Abstract
In this article I address the reception of game-theoretic methods in political science. In particular I challenge the notion that such methods afford a plausible basis for what is commonly called ‘positive political theory’ (PPT). The standard rationale for PPT suggests that the point of formal models is, starting from ‘the’ rationality assumption, to derive predictions that can then be tested empirically. I argue that this standard rationale is hopelessly confused. The confusion stems from the assumption that game-theoretic models are empirically testable in some direct sense. This view is far from unanimously accepted among game theorists outside political science. I argue instead that game-theoretic models are best understood as tools for exploring the operation and limits of one set of basic causal mechanisms. I show how this works in practice and on that basis reassert the value of formal models in political science.
I believe that discussion or application of game theory is utterly meaningless without a proper interpretation. This task cannot be left entirely to philosophers of science, for it constitutes the very essence of the theory (Rubinstein, 1991, pp. 909–10).
In analyzing games the theory does not assume rational behavior; rather it attempts to determine what ‘rational’ can mean when an individual is confronted with the problem of optimal behavior in games and equivalent situations (Morgenstern, 1968, p. 62, emphasis in original).
You may at this point be scratching your head and wondering what sort of mess all this is, if we get into such muddy philosophical issues (Kreps, 1990, pp. 35–6).
In this article I concentrate on the reception of game-theoretic methods in political science. In particular I take issue with the notion that such methods afford a plausible basis for what is commonly called ‘positive political theory’ (PPT). I believe that the standard rationale offered for this enterprise is hopelessly confused, that the confusion stems from the influence of insupportable philosophical views, and that the confusion has generated baleful consequences in the discipline. Specifically, advocates of PPT have reinforced a nearly exclusive, but unjustifiable, focus on empirical performance as the chief, perhaps exclusive, criterion of assessment in social and political inquiry. In the process, they purvey an overly constricted understanding of models and their uses (Clarke and Primo, 2007; Hausman, 1992, pp. 70–82). Finally, they contribute to an uncivil and divisive rhetoric that informs debates in the discipline.
I find game-theoretic models interesting and useful in something like the modest way David Kreps suggested some time ago.
As for … the insights contributed by game theory, I contend that the major successes have come primarily from formalizing common sense intuition in ways that allow analysts to see how such intuitions can be applied in fresh contexts and permit analysts to explore intuition in and extend it to slightly more complex formulations of situations … [G]ame theory has succeeded when it begins from a common sense observation and takes a few small steps further along (Kreps, 1990, pp. 87–8).
Although I would not follow Kreps in conflating common sense and ‘intuition’ — a move itself laden with suspect positivist philosophical baggage — I do think there exists a widely shared, common-sense understanding that many people are instrumentally rational much of the time in most domains of social life. 1 When anyone premises her instrumental actions on what she expects some relevant others might do, she confronts a situation of strategic interdependence. Game-theoretic models, as Oskar Morgenstern suggests in the second of my epigrams, help us understand what it means to be rational in a variety of more or less complex strategic settings. 2 It is in this sense that they are tools useful for the ‘analysis of the concepts used in social reasoning’ (Rubinstein, 1991, p. 909). Like economic models more generally, game-theoretic models arguably are most useful for conceptual rather than for primarily empirical purposes. 3 Failure to recognize this is part of the residual positivism to which far too many political scientists subscribe (Johnson, 2006).
By contrast, I find the prevailing case for game-theoretic methods among political scientists almost entirely unpersuasive. Too often it involves claims to the effect that, relative to competing modes of social and political inquiry, PPT affords its practitioners a monopoly on ‘rigor’, ‘clarity’ and ‘precision’. 4 Such claims are simply mystifying to me. This is especially so because advocates of PPT rarely, if ever, provide much evidence that they base their proclamations on careful and charitable examination of even the exemplars of competing modes of social inquiry. My aim in this article, however, is not to recommend some alternative approach to thinking about politics. Instead I aim simply to deflate common justifications of PPT in the hope of clearing the way for a more modest and hence more plausible defense of game theory and its uses in the discipline.
It will be helpful at the outset to state the obvious. Many political scientists have embraced game-theoretic analysis. Over the course of two-plus decades, advocates of PPT have written a number of systematic textbooks on the subject (Austen-Smith and Banks, 2005; McCarty and Meirowitz, 2007; Morrow, 1994; Ordeshook, 1986). In this respect, game theory is arguably unique among approaches to mathematical modeling. 5 So when enthusiasts, for example, announce that ‘Investing in formal theory is investing in our discipline's basic intellectual infrastructure’ (Cameron and Morton, 2002, p. 804), it is fair enough to imagine that they not only have great faith in formal modeling in some generic sense, but game-theoretic approaches in particular.
The problem is that game theory is not one. 6 It is, as some practitioners sometimes admit, merely a ‘methodology’, a set of mathematical techniques for modeling strategic interaction (Austen-Smith and Banks, 1998, p. 261; Cox, 1999, p. 158; 2004, pp. 177–83; Kreps, 1990, p. 1). And while this methodology is, I think, extremely useful, it is not in itself a ‘theory’ of politics or of anything else.
Having stated the obvious, however, the important question remains: what are game-theoretic methods useful for? I have already intimated my answer. It is just here, however, that proponents of PPT step forward and confidently advance a very different interpretation of game-theoretic models and how they fit into the larger enterprise of social scientific inquiry. On this account game-theoretic methods are useful because, starting from a set of explicitly stated assumptions — in particular the assumption that the agents who populate our models are rational — they allow us to derive predictions about ‘real-world’ behavior that can, in principle at least, be tested empirically. This interpretation animates most critical discussion of game-theoretic methods among political scientists. 7 Even quite vociferous critics of positive political theory accept it. 8 Unfortunately, this interpretation is contestable at best. It proceeds from the unstated assumption that game theory is properly understood as an empirical enterprise in the first place. In so doing it ignores the qualms of esteemed practitioners who think it dubious that ‘the object of game theory is to predict behavior … or indeed, that it is capable of such a function’ (Rubinstein, 1991, p. 909; 2006).
At bottom, then, my skepticism about efforts to subsume game-theoretic methods under the orthodox PPT project has less to do with the technical apparatus on which it relies than with the interpretation of that apparatus that advocates of PPT advance and with the uses to which they claim to put it. The thrust of my argument will be that, to be useful, game-theoretic models presuppose interpretation in several ways that render them continuous with, rather than distinct from, competing modes of political inquiry. I thus agree with Ariel Rubinstein when he insists in the first of my epigrams that the technical apparatus of game theory requires interpretation where, as he subsequently explains, an interpretation just ‘is a mapping which links a formal theory with everyday language’ (Rubinstein, 1991, p. 909). The problem is not simply that advocates of PPT devote very little attention to such matters. Worse, when they do worry about matters of interpretation they labor under the influence of an unpersuasive, vaguely positivist understanding of the task (e.g. Krehbiel, 1998, pp. 7–8, p. 20; Riker, 1990). So I also want to distance the recognition that formal models stand in need of interpretation from indefensible positivist understandings of what it means to interpret a particular model or the enterprise of modeling more generally. None of this is especially contentious in disciplines outside political science. Indeed, my argument draws on the views of some respected philosophers and economists. And while I do not offer a fully developed alternative to the PPT interpretation of game theory, I do hope to point in the direction of one.
The Rhetoric of PPT
Advocates of PPT regularly announce that their work is characterized by a level of ‘rigor and precision’ (Gates and Humes, 1997, pp. 5–6; Morrow, 1994, p. 6) which, tacitly at least, they find lacking in other research traditions. Sometimes this tacit comparison breaks through in refreshingly frank ways, as when we are told that research that incorporates game-theoretic modeling ‘seeks to satisfy a rigid definition of “theory”, and not some ambiguous criteria of good journalism and insightful comment’ such as, presumably, characterizes most of what passes for social science in competing research traditions (Ordeshook, 1986, p. ix). 9
I find such claims increasingly irksome and assume that advocates of PPT advance them as much to stiffen resolve among the faithful as to persuade unbelievers. Since this rhetoric typically appears either in the introduction to texts or in their resounding conclusions, I can usually pass it over quickly enough. Eventually, though, one wonders just what advocates of PPT have in mind when they arrogate clarity, rigor and precision to themselves while thereby at least tacitly withholding such virtues from others. The answer seems to consist in two claims. First we have what I call the explicitness thesis. It holds that:
Formal models incorporate precise, explicitly stated assumptions.
Thus, we are told that game theory demands a rigor that ‘forces the modeler to decide precisely what the assumptions of the argument are’ and so to avoid the poorly specified or unstated assumptions to which verbal argument is susceptible (Morrow, 1994, p. 6). Others likewise insist that ‘First and foremost, formal analysis requires that the modeler make assumptions explicit’ whereas merely verbal arguments ‘often possess hidden or blurred assumptions’ (Gates and Humes, 1997, p. 6).
The explicitness thesis grounds a further thesis which I will call the deduction thesis. It holds that:
Formal models show unambiguously how, starting from explicitly stated assumptions, the analyst deduces particular predictions about the ‘real world’.
Hence, proponents of PPT insist that ‘Arguments structured by formal logic and mathematical analysis are explicit and unambiguous. Such models demand that the links between assumptions and analysis are clear … there is no room for whitewashing the details. Formal modeling requires a precision that rewards the investigator with clear insight, consistency of argument, and explicit reasoning’ (Gates and Humes, 1997, p. 6). Likewise, ‘formal models allow us to see exactly why the conclusions of a model follow from its assumptions’ (Morrow, 1994, p. 6).
In the remainder of the article I critically assess these two theses. Although they are entangled in practice I will separate them for purposes of argument and address them roughly in order. 10
Questioning the Explicitness Thesis
Simply stating one's assumptions, of course, is hardly a virtue in and of itself. This becomes apparent upon reading work that incorporates formal models. There one regularly encounters a significant gap between the mere statement of an assumption and any effort actually to justify it. 11 In other words, there is frequently a marked disparity between the formulation of a model and the interpretation offered for it.
Consider a convenient and ironic illustration of this pattern. In her treatment of the exigencies involved in systematically linking formal (mostly rational choice) models to empirical research, Rebecca Morton endorses the general view that formalization contributes to rigor by insuring the precision and clarity of basic assumptions. Equally she tacitly assumes that merely verbal, ‘non-formal’ statements are somehow methodologically suspect (Morton, 1999, pp. 39–45). 12 In making her more general argument she relies on several running examples. For present purposes her discussion of one paper — by Jeffrey Banks and Roderick Kiewiet (1989) — is especially revealing. 13 Morton is concerned, among other things, to show how formal models can illuminate substantive problems — in this instance perplexing patterns of candidate competition in US Congressional elections — in ways that research not informed by formal theory cannot. In particular, she hopes to show how, because Banks and Kiewiet develop a model that proceeds from ‘explicitly stated assumptions’, they not only improve on prior, largely inductive research, but also establish the ‘agreed-upon premises for all subsequent arguments’ (Morton, 1999, pp. 36–7).
The curious thing is that, having chosen Banks and Kiewiet to exemplify the virtues of formal rational choice models, Morton herself tacitly but quite thoroughly undermines our confidence in the explicitness thesis (Morton, 1999, pp. 36–8). She first lists ‘some of the assumptions’ that Banks and Kiewiet make:
that there are three possible candidates (an incumbent and two challengers);
that the candidates are motivated by the prospects of electoral success rather than policy preferences;
that the incumbent (credibly) aspires to only one more term in office and, if she wins it, will then retire;
that the challengers face a dynamic strategic problem — at t1 each must decide whether to enter a primary to select the candidate to run against the incumbent and at t2 each must decide whether to enter a primary race for the open seat the incumbent will have vacated;
that the challengers can run in only one general election and that if either wins the primary at t1 and then defeats the incumbent, the other will not challenge at t2.
This indeed is only a partial list of the assumptions in the Banks/Kiewiet model. Morton concedes that several of them are unrealistic, that they may be ‘either unverified or false’ and that Banks and Kiewiet might well have deployed a different model based on alternative assumptions. None of that, from my perspective, is either surprising or terribly problematic.
The real trouble is that, despite the fact that she selected this paper as an exemplar of how PPT trades on explicitly stated assumptions, Morton herself does not seem entirely clear on why Banks and Kiewiet proceed as they do. After listing the assumptions in their model, Morton states: ‘I suspect that Banks and Kiewiet assume three candidates in order to …’ and ‘I also surmise that Banks and Kiewiet assume that candidates maximize the probability of winning in order to (p. 37, emphases added). 14 If clarity and precision in PPT reflect the rigorous, explicit formulation and defense of assumptions, why is Morton left supposing and speculating? And if even an accomplished and sympathetic reader such as Morton remains unclear about what motivates the very authors whose essay she herself uses to illustrate the virtues of formalization, why ought we to expect that others, less adept at, or less charitably disposed toward, formal modeling will find the enterprise as clear and precise and rigorous as advocates of PPT proclaim?
This predicament reflects the ill-founded character of the explicitness thesis. The modern positivists from whom advocates of PPT derive their brand name were preoccupied with formalizing the scientific enterprise and conceived of formal constructs as ‘un-interpreted’. Positivism is unpersuasive generally and with respect to social sciences in particular. There is no need to rehearse the reasons here. 15 Nor is there any reason to chastise advocates of PPT for failing to implement faithfully the positivist program. It is by no means clear that they could do so if they wanted to. The important thing to see is that advocates of PPT still presume that the move from ‘non-formal’ to ‘formal’ representations magically banishes (or at least radically mitigates) the ambiguity and imprecision that purportedly characterize merely verbal formulations. This should be apparent from the discussion thus far. The point nevertheless bears emphasis.
Morton draws the distinction between ‘non-formal’ and ‘formal’ models in the following way:
Non-formal model — a set of verbal statements about the real world. These statements involve idealization, identification and approximation, but are given in terms of real observables rather than symbols or abstracts. The statements may be presented in a diagram or a graph. Sometimes these statements are directly tested as hypotheses about the real world.
Formal model — a set of precise abstract assumptions or axioms about the real world presented in symbolic terms that are solved to derive predictions about the real world (Morton, 1999, p. 61). 16
Morton actually discusses this basic distinction at considerable length (Morton, 1999, pp. 33–49). She makes it clear that, like most proponents of PPT, she believes that formalization not only confers a sort of clarity, precision and rigor unavailable to verbal formulations in particular instances, but that it is necessary to scientific progress more generally. It is also clear that this distinction and the virtues she attributes to formalization faintly echo the aspirations of modern positivism. Yet the echo is quite weak. In practice, advocates of PPT depart significantly from positivist impulses just in so far as the formal apparatus they deploy is hardly un-interpreted in anything like the positivist sense.
Proponents of PPT typically have little to say about the task of interpreting formal models. In practice they reduce this task to the evaluation of results or, sometimes, of assumptions, where evaluation specifically means empirical evaluation (Gates and Humes, 1997, p. 12; Krehbiel, 1998, p. 21; Morton, 1999, p. 102). And they treat this as a fairly unproblematic, if quite important, process which involves supplying verbal ‘embellishment’ that facilitates translation of the predictions of a model into hypotheses that might be empirically tested (Shepsle and Bonchek, 1997, p. 11). I return to the unexamined assumption that grounds this preoccupation — namely, that game-theoretic models actually are in any plausible sense directly empirical — in the next section. For present purposes I focus instead on how the need for interpretation enters into PPT in ways that many advocates of the enterprise neglect. This, in turn, allows us to question whether they can draw a sharp distinction between ‘formal’ and ‘non-formal’ models in anything like the categorical way Morton purports to do.
The problem is that ‘formal’ models necessarily come pre-interpreted. This is obvious when we consider the various toy games discussed in elementary expositions of game theory — ‘chicken’, ‘battle of the sexes’, ‘prisoner's dilemma’ and so forth — each of which is animated by a stock narrative (Norton, 2004, p. 124). 17 Advocates of PPT no doubt will dismiss observations regarding such off-the-shelf examples as of dubious merit. So consider again the Banks/Kiewiet model. As will become clear in the next section when I discuss it in detail, we encounter there a whole raft of political concepts — ‘candidate’, ‘running for office’ (as opposed to, say, standing for a seat), ‘general election’ and ‘primary’, ‘open seat’, ‘incumbent’ and ‘challenger’ (including both ‘strong’ and ‘weak’ types of the latter), ‘winning’, ‘deterrence’ and so forth — all stated verbally. These concepts shed none of their pedestrian meanings or everyday ‘imprecision’ in the model. Yet crucially they provide the very terms within which, unavoidably, Banks and Kiewiet are able to stipulate the components of their model. Here, in other words, as in the process of constructing models generally, everyday language sustains the ‘substantive interpretations’ we ascribe to the abstract parts of the model (Ordeshook, 1986, p. 9). Absent such interpretations, the model remains quite literally meaningless.
Advocates of PPT may not be overly troubled by this observation. But this is an instance of a much broader point which ultimately deflates their exaggerated claims to precision, clarity and rigor. For it simply is not enough to specify abstract sets of actors, their goals and preferences, the actions available to them and possible outcomes as components of a model. As Rubinstein suggests, in constructing and solving a game-theoretic model we are necessarily concerned with, and solely with, what the players deem ‘relevant’. A model thus must aim not just to represent the ‘physical rules of the game’ but to capture ‘the relevant factors of the situation as perceived by the players’ (Rubinstein, 1991, p. 917). 18 In other words, the concept of rationality remains ill-defined outside particular contexts of action as the agents inhabiting our models see and understand those contexts. 19 In constructing a model of some situation, then, we cannot assume rationality largely because we do not know what it might mean in the abstract; that is, outside some situation. The task of modeling strategic interaction, therefore, is more complex than even Morgenstern, for instance, lets on. This is so just in so far as what counts as the ‘situation’ cannot be specified independently of the understandings that we can plausibly attribute to the agents who populate our models. The implications of this general point emerge when we turn to the deduction thesis.
Before proceeding, however, it will be useful to enter an important caveat. Advocates of PPT proceed as though articulating the rationality assumption requires nothing more of them than being able to specify a preference ordering or utility function for the agents who populate their models (e.g. Austen-Smith and Banks, 1998, pp. 263–4; Doron and Sened, 2001, pp. 20–2; McCarty and Meirowitz, 2007; Riker, 1990, p. 172). Such formalizations, however, are merely modeling devices. They afford convenient ways of representing the beliefs and desires that constitute reasons for intentional agents. In other words the formal apparatus used to specify a preference ordering or utility function provides a technology for modeling unobservable features of agents. And while they do incorporate familiar criteria of consistency (such as completeness and transitivity) which capture the common-sense conception of rationality I mentioned at the outset, they say little if anything about what counts as consistency in any particular setting. The tools laid out in the opening chapters of standard game-theoretic texts provide us with a technology for talking about what rationality might mean and no more. They simply allow us to ask ‘what “rational” can mean’.
Questioning the Deduction Thesis
Advocates of PPT speak regularly about the rationality assumption as though it were well defined in some abstract sense. Consider, for instance, the following, wholly unsystematic sampling of remarks.
Game theory … requires the assumption of rationality (Morrow, 1994, p. 7).
Much of political game theory is predicated on the idea that people pursue goals subject to constraints imposed by physical resources and the expected behavior of other actors. The assumption of rationality is often controversial. Indeed one of the most lively debates in the social sciences is the role of rationality and intentionality as a predictor of behavior (McCarty and Meirowitz, 2007, p. 6).
Recall the two basic assumptions of game theory: rationality (utility maximization) and common knowledge (Gates and Humes, 1997, p. 12n).
The rationality assumption has been used most extensively and has seen its fullest flowering in economics. But there is nothing distinctly economic about rational behavior, as we shall see (Shepsle and Bonchek, 1997, p. 15).
Perhaps the most serious intellectual threat to the rational choice approach comes from empirical findings that challenge the rationality assumption (Lohmann, 1995, p. 128).
Of course, this challenge to rational choice theories only makes sense if individual theoretical statements, such as the rational actor assumption, can be tested in a meaningful sense (Diermeier, 1995, p. 62).
Rational choice theory is based on two central assumptions: methodological individualism and purposeful action … Purposeful action requires further clarification because it lies at the heart of the rationality assumption on which this entire research program is founded (Doron and Sened, 2001, pp. 20–1).
On the canonical PPT interpretation, when we construct game-theoretic models we start from an assumption of rationality which, in combination with various subsidiary assumptions, allows us to deduce predictions that we, in turn, treat as hypotheses about the ‘real world’. 20 The latter can be (and, at least in principle, are) tested empirically.
Here proponents of PPT proceed from a crucial, unexamined and indefensible assumption. They proceed as though empirical performance is the primary, perhaps the sole, criterion for assessing social science. Philosophers of science, of course, have for some time rightly argued that this basic premise is mistaken. They remind us, quite plausibly, that assessments of sciences and how they advance are ‘multidimensional’ in the sense that when making any such assessment we must concern ourselves not simply with empirical performance but also, for instance, with the resolution of conceptual problems and the development and refinement of instruments (Hacking, 1983; Hausman, 1992; Kitcher, 1993, pp. 90–126; Laudan, 1977; 1981; 1984). Advocates of PPT who, like practicing social scientists generally, tend to be philosophically disinclined, might complain that proponents of this revisionist view disagree among themselves. So what? We need neither adjudicate those disagreements nor remedy all of the difficulties with any particular philosophical position to appreciate the basic point that what political scientists commonly and naïvely call ‘the accumulation of empirical knowledge’ is a woefully inadequate basis on which to describe or assess social scientific progress (Johnson, 2002; 2003; 2006).
Proponents of PPT — and their critics — proceed undeterred. It is fair to say that the entire discussion of rational choice models in political science has been framed as an epistemological debate between realism and instrumentalism (MacDonald, 2003). 21 As a result, that discussion focuses almost exclusively on matters of empirical performance with realists preoccupied with the empirical adequacy of assumptions and instrumentalists with the empirical adequacy of predictions. 22 This dichotomous framework truncates debate by encouraging the discipline to neglect views of science — and how we ought to assess it — that cut across the realist—instrumentalist divide. Pragmatists, for instance, are realist about theoretical entities and instrumentalist in so far as they see theories as tools for solving both empirical and conceptual problems (Laudan, 1981). Pragmatism thus provides a framework for interpreting the modeling enterprise less as the deduction of claims for empirical testing than as a sort of conceptual analysis (Hausman, 1992, pp. 78–82). 23 Rather than present an abstract theoretical argument for this possibility I will instead illustrate it.
Consider the Banks/Kiewiet model yet again. This model does not — Morton's claims to the contrary notwithstanding — assume rationality and deduce predictions from that assumption. 24 Instead, Banks and Kiewiet ask what it can mean to be rational in a quite specific and seemingly not terribly conducive strategic circumstance. They provide an answer and, counter-intuitively, establish the sufficient conditions under which what appears to be a perplexing (because seemingly irrational) pattern of observed political behavior can actually be shown to be rational in just that sense. In other words, Banks and Kiewiet rationalize the political behavior in question. 25 In so doing they extend the domain over which our common-sense conception of strategic rationality plausibly offers explanatory leverage. The conclusion of their modeling exercise, in other words, is not a prediction. Instead, their results warrant greater confidence in our ability to invoke particular causal mechanisms when we offer explanations.
Advocates of PPT may well find this re-interpretation of the Banks/Kiewiet model wrong-headed. It may therefore be helpful to sketch how I read the paper. Banks and Kiewiet start from a set of empirical observations which suggest what they consider a ‘puzzling’ pattern of electoral competition (Banks and Kiewiet, 1989, p. 1000). In races for seats in the US Congress, incumbent legislators tend to encounter relatively weak challengers even in circumstances where stronger challengers are available. 26 Two features of this pattern are important. First, strong challengers are more likely to wait until an incumbent legislator retires from office and run for an ‘open’ seat rather than challenge the incumbent directly. Second, weak challengers are more likely to run against the sitting legislator despite the quite significant and fairly well-recognized electoral advantages that incumbency bestows. While the first of these features might seem unproblematic, the second is difficult to fathom. Prior research had ascribed this propensity of weak challengers to mount seemingly quixotic campaigns to a variety of irrational or non-rational factors such as partisan duty, expressive motivations, wishful thinking and so forth.
Banks and Kiewiet find such accounts wanting. They are right to do so. It is only possible to characterize the behavior of some group of agents as irrational or extra-rational against the background of some notion of what would constitute rational behavior on their part. At bottom, Banks and Kiewiet are trying to establish that background. They ask what it would mean for challengers — whether weak or strong — to act rationally in the particular context of candidate entry in US Congressional elections. They answer that it would be rational for a challenger of either sort to act in such a way as to maximize his or her probability of electoral success and they build a relatively simple game-theoretic model that establishes sufficient conditions under which the apparently perplexing pattern observed in empirical studies constitutes a Nash equilibrium. 27 As Banks and Kiewiet put it, they ‘show … that under certain circumstances weak challengers making accurate, unbiased probability estimates will choose to run against incumbents for the same reason strong challengers decide to wait for an open seat — to maximize the probability of their being elected to Congress' (Banks and Kiewiet, 1989, p. 1002).
The reasoning runs roughly as follows. Although the probability of defeating an incumbent legislator in a general election is very low, for a weak challenger it is higher than the probability of defeating any one of several possible strong competitors in a primary election that would decide his or her party's nominee for a general election. By contrast, for a strong challenger the probability of winning a primary, even against other strong competitors, and of then beating a non-incumbent from the other party, is greater than that of defeating an incumbent legislator, assuming that the latter is not unusually vulnerable for some idiosyncratic reason (e.g. scandal). In short, what Banks and Kiewiet do is establish the relevance of competition in the primary as opposed to the general election for the decision making of both weak and strong challengers. They specify the context within which potential challengers, weak and strong, reach a decision regarding whether or not to mount a campaign. The mathematics of their argument derives whatever cogency we attribute to it from this initial interpretive shift, not from the trivial ‘assumption’ that the actors who populate their models are utility maximizing.
Three things are important here. First, what Banks and Kiewiet are doing is specifying the basic mechanism used in making a rational choice explanation. They are telling us, in Morgenstern's phrase, ‘what “rational” can mean’ in a particular situation and, importantly, identifying the conditions under which their conception holds. This is a conceptual task which, while essential to rational choice explanation, is not directly empirical. 28 Second, the Banks/Kiewiet model is not idiosyncratic. It exemplifies the general pattern spelled out in texts on the use of game theory in political science. According to that template, when constructing a model we specify a set of actors, a set of available strategies and the conditions under which strategy combinations will generate equilibrium outcomes. 29 Finally, the model that Banks and Kiewiet construct and the use to which they put it departs significantly from the standard interpretation advocates of PPT offer for their own enterprise. What they offer is ‘an explanation for the paradoxical pattern of congressional election competition’ (Banks and Kiewiet, 1989, p. 1008) which, because it trades on a well-specified mechanism, allows them to expand somewhat the domain within which we might plausibly expect, provided specifiable conditions obtain, that mechanism to operate. In short, they are using game theory in precisely the modest sense that Kreps, in the passage I quoted at the outset, suggests.
One Obvious Objection
Those wedded to the standard PPT view of game theory might well find my reading of Banks and Kiewiet misguided. It is unlikely that they will deny that the Banks/Kiewiet model of candidate entry is meant to be explanatory. That would require them, for example, to ignore the aim Banks and Kiewiet explicitly announce in their title. They might well object, though, that the model of candidate entry presented in the paper is not just explanatory — in the sense of addressing the conceptual problem of specifying the causal mechanism animating an account of a perplexing pattern of behavior — but somehow directly empirical too. In other words, the orthodox might insist that Banks and Kiewiet do more than ‘merely’ specify how an unobservable mechanism (i.e. the beliefs and desires that constitute reasons for potential challengers in Congressional elections to act in one way or another) operates under certain conditions in a manner that previous accounts lead us not to anticipate. They might insist instead that Banks and Kiewiet derive a prediction about how rational candidates will behave and then test it. After all, the final third of the original paper is devoted to an ‘empirical examination of the model’ (Banks and Kiewiet, 1989, pp. 1008–3).
Morton indeed asserts not only that ‘Banks and Kiewiet restate their results in the form of empirical predictions’, but that they explicitly ‘devised’ their model to ‘to evaluate predictions or assumptions’ (Morton, 1999, p. 56, p. 57). She seems clearly to interpret their paper in terms of the standard schema of ‘build a formal model, derive hypotheses or predictions from it and test them empirically’. It is therefore important to ask whether this schema captures what Banks and Kiewiet are actually up to when they examine their model empirically. When we attend to that question it is plain that they are not engaged in the enterprise Morton believes them to be.
Banks and Kiewiet rightly indicate that their ‘model gives only the conditions under which it makes sense for weak candidates to challenge incumbents while the strong do not. Other conditions will dictate other strategies’ (Banks and Kiewiet, 1989, p. 1008). After acknowledging the difficult measurement issues involved in specifying what counts as ‘strong’ and ‘weak’, they turn to their first ‘empirical’ task. Importantly, this involves the evaluation neither of assumptions made in the construction of, nor of predictions derived from, their model. Banks and Kiewiet simply ask whether the conditions necessary for the results generated by their model to hold actually obtain. That is, they ask whether, given the perplexing pattern of behavior that initially prompted their inquiry, ‘weak candidates typically do face circumstances similar to’ those they capture in their model (Banks and Kiewiet, 1989, p. 1008). It is those conditions, those ‘circumstances’, that sustain the simple probability estimates that inform the decisions of potential challengers.
Banks and Kiewiet, in other words, are interested not in establishing whether their model is true or false, but in persuading us that it might be useful in thinking about the problem that troubles them in the first place. This is a crucial task. Banks and Kiewiet must establish whether and to what extent the conditions actually obtain under which the seemingly ‘irrational’ entry decisions of challengers can be characterized as Nash behavior. Otherwise, the explanatory mechanism they propose as an alternative to those that animate various accounts in the then extant literature would remain strictly speaking irrelevant. In the event, they are indeed persuasive on this point. While this is clearly crucial to their enterprise, however, it is just as clearly not an empirical ‘test’ of their model, its assumptions or its predications.
In the next component of their ‘empirical examination’, Banks and Kiewiet aim to determine whether strong and weak candidates ‘in fact’ behave the way the actors who populate their model behave (Banks and Kiewiet, 1989, pp. 1009–10). To this end, however, they do not derive and test a ‘prediction’ from their model. Instead they essentially re-establish with a new set of data the pattern of behavior — weak challengers entering against incumbents while strong challengers wait to run until the relevant seat is open — that puzzled students of political campaigns in the first place. This does not fall into any of the ‘four categories’ of prediction that Morton delineates because it is not a prediction in any obvious sense at all. 30 One does not ‘predict’ what one already knows in anything but the most trivial sense. 31 Surely any such ‘prediction’ in no way constitutes an empirical test of their model in the sense of providing evidence for or against it.
Finally, Banks and Kiewiet (1989, pp. 1012–3) invoke the underlying mechanism they identify with their model as a basis for exploring other features of their data set. In particular they suggest that the ‘rational choice’ mechanism they specify might afford a way of accounting for particular characteristics of ‘freshman’ classes in several Congresses. Maybe so. But in the first place, they do not offer much more than speculation on this matter. In the second place, this is not a prediction derived from their formal model. So if this is an ‘empirical implication’ of the Banks/Kiewiet model, it would be helpful to have some account of the sense in which that is the case. On the PPT interpretation we lack such an account and, arguably, the theoretical resources from which we might construct one. By contrast, on the interpretation I have advanced, what Banks and Kiewiet have done is to show how the mechanism they explore might prove useful in explaining a related empirical phenomenon.
In short, what Banks and Kiewiet refer to as the ‘empirical examination’ of their model in no way conforms to the orthodox schema of ‘formulate a model — derive predictions from it — test those predictions' that is central to the interpretation of game theory that advocates of PPT embrace. Contrary to their own claim, Banks and Kiewiet hardly offer a ‘critical test’ of ‘predictions’ derived from their model. Indeed, they do not actually offer a test of the model at all. While this represents a failure, on my view, of the orthodox PPT interpretation of game theory, it does not represent a failure of game-theoretic methods more generally. For as I noted at the outset, there is no particular reason to assume, as proponents (and critics) of PPT do, that game-theoretic models are amenable to empirical testing in the first place. That is an assumption that needs to be defended. And those who advocate the PPT interpretation of game-theoretic methods simply do not provide such a defense.
Conclusion
Rubinstein is right. A ‘proper interpretation’ is central to the use and assessment of game theory. I have argued that the PPT interpretation of game-theoretic models widely accepted among political scientists is unpersuasive. I hope that the nature of my argument is clear. I am not offering an empirical survey and analysis of the ways political scientists have incorporated game-theoretic methods into their work. I have not canvassed a sample of studies that incorporate models. 32 Instead, I have criticized the most common — I would say orthodox — interpretation of how we should understand the use of game-theoretic models in the discipline. I have focused on Morton's arguments because she offers the most sustained recent case for embracing that interpretation. I have suggested that neither the explicitness thesis nor the deduction thesis — both of which are central to the PPT interpretation — apply to the example that Morton herself advances as paradigmatic of the virtues of formal theory generally and game-theoretic modeling in particular. And I have gestured toward a substantially different way of understanding the point of using game-theoretic models.
I hardly anticipate that advocates of PPT will find my argument persuasive. They may want to distance themselves from the PPT interpretation of game theory. Alternatively, they might simply want to distance themselves from the particular way that Morton articulates and illustrates that interpretation. 33 In either case, the challenge they confront is to offer an alternative interpretation not just of this or that component of this or that model (crucial as that task is), but an interpretation of game-theoretic modeling as an intellectual enterprise. 34 Fortunately, in recent years a number of younger researchers have undertaken that task. 35 Unfortunately, I find no evidence that the orthodox have in any way directly addressed their concerns. Such dismissiveness, however, ignores Rubinstein's challenge. The mathematical apparatus of game theory stands in need of interpretation. Otherwise, game-theoretic methods rest on shifting sands.
Obviously, I have not offered a full-blown interpretation of game theory and the ways in which political scientists can and should use it. 36 I was clear about that at the outset. In so far as they operate in the way I propose, game-theoretic models allow us to make conceptual progress in a fairly simple and unproblematic way. They provide us with tools for specifying how our common-sense conception of rationality operates as an explanatory mechanism and for identifying the conditions under which we can expect it to operate reliably. 37 The methodological lesson here is that we might move in the direction of generality without embracing the idea that we can specify covering laws. Advocates of PPT tend to assume that we can and ought to pursue the latter (Riker, 1990). Yet the quest for generalizations need not follow that pattern (Little, 1993). Nor need a preoccupation with causal mechanisms induce skepticism about generalization due to the difficulty of specifying the conditions under which they operate in expected ways. Game-theoretic models are useful in part because they afford an example of how we might avoid such skepticism.
That said, we — and this includes advocates of PPT — cannot ‘assume’ rationality because in many situations we do not know what rationality might consist in. Robert Nozick (1993, pp. 133–5) rightly points out that the common-sense concept of instrumental rationality occupies the intersection of nearly all more expansive conceptions of rationality. He also points out that even though this means that when we discuss rationality we must have in mind at least the common-sense understanding, we have thereby made scant progress. This is because our more particular conceptions of rationality and our broader understandings of the world, the possibilities it offers and of ourselves are thoroughly interdependent. Game theory is useful for helping us explore that interdependence. And that is useful enough to allow us to set to one side the misguided claims bandied about by advocates of positive political theory.
Footnotes
I presented earlier iterations of this article at a ‘Workshop: Dialogue and Innovation in Contemporary Political Science’, co-hosted by Political Studies and The Centre for Research Methods in the Social Sciences, Oxford University, June 2008; as part of the Blalock Lectures on Advanced Topics in Social Research; ICPSR Summer Program — University of Michigan, August 2005; and at a conference on ‘Epistemologies of Rational Choice’, Department of Politics, New York University, December 2004. I thank Susan Orr for her skeptical comments on this version.
1
2
This view, while not commonly endorsed, is not wholly idiosyncratic either. Hence after discussing the assumption that actors in game-theoretic models have complete, transitive preferences, the author of one primer suggests: ‘These assumptions, though, are preliminary and do not define what we mean by rational action. With them alone we cannot yet say what actions or strategies a person should choose in an interdependent-choice environment. Thus, because game theory's ultimate purpose is to formulate general rules of action in such choice situations, game theory does not assume that people are rational; rather, it attempts to define what we might mean by this concept. Put differently, game theory seeks to identify the decisions that people might reasonably be expected to make in interactive decision-making situations, and these decisions correspond to what we mean by rational action’ (Ordeshook, 1992, p. 61, emphasis added).
3
This is a possibility typically neglected in putatively methodological discussions: ‘few writers on economic methodology recognize that the activities of formulating economic models and investigating their implications are a sort of conceptual exploration. Instead, most mistakenly regard these activities as offering empirical hypotheses and assess them in terms of some philosophical model of confirmation or falsification’ (Hausman, 1989, p. 115).
4
This is not uniformly the case. It is hard, for example, to take umbrage at this pronouncement: ‘Positive political theory is concerned with understanding political phenomena through the use of analytical models which, it is hoped, lend insight into why outcomes look the way they do and not some other way’ (Austen-Smith and Banks, 1998, p. 259). Yet while this statement is modest enough, the authors remain wholly agnostic about the matters I take up in this article.
5
Compare De Marchi (2005) and 
, both of which are introductions to agent-based or complex systems models. Neither is a textbook in the same sense as those I have cited in the text.
6
Game theory is, on my view, simply one ‘family of models’ among others collected together under a name ‘appropriated for dramatic effect’ (Schelling, 1978, pp. 87–102). And, of course, one might argue that a theory is nothing but a collection of models (Clarke and Primo, 2007). While I am skeptical of that claim, I set it aside for present purposes.
7
It informs recent notorious criticism of the enterprise (Green and Shapiro, 1994). It also informs nearly all replies to that criticism by advocates of PPT (e.g. Cox, 1999; Diermeier, 1995; Lohmann, 1995). Likewise, it inspires the current enthusiasm for the empirical testing of formal models generally (Cameron and Morton, 2002; Morton, 1999) and for the well-funded initiative on the ‘empirical implications of theoretical models’ in particular (Aldrich and Alt, 2003; Granato and Scioli, 2004). For a partial, not entirely satisfactory dissent from both the critics of game theory in political science and the standard pattern of defense, see .
8
Hence, even , p. 27) who goes to great — indeed, I think quite excessive and misguided — lengths to establish that central claims of positive political theory are not supported empirically, concedes: ‘I cannot imagine doing without noncooperative game theory, which in the right hands yields rich insights into social life, along with testable, and supported, predictions’.
9
This contrast sometimes comes packaged as a thumbnail teleology in which PPT emerges as the pinnacle of political inquiry. Thus in their undergraduate primer on PPT, Shepsle and Bonchek (1997, pp. 5–8) relate an inspiring tale of how post-Second World War political science freed itself from the limitations of ‘story telling’ and ‘normative hand wringing’ in order to produce ‘scholarly tomes’ inspired by ‘reformist sentiments’ and packed with ‘detailed contemporary description and political history’. Then, based on more systematic description and quantification, the discipline was ready for theory. Compare Morton, 1999, pp. 13–22; Cameron and Morton, 2002, p. 797.
10
The entanglement is fairly clear in the passages I cite in the text. Consider another couple of examples: ‘Formal theories … tend to be explicit, they are cumulative in many respects, and often they generate plausible and testable propositions about observable political phenomena’ (Krehbiel, 1998, p. 18). Likewise: ‘A nonformal model becomes a formal model when a researcher expresses the real world situation in abstract and symbolic terms in a set of explicitly stated assumptions … Formal models have explicitly stated assumptions about reality which are used to derive predictions about reality. Formal models are deductive, because conclusions proceed from assumptions’ (Morton, 1999, pp. 36–7). Compare Cameron and Morton, 2002, pp. 793–4.
11
I want to forestall an objection here. I am not worried that assumptions are not ‘true’ or that modelers make no effort to establish whether they are or are not. In other words, I am sidestepping the realism—instrumentalism dichotomy into which most critical discussion of modeling rapidly falls (e.g. MacDonald, 2003). I merely note that practitioners of PPT often skip the important interpretive step of motivating this or that assumption in the quite banal sense of explaining why they are making it.
12
‘One source of puzzlement among formal modelers is the belief by some in political science that non-formal models make less restrictive assumptions than formal models and that, because of this, non-formal models have advantages over formal models in empirical study. Imprecision is argued to have an advantage over precision because ambiguity is assumed to be more general and flexible than exactness’ (Morton, 1999, p. 41). For another version of this complaint, stated even less charitably, see Cameron and Morton (2002, p. 794). Although I have never met one, I will take Morton's word for it that there are political scientists who affirm, either explicitly or as an ‘unstated assumption’, the value of imprecision and ambiguity. Observe, though, that the authors whom she invokes to illustrate her point at no point sing the praises of ‘imprecision and ambiguity’. In fact, I suspect that most critics of PPT simply challenge whether formal theory somehow has the sort of monopoly on clarity, precision and rigor that its advocates regularly claim. Their point, I suspect, is not to endorse imprecision but to ask what it means to be precise. See, for instance, Norton, 2004.
13
On several occasions one of my colleagues has protested that this is a paper that the authors themselves would not consider their best work. As a matter of both biographical fact and independent assessment that may well be so. But it is strictly speaking beside the point here. I focus on this paper because Morton presents it as an exemplar of how formal models help illuminate seemingly perplexing aspects of politics. It therefore allows me to assume the burden of argument. The choice of example, in other words, is hers, not mine.
14
This is not a minor concern. The second of these assumptions turns out to be conventional among practitioners of PPT. That does not make it innocent. For instance, in an otherwise quite laudatory review of Austen-Smith and Banks (2005), makes clear how much rides on it. In this instance one might have ‘surmised’ that Banks and Kiewiet adopted this assumption because it sharpened the contrast with the non-electoral motivations postulated in the extant literature. This, at least in part, seems to be Morton's guess.
15
See, for example, Hausman, 1992, pp. 70–82, pp. 283–5, pp. 297–8; Walsh, 1987. See also on the dire consequences of positivism for common understandings of political inquiry.
16
One wonders what rhetorical effect Morton hopes to sustain by drawing this distinction as she does. Rather than simply differentiating verbal from mathematical or formal, she assimilates the former to the ‘non-formal’ and thereby tacitly depicts it as derivative or subsidiary, as ‘non’. I set this matter aside here. It is nevertheless useful to compare Morton's discussion of models and their uses with another view. Thomas Schelling, for instance, suggests that a model consists in ‘a precise and economical statement of a set of relationships that are sufficient to produce the phenomenon in question’ and that a model is a ‘tool’ that affords ‘help in communicating’ (Schelling, 1978, p. 87, p. 90). Likewise, Kreps asserts: ‘The great successes of game theory in economics have arisen in large measure because game theory gives us a language for modeling and techniques for analyzing specific dynamic competitive interactions’ (Kreps, 1990, p. 41, emphasis shifted). For a philosophical account compatible with these views see , pp. 70–82).
17
In delineating what he sees as ‘the successes of game theory’, Kreps (1990, pp. 37–90) not only starts by invoking such simple games, but proceeds to animate the rest of his discussion with a ‘story’ (a word he uses repeatedly) about entry and deterrence in a restricted market. This is not a shortcoming. As Schelling notes in the same passage I cited in Note 16, a model is useful for facilitating communication ‘especially if the model has a name’. And even more pointedly, Myerson (2004, p. 102) asserts: ‘Mathematical models in the social sciences are like fables or myths that we read to get insights into the social world in which we live’. On this point, compare who portrays game theorists as ‘tellers of fables’ who, like all such tellers of tales, do so for a purpose.
18
‘The single most important decision in modeling is the design of the game. The game states what choices we believe the actors see in the situation, what they understand about their choices, what consequences they believe follow from their decisions, and how they evaluate those consequences’ (Morrow, 1994, p. 57). Compare, surprisingly enough, Riker (1990, pp. 172–3). I take it that this, at least in part, is what , p. 4) means when he insists that the players who populate game-theoretic models are not just rational but ‘intelligent’ as well. This, of course, raises the issue, which I set aside here, of how to understand ‘see’ or ‘perceive’.
19
There are various ways to support this claim. See Schelling, 1960; Nozick, 1993; Sen, 2002.
20
Using game-theoretic technology does not entail a commitment to the canonical rational choice approach. See, for instance, Camerer, 2003; Rubinstein, 1998.
21
For examples of how these positions inform debate see Elster (1986); Hausman (1995); Satz and Ferejohn (1994). offer a promising recent effort to set this unhelpful dichotomy aside.
22
Prompting Morton, for instance, to address both sorts of concern in her discussion of the fundamentals of empirical evaluation (Morton, 1999, pp. 101–277).
23
Morton acknowledges that not all formal models are empirical. Some, like Arrow's theorem, are normative. Others, like the Rubinstein bargaining model, are exercises in ‘pure theory’ and so explicitly not designed to be empirically evaluated. See Morton, 1999, pp. 79–80, pp. 59–61. At least three disquieting questions arise here. First, are the normative concepts (embodied in his axioms) that Arrow explores part of the ‘real world’ or not? Second, if ‘pure theory’ is not aimed at empirical inquiry, of what use is it? Finally, what does this concession mean in terms of the fact that, as I noted earlier in the text, Morton defines formal theory in terms of models that ‘are solved to derive predictions about the real world?’ By so doing she unjustifiably truncates the set of purposes for which we might use models. I suspect that the answers to such questions push us in the direction of interpreting all models — applied as well as pure, explanatory as well as normative — as conceptual exercises.
24
Morton can be forgiven for this misinterpretation given that Banks and Kiewiet themselves claim that their model is susceptible to ‘empirical examination’ precisely because it enables them to ‘make predictions about candidate behavior’ (Banks and Kiewiet, 1989, p. 105).
25
‘What is the relation between a reason and an action when the reason explains the action by giving the agent's reason for doing what he did? We may call such explanations rationalizations, and say the reason rationalizes the action’ (Davidson, 1980, p. 4). For current purposes, this notion of intentional explanation trades on the underlying view that canonical game-theoretic models invoke desires (preferences) and beliefs (expectations) in an unavoidable way (Cox, 2004; Elster, 1986). This is perhaps a bit strong. Game theorists can depart from that underlying view at a cost — namely, abandoning the Nash program (Hausman, 2000).
26
Banks and Kiewiet differentiate ‘weak’ and ‘strong’ candidates in terms of their past political experience, in particular whether the potential candidate has held prior elected office.
27
These conditions — specified for different actors in the model both in terms of the probability that he or she might prevail in some election and the utility he or she would derive from various electoral outcomes — emerge as results of Banks and Kiewiet's model. They are not assumptions of the model. Rather they are meant to capture the circumstances under which the seemingly inexplicable entry decisions of actors might constitute Nash behavior. Likewise, they are not predictions of the model. They do not represent a characterization of the anticipated behavior of actors in the model. Instead, they specify the anticipated consequences for different actors of adopting one strategy or another. Presumably each actor's reasons for acting will consist primarily of an assessment of these consequences. These distinctions become important when we turn to the ‘empirical examination’ Banks and Kiewiet conduct of their model.
28
Here I assume without argument that rationalizations are explanations and that they are causal. This is in keeping with the claim that game theory contributes to causal explanation (Ordeshook, 1986, p. xiii). I argue elsewhere that the task of specifying mechanisms is crucial to explanation (Johnson, 2006).
30
Morton (1999, p. 102) identifies the following four sorts of prediction that might be derived from a formal model: ‘Point or equilibrium predictions; multi- or disequilibrium predictions; comparative static predictions; process or dynamic path predictions’. The differences between these are irrelevant for present purposes.
31
‘Note that a prediction is any testable implication. It need not be about the future and it may already be known’ (Hausman, 1992, p. 304).
33
It should go without saying that while I find Morton's exposition of the canonical PPT interpretation of game theory unpersuasive, it remains the most ambitious and systematic account on offer. When, as has regularly happened, proponents of PPT defend their work by trying to distance themselves from her account I simply point out that the burden thus falls on them to improve upon it. To date no-one has undertaken that task.
34
For examples of this sort of enterprise see Kreps (1990); .
35
See MacDonald, 2003; Lovett; 2006; Clarke and Primo, 2007.
36
I have said nothing, for instance, about the claim that game theory is most useful for purposes of normative assessment (e.g. Myerson, 1999).
37
Here an analogy might help. Case studies are useful, in part, because they exploit relatively ‘thick’ descriptions of events in order to specify explanatory mechanisms and explore how they operate. On this point see Johnson (2006). Likewise, formal models use what we might call 'thin descriptions' to do the same thing. This analogy is not terribly contentious; it is how I understand Schelling's brief for using models (Schelling, 1978, pp. 87–91).