe an important secondary feature of political argument is that participants are often acutely aware that a principle or precedent
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accepted today gains additional weight in future applications; we postpone, however, any further consideration of this aspect of argument.28 A Partial Analytical Approach Although we envision political life as consisting of communication and action phases repeated in an indefinite series, our subsequent analysis focuses on a specific and narrow form of influence of communication and action upon the future. We concentrate on how, within a given interaction, outcomes in the communication phase influence outcomes in the action phase.29 The analytical approach we develop below is partial in that it ignores several other features of political argument as sketched here. First, the model we develop is not one of repeated games; instead, it examines the force of argument within a single stage of the ongoing process of political life. Second, as just noted, we ignore for the moment the development of principles over time. Third, of course, our single-situation focus means that we have nothing to say here about the dynamics of the cultural-historical background. Moreover, our analysis has nothing whatsoever to say about the content of argument, or about the force of specific principles. Rather, we are interested for now in the abstract question of how a particular structure of common expectations about the effects of arguments will affect outcomes. In particular, we focus on whether normative qualities implicit in the effects of argument can carry over into the resulting outcomes. In order to gain some real analytical purchase on political argument and on its strategies and outcomes, we now proceed to abstract the process further, rendering it as a specific type of noncooperative game. We can then deduce how the structure of political argument may or may not lead to political outcomes that have desirable normative properties. Our specification of the game is obviously not the only one that could be given in order to model a process like the one described above. However, it does offer interesting results connecting the nature of argument with the qualities of outcomes, and provides a template for other, similar analyses in the future.
Modeling Political Argument The defining feature of our approach to modeling political argument lies in our treatment of participants’ understanding of meanings in the language, and of the linkage between communication and action. We assume that the basic problem of democratic politics is to arrive at a relatively good coordination equilibrium. In the analysis of this section, “good” means giving relatively high utility to relatively many participants. In order to be actually realized, any outcome chosen in advance by a political process must be a Nash equilibrium – that is, there must be no incentive for any individual, expecting that outcome, to change her behavior to be incompatible with it. 28
29
An initial attempt to motivate a theory along these lines appears in Calvert and Johnson (1997).
There may be multiple “stages” of communication in a commnication “phase;” likewise for the action phase. Implicitly, we allow for the behavior in the earlier stages of a single communication or action phase to affect choices in later stages in that phase.
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The role of principles, precedents, analogies, appeals to fairness, and all the contents usually thought of as part of “political argument” have their effects through this link. If a small group of people simply demands a particular outcome that is good for them, the majority may ignore them and produce a different outcome. But the same majority might respond if the group invokes some fairness principle that leads to the same outcome. This is the exactly the effect of “argument” in Elster’s (1995) terms. We use the model constructed below to examine Pareto efficiency as the ultimate normative concern. The analysis of efficiency is really a demonstration of how any individual normative property could be analyzed, provided it has the following characteristics: the property leaves some ambiguity about how the possible outcomes should be ranked; different individuals have different ideas about how that ambiguity ought to be resolved, within the given normative constraint; and, through political argument, ancillary reasons may be offered to attempt to convince others that a given ranking is the most appropriate or the most likely to gain widespread acceptance, or at least to guide most people’s later actions. We expand on this application of the model in the concluding section. The question this model answers about such a normative property is this: does well-ordered political argument concerning the resolution of disagreements and ambiguity about the normative ordering, using some combination of bargaining, ancillary principles, analogies, precedents, or other potential reasons that individuals may adduce, lead to an outcome that realizes the main normative criterion reasonably well. Specifically, does the outcome realize all existing agreement among individuals concerning how the main normative criterion should be applied? The Model The action game. Let G be a game to be played by participants in N = {1, 2, . . . , n}. Each i in N will choose an action according to some mixed strategy chosen from Ai. Let A = A1 × . . . × An . If the players choose mixed action profile a from A, then each player i receives an expected payoff of ui(a). Let E f A represent the set of subgame perfect Nash equilibrium strategy profiles of G, and let E* be the Pareto-efficient subset of E, that is, E* = {a0E | for no b0E is [ ui(b) $ ui(a) for all i and uj(b) > uj(a) for some j ] }. For any profile a0A, designate by E(a) the set of profiles in E that are strictly Pareto-superior to a; that is, E(a) = {b0E | ui(b) > ui(a) for all i0N}. For use in the proofs of theorems, we construct the following sequence of subsets of E: let E0 / E*, and for every integer k > 0, define Ek / {e 0 E | E(e) f Ek!1 c ... c E0 }. Given that the E is finite, of course, the sequence will have some K that k, k' > K implies Ek = Ek'. Communication stages. Let Mi be a finite set of possible messages that player i can send, with M = M1 × . . . × Mn. Then we portray a political argument process as a game '(G, T) in which G is augmented by T pre-play cheap talk stages. Thus '(G, T) proceeds as follows: Stage 1: the players in N simultaneously broadcast messages from their respective Mi. Stage 2: they do so again. !
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Stage T: they do so again. Stage T+1: they play G. At each stage of '(G, T), the previous choices of all players are common knowledge. Let Ei represent the strategy set (including mixed strategies) for player i in '(G, T); we denote a typical strategy for player i by Fi and a mixed-strategy profile by F. As a result of the play of F, the action game G results in an outcome (or profile of pure action choices) g. Language, communication, and political outcomes. Our goal is to understand what outcomes can result from political argument when the participants choose equilibrium strategies in the overall argument-and-choice process. The messages represent the various statements players can make implying that particular outcomes of G should be taken; a message may represent a statement of principle, a negotiating point, an individual's vote, or any other communication that, taken together with the communications of others, may lead players to expect one another to act in particular ways when the action phase is played. In general, if G has more than one equilibrium and M contains more than one message, '(G, T) has many equilibria. If this communication-augmented game is to represent a process of political argument, however, it is only reasonable to suppose that the possible messages have meaning to the players, meaning that is determined exogenously to '(G, T). Such meanings imply certain expectations that players will have about one another's subsequent actions given what is said in the process of argument. They represent the potential force of some arguments against others. A message advocating an outcome for one specific reason may influence people to expect all to play according to that outcome, while a message advocating the same outcome for a different reason may have no influence on the other actors. Moreover, a message may be effective when sent in the context of certain combinations of current and past messages from others, but not in other contexts. Finally, the force of messages may result from the existence of a commonly accepted institutional or decision-making structure, such as when a majority of votes cast in an appropriate context are taken by all participants to create a binding law. If we place prior, common-knowledge restrictions on the meanings of messages in the Mi, we are in effect restricting our consideration to a subset of the equilibria of '(G, T) in which the actions taken correspond to these meanings. This is the approach taken in Farrell (1987) and Rabin (1994), for example, in modeling communication games. As Rabin says, “Because [of] the cheap-talk structure, some behavioral assumption about how language focuses expectations must underlie claims about the effects of this form of pre-game communication” (1994: 375). Throughout the analysis that follows, we maintain two general assumptions about the “meanings” of messages, and therefore about equilibria in '(G, T). These assumptions are meant to create a context highly favorable to the claim, central to the literature on democratic deliberation, that appropriately restricted political argument will result in outcomes with good welfare or other normative properties. Despite using such strong assumptions, we conclude that this claim is very hard to maintain. The general approach is adapted from that of Rabin (1994), who analyzes a much more specialized variety of communication games. Assumption 1: provisional agreements and actions. We assume first of all, then, that at the beginning of each stage of '(G, T) there is some provisional agreement in force concerning the
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play of G. At the beginning of stage 1, the provisional agreement in force is some default action profile a0 0 A. The profile of messages sent in any stage t # T may change the provisional agreement to some other a, always, we assume, in E. It is the common assumption of the players that all will choose in G according to the provisional agreement in force at T+1. This assumption places a rather restrictive structure on the process of political argument, but it is really merely a tractable stand-in for any combination of more complex possibilities. It serves the purpose, moreover, of biasing the normative case in favor of deliberation, an appropriate bias given our ultimate point about the weakness of deliberation for assuring normative quality. Given a provisional agreement a, for any b0E let Q(b; a) represent the set of message profiles m0M that shift the provisional agreement to b for stage t+1. If m0Q(b; a), then we could say that b is the meaning of m, or of mi in the context of a and m!i . We assume throughout that message profiles have well-defined meanings: if b, b'0E and b… b', then Q(b; a)1 Q(b'; a) = i. In particular, for simplicity we assume that the meaning of a message depends on previous messages only through its dependence on the provisional agreement. We refer to Q, and to the meanings implicit in it, as a “language.” Assumption 2: equilibrium. We assume players will use a profile F of strategies that is a subgame perfect equilibrium in '(G, T) under assumption 1. Thus we assume that all participants have common expectations about the language, that is, about what the meanings of messages and what appeals to what principles are likely to be effective in the abstract. Moreover, through assumption 2 we invoke a sort of strategic stability: participants in political argument strategize in full anticipation of the strategizing of others. To assume otherwise would be to admit the possibility that participants could suffer a kind of coordination failure at the level of political argument, making it difficult indeed to solve the overall coordination problem of choosing a “good” equilibrium in G.30 Again, this assumption appropriately biases the case against our argument about the weakness of deliberation. However, we also believe that the assumption of equilibrium in the overall argument process, like the assumption of commonly held meanings, is an appropriate game-theoretic model of the nature and use of language for political argument. Language and argument in real life might often produce misunderstanding and surprise, but surely their most outstanding characteristic is the extent to which we succeed in making ourselves understood and, partially, in anticipating strategies. A Welfare-Enhancing Language Our first result illustrates the kind of normative result one would like to derive concerning a process of argument, namely that political argument of a suitable type ensures that the outcome will have good normative qualities. We define the following class of languages:
30
The strategies used in such an equilibrium may be mixed strategies, so even these leave some leeway for coordination failure in actually realized outcomes. Assumption 2 only rules out complete failure to anticipate the distribution of possible strategies used by others.
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Definition 1: Q is a welfare-enhancing language if, in addition to Assumptions 1 and 2, it has the property that for every provisional agreement a at any period t # T, for every profile of messages m, m 0 Q(b; a) for some b 0 E(a). It comes as no surprise, with such a strong assumption about Q, that the following normative property holds for outcomes of G following equilibrium communication. Again, although we use Pareto-optimality as a specific normative criterion, an identical result would obviously substituting any welfare criterion for E(a) in the definition of a welfare-enhancing language and in the statement of the theorem. Theorem 1. Suppose Q is a welfare-enhancing language. Then for sufficiently large T, '(G, T) always yields an outcome of G in E*. Proof. Let K be a finite integer such that Ek = Ek' for all k, k' > K. Following the initial period, the provisional agreement will move from a0 into some Ek where k # K Thereafter, it will move into Ek' for some k' < k, and, if T is sufficiently large, continue this until it reaching E0 = E* as required. Thus any T $ K will suffice. € This result, however, really tells us nothing about the behavior of strategic political arguers or about the outcomes they will produce, since the language gets them to Pareto efficient (or otherwise normatively best) outcomes no matter what they say. It really is the language itself that enhances the welfare, rather than the players' choices of arguments or messages. Welfare Improvement Due to Strategy A more substantial result concerning the welfare properties of political argument would have to place less structure on the language of political argument, and use the equilibrium strategies of the participants to determine the quality of the outcome. For a version of the game with only two participants, we adopt an approach based loosely on a result of Rabin (1994, theorem 3). Definition 2. Q is a progressive argument process (PAP) if it obeys Assumptions 1 and 2 above and satisfies the following properties for all T. (1) For every a0Ec{a0} and every b ó {a}cE(a), Q(b; a) =i. (2) For every provisional agreement a 0 [{a0}c E] \ E*, at any period t # T, let m be a profile of messages (possibly the realization of a mixed strategy) to be used in period t. For every player i, if m ó cb0E(a) Q(b, a), then there exists miN … mi such that (m–i , miN) 0 cb0E(a) Q(b, a). Condition (1) of the definition says that no message profile can ever change the provisional agreement to an outcome that is not strictly Pareto-superior to the current one. This implies, in particular, that once the Pareto efficient set E* is reached, no further changes in the provisional agreement is possible. Condition (2) of the definition ensures that if the profile of message strategies µ specified by F for the present period yields a zero probability of the provisional agreement moving immediately into E(a), then every player i has an alternative message which would make that probability positive if player i alone made the switch.
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Condition (2) is a particularly strong assumption. It is needed, however, if the participants are to avoid the simplest kind of coordination failure in the argument process. Suppose that, at the beginning of period T, the provisional agreement is some outcome aóE*, and that b, c, and d are outcomes in E(a). Suppose that, under Q, player 1's message makes only transitions to the new provisional agreement b possible, and player 2's makes only transitions to c possible; then there is no way for player 3 to assure a positive probability of any transition. If player 3 chooses a strategy that allows only transitions to d, then the players' strategies are in equilibrium, and do not allow any available Pareto improvement to be realized. All three players are using best-response strategies, yet this equilibrium is strictly Pareto dominated. Condition (2) ensures that any of the three players will be able unilaterally to break such a deadlock, so that it will not be possible in equilibrium. A hypothetical example of a PAP would be a language in which each Mi is just equal to A, and in which Q is defined by a sort of “plurality rule” at each period: if there is a unique, new provisional agreement among those feasible under Condition (1) named by more players than any other, then that outcome in fact becomes the new provisional agreement. But if there is a “tie vote” (or if no player names any feasible new provisional agreement) then the old provisional agreement remains in force. In the latter case, any single player could change his message to break the tie, so Condition (2) for a PAP is satisfied. A PAP is “progressive” in the sense that all changes in the provisional agreement can move toward increased achievement of the Pareto criterion, and cannot move in any other direction. Unlike the welfare-enhancing language of Definition 1, however, a PAP does not guarantee constant movement toward Pareto improvement. It leaves room for players to use mixed strategies whose realizations in any given communication round fail to coordinate on a Pareto-improving move. It also leaves open the possibility that players may “hold out” by insisting in earlier rounds upon changes in the provisional agreement that they strongly prefer, giving in only later if others will not. Nevertheless, as Theorem 2 shows, every subgame perfect equilibrium of '(G, T) whose communication strategies constitute a PAP yields expected payoffs that achieve some Pareto improvement over the default provisional agreement a0, if any is possible. Specifically, as the number of communication rounds becomes large, the players are guaranteed a payoff arbitrarily near the minimum they could receive from an efficient outcome of G. Theorem 2. Suppose E is a finite set and Q is a PAP. For every i0N and every T = 1, 2, . . ., let uiT = min {ui(F) | F is a subgame-perfect equilibrium in '(G, T)}. Then limT64 uiT $ mine 0 E* {ui(e)}. Proof . Define the following payoff values: ui* = mine0E* {ui(e)} and uiE = mina0A {ui(e)}. In words, ui* is the lowest payoff i could receive from an efficient outcome of G, and uiE is i's lowest possible payoff from G.
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Let M–i be the set of all message profiles by players other than i. By condition (2), for every a 0 {a0}cE \ E*, for every m–i 0M–i, there is some mi such that (m–i , mi) causes a transition to a new provisional agreement in E(a). Even if all players other than i use mixed strategies to choose their messages, at least one of the message profiles in M–i must occur with probability at least 1/|M–i|. Thus player i can respond to any particular m–i so as to assure at least this probability of a transition to E(a). For convenience, call this probability p. Let F be any subgame perfect Nash equilibrium in '(G, T). If F does not generate a transition probability of at least p in each period when the provisional agreement is not yet in E*, any given player i can change to some strategy FiN so that (F–i , FiN) does generate such transition probabilities. Again let K be a finite integer such that Ek = Ek' for all k, k' > K, and assume T > K. The probability of failing to transit at least K times is then B(K–1; p, T) , the binomial cumulative probability of K–1 or fewer successes in T trials. This value approaches 0 as T becomes large. Thus provided T > K, against F–i , i can assure herself of a payoff of at least [1 – B(K–1; p, T)]ui* + B(K–1; p, T) uiE, which approaches ui* as T becomes large, as required. € Discussion Depending on the details of G, the conclusion of Theorem 2 may or may not be a strong result. If distributional extremes are possible in equilibrium, then Theorem 2 only guarantees each player what she would receive in her “worst” efficient equilibrium of G, which may be very low. On the other hand, in the standard battle of the sexes game, Theorem 2 ensures a payoff that, although not efficient, is higher for both players than in the symmetric mixed-strategy equilibrium. Thus in a PAP, the outcome of political choice given a sufficient opportunity for argument of the sort modeled here yields outcomes that have somewhat good normative properties. In the straightforward normative setting of Pareto optimality, for example, sufficient communication leads to outcomes that are at least as good from every player's point of view as the worst efficient outcome. This is not a strong property in general; although in some cases, such as the battle of the sexes, it guarantees that not all potential gains will be forgone due to lack of coordination, it does not guarantee any sort of fair distribution of gains, and still allows a significant shortfall from efficiency in some settings. And the assumptions needed in order to assure even this modest result are strong, even if the argument being modeled is a straightforward process of negotiation over mutual gains. If there is any lack of agreement about meanings, or any failure of common knowledge about the equilibrium in the communicationaugmented game, we have no guarantee that even the level of agreement and mutual gains shown in Theorem 2 will be obtained. Generalizing beyond the Pareto criterion, participants may fail to realize even outcomes that they unanimously agree would be better than the one obtained. We return to this matter below.
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Conclusion The model in this paper contributes to the analysis of political argument in two main ways. First, it identifies and analyzes a mechanism that gives force to argument among rational actors. The actors in our model are strategic both with respect to their political argument and with respect to their subsequent behavior, so, unlike many classical rational choice analyses, ours requires equilibrium conditions to apply throughout the political process.31 At present this model is too abstract by far to allow us to generate empirical results about the specifics of real-life instances of political debate. It does, however, offer a promising new approach to the analysis of how interests, strategies, and expectations can combine with the reasons – principles and precedents – invoked in political argument to produce political outcomes. In particular, we challenge those who posit information transmission as the sole function of political argument to offer a more parsimonious account than ours for why one would observe the universal preoccupation with principles and precedent we see in political life. The burden of proof is either to reduce the processes we focus on to informational processes, or to explain those processes away as mere rationalization or dissembling. Second, our model offers an analysis, partly in the manner of social choice theory, of the normative properties of political argument. As a result, the analysis contributes to our understanding of the interaction of deliberation and representation in democratic regimes. In particular, it indicates how stringent are the conditions under which political argument can ensure justified outcomes according to some commonly held normative criterion. This places a burden on advocates of democratic deliberation to show how some additional set of normative constraints on argument might nevertheless generate more optimistic results. We conclude by spelling out in some detail the nature of this generalization of the model and its implications. Although the model is stated, as traditional in game theory, in terms of private payoff maximization by players and with Pareto efficiency as the normative criterion, the same setup can be applied identically to a broader normative setting. The definitions of E* and E(a), as well as Definitions 1 and 2, are all described as matters of Pareto efficiency and Pareto-improving shifts in the provisional agreement. Assume for present purposes that the ultimate action game, G, will still be played as before, its payoffs representing private interests, and still let E be its set of equilibria. However, let us now choose some other normative criterion to guide political argument during the communication phase. The only requirement for this alternative normative criterion is that, like Pareto efficiency, it partially order the set {a0}cE of feasible provisional agreements. Examples of such a criterion might be that outcomes provide as much freedom or as much equality as possible. These are well known normative goals that nevertheless engender considerable disagreement in application, even among impartial commentators. For the communication phase, rather than using the ultimate payoffs from G as the relevant payoff values, we use a different set of “payoffs” to outcomes in E which represent the extent to which each individual feels each outcome realizes this new normative criterion. 31
We have in mind here such treatments as that of Brennan and Buchanan (1985). This argument is made more generally with respect to the treatment of political institutions in the “new institutionalism” literature in Calvert (1995 a, b).
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Individuals may disagree about the ranking of outcomes under this criterion, and E(a) now represents the set of outcomes unanimously regarded as being better than a under the new criterion. Political argument now consists of the offering of ancillary reasons for deciding that one outcome should be considered normatively superior to another, given that individuals initially differ over how to compare them under the new normative criterion. Definition 1 and Theorem 1 now say: if Q, whenever possible, provides a new provisional agreement that is unanimously regarded as normatively better than the old.; and if the communication phase is sufficiently long; then the final outcome is always “efficient” in the sense that there is no alternative choice that could have attained consensus as being normatively superior to the actual choice. We suggest that the normative restrictions on argument, and the normative conclusions, of deliberation theory might be treated in this manner. The assumptions and definitions of the model restrict political argument to consist of offering reasons, potentially acceptable to others, about how a criterion, such as fairness, justice, equality, or liberty, should correctly be applied in making a political choice. Definition 1 says that there is sufficient consensus about the applicability of potential reasons to allow continual, consensual improvements in the provisional agreement whenever consensual improvements exist. The final outcome will at least have minimal qualities of justifiability, in there is no alternative outcome that all can agree would be better under the accepted normative criterion; and minimal qualities of legitimacy, in that there is no other outcome that everybody would have preferred. These would be unsurprising results: Definition 1's assumptions are strong, and are made directly on the model’s “language” without reference to the communicative actions of individuals; and Theorem 1's conclusions about justifiability and legitimacy are weak. This, together with Definition 2 and Theorem 2, brings us to our main application of the model to deliberative democracy: even a slight weakening of the assumptions seems to force an even weaker conclusion. In terms of an accepted normative criterion, Definition 2 places a weaker, if still fairly demanding, condition on the structure of the political argument process. It prevents changes in the provisional agreement that any player believes will not produce an improvement on the central normative criterion. Definition 2 also requires that, if a unanimously regarded improvement exists but, due to the profile of reasons being offered, no such improvement can be realized, any one player can instead advance some alternative reason that will produce a consensual improvement. Even though weaker than Definition 1, Definition 2 is still fairly strong. In that case, however, Theorem 2 can only promise an outcome that, in each individual’s judgment, is at least good in terms of the normative criterion, as the worst of the “efficient” outcomes. It may still be the case that some alternative to the final outcome is unanimously regarded as normatively superior to it. This raises real questions about whether and how any achieved outcome can be regarded by participants as normatively justified, or the process that produced it as legitimate. It also places a burden of proof on those who would advance a plausible case for democratic deliberation to specify normative conditions that might mitigate our conclusions. To be plausible, such conditions should, in the sense of Definition 2, leave scope for individual disagreement and discretion in argument, rather than, as in Definition 1, placing strong requirements directly on the structure of argument as a mechanism of coordination.
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