Modeling the World. Speakers & Abstracts |
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Maximizing, Satisficing, and Entrenchment Maximizing and satisficing have been seen as competing theories of human decision making, and more recently of evolutionary change. Entrenchment or "lock in" has been advanced also in criticism of the traditional maximization models. These have been treated each as universally applicable theories. I want to argue that these are better seen as context-sensitive local approximations that can be articulated into a larger framework giving a more plausible picture of the actions of all three. The picture I seek begins with A. J. Lotka's picture of "moving equilibria", in which a process nearly at equilibrium (and with strong equilibrating tendencies—short relaxation times) changes its equilibrium point due to parameter changes in other processes on longer time scales the change the equilibrium set point. If the parameter changes are not those of a continuous variable, but of a stochastic process which makes changes of different sizes in the set point, we arrive at a picture like that for mutation-selection balance-driven evolution or technological or institutional change, in which rarer larger changes initiate adapting smaller changes on shorter time scales. This system is equilibrating, but rarely in equilibrium, and is nicely illusrated by the dynamics of a Monte-carlo simulation of the action of generative entrenchment in a multi-locus system. This simulation also provides a lovely example of the dynamics of near-decomposability in the sense of Herbert Simon. Though Simon never discussed entrenchment as one of the factors interacting with satisficing, I believe that the overall picture is in many other respects like that he envisioned for evolutionary processes. Entrenchment comes in through the local coadaptation of shorter-term modifiers to adapt to the presence or occurrence of larger-effect mutations. Entrenchment ends up defining the constraints within which the shorter-term processes optimize. They can also, if sufficiently entrenched come to define a kind of canonical situation that is taken as paradigmatic for systems of a given kind.
Evolutionary Models and Cultural Change Many people have argued that cultural change is, or is sometimes, a Darwinian process. Many others have denied it. I assess this idea from the point of view of the methodology of model-building. Some mechanisms of social learning give rise to a Darwinian pattern of change at the level of ideas or behaviors, and others do not. The ones that clearly do, and the ones that clearly do not, are idealizations of actual human psychology. Which idealizations in this area might be closer to the truth? Might the ones which are not so close to the truth have other benefits from a modeler's point of view?
Three-Sex Mating (and other models without targets) Fisher wrote that “No practical biologist interested in sexual reproduction would be led to work out the detailed consequences experienced by organisms having three or more sexes.'' Indeed, paradigm cases of modeling involve the indirect theoretical investigation of *real world* phenomena, or target-directed modeling. While this practice is certainly the standard case, all that a theoretical activity requires to be called modeling is the construction and analysis of a model. Theoretically important models can be constructed independently of any target at all. Hence, practical or not, theorists may want to consider models of three or more sexes. Or as Fisher put it, “what else should he do if he wishes to understand why the sexes are, in fact, always two?'' Following Fisher's lead, targetless modeling and modeling non-specific targets is now common in theoretical biology. In this paper, I will analyze four instances of the practice: modeling contingently non-actual targets, modeling physically impossible targets, modeling generalized targets, and modeling without targets at all. Three-sex mating and xDNA will be used to illustrate how theorists model targets which they do not believe to exist. Mathematical models of infinite population growth and perpetual motion will illustrate the second category. Modern, individual-based models of predation and segregation will be used to illustrate how theorists model generalized targets. And, finally, I will discuss how classes of computational models such as cellular automata and genetic algorithms can be informative without a target at all.
Explanations in search of observations In my paper ‘Experiments as exhibits and experiments as tests’ (Journal of Economic Methodology, 2005), I discussed a methodological strategy that starts from exhibits (which might be described as observations in search of explanations). An opposite strategy is to start with a theoretical model and derive a conclusion about an effect which would occur under certain conditions; the suggestion is that, were such an effect found, the model would provide an explanation. If the relevant conditions are directly observable, this conclusion can be regarded as a testable hypothesis. But in many cases in economics, direct observation is infeasible (for example, when the conditions specify properties of preferences or beliefs). Thus, the model is used to support the conclusion ‘This effect *could* occur in the real world’ without any clear criterion for identifying the conditions under which it *will* occur. Hence the idea of ‘explanations in search of observations’. I will discuss examples of the use of this strategy in economics, and what seem to me to be corresponding examples in theoretical biology. (The difficulty of measuring fitness independently of selection may be the biological analogue of the difficulty of observing preferences and beliefs independently of the behaviour they induce.) I will ask whether this methodological strategy has a useful role in science. My provisional conclusion (which may change as I write the paper) is that the strategy *can* be useful, but it is liable to encourage an unhealthy separation between theory and empirical investigation, and it makes it difficult for any failures of the underlying theory to come to light.
Identity, Structure, and Causation in Economic Models Recent debates over the nature causation, casual inference, and the uses of causal models in counterfactual analysis, involving inter alia Nancy Cartwright (Hunting Causes and Using Them), James Woodward (Making Things Happen) and Judea Pearl (Causation) hinge on how causality is represented in models. The special demands of economics – particularly, the need to incorporate intentional and forward-looking behavior suggests an approach to causality in economic models that ultimately derives from early work of Herbert Simon and offers a more refined representation of causal relations that clarifies some of the recent debates. The paper develops the representation and uses it to evaluate the recent debates – particularly, with respect to the nature of causal structure, the identity of causes, causal independence, and modularity – and to account for the relationships among different approaches to causality.
Simple and complex models in population ecology - an ecologist's perspective Theoretical ecology was established as a discipline in the 1970s, though mathematical models had been sporadically applied to population ecological questions from the early part of the last century. The early influential models were simple and general, and theoreticians often developed models and concepts in parallel. A good example is models of deterministic chaos applied to temporal population fluctuations. Later on, the simple models and much of early theoretical ecology have been challenged on the grounds that they don’t lead to testable predictions. Nonetheless, one could argue that the most valuable models are simple ones that make interesting qualitative predictions. In the past decade, there has been a minor revolution in the application of statistical models that require much computing but which allow rigorous quantitative inference from empirical data. I illustrate various kinds of models and modeling approaches as employed by one practicing scientist (myself).
Truth and falsity in modeling In considering how scientists go about “modeling the world” an obvious notion to invoke is that of truth: scientists are successful in modeling the world when they build models that are true about the world. But models have a most uneasy connection with truth. Model users and commentators often refrain from claiming that a given model is true or has a great deal of truth in it. Among the reasons are that there appears to be too much falsehood in a model due to its idealizations or else that models are wrong sorts of creature to invite ascription of truth value at all. Many hold the view that models have a chance of becoming true only once their idealizing assumptions start being relaxed (see Wimsatt 2007). In resisting these ideas I employ what I call the functional decomposition approach to examining the issue of truth in relation to models conceived as isolations and surrogate systems (MISS) that are constrained both ontologically and pragmatically (for recent formulations, see Mäki 2008, 2009a, 2009b). The point of the approach is to decompose a model and the representations it is embedded in so as to determine what functions are served by the various components. This strategy enables locating the relevant truth bearers in modeling the world. It illuminaties the roles played by idealizing assumptions and their various paraphrases as parts of model descriptions and model commentaries. This helps to clarify the ways in which truth, tractability and other theoretical virtues are related (see Mäki 2000. Hindriks 2006, Weisberg 2006). Examples mainly from economics illustrate the suggestions of the paper. References Hindriks, Frank (2006) “Tractability assumptions and the Musgrave-Mäki typology”, Journal of Economic Methodology, 13, 401-423. Mäki, Uskali (2000) "Kinds of assumptions and their truth: Shaking an untwisted F-twist", Kyklos, 53, 303-322. Mäki, Uskali (2008) “Models and the locus of their truth”, to appear in Synthese Mäki, Uskali (2009b) “MISSing the world: Models as isolations and credible surrogate systems”, Erkenntnis 70, 29-43. Mäki, Uskali (2009a) “Models and truth. The functional decomposition approach”, to appear in European Philosophy of Science 2007, ed. M. Dorato, M. Réder, M. Suarez. Springer. Weisberg, Michael (2007) “Three kinds of idealization”, Journal of Philosophy, CIV: 639-659. Wimsatt, William (2007) Re-engineering philosophy for limited beings. Harvard University Press.
Natural Selection and the Moniac: the diverse relations between models and mechanisms In this paper, we argue that the recent debate over whether or not natural selection is a mechanism is largely fuelled by not clearly distinguishing mechanisms from mechanistic models, and by failing to analyse the variety of relations between them. The implications of this debate are important for the scope of mechanistic explanation more generally -- whether or not they apply to the social sciences, for example. To illustrate our argument, we compare the case of natural selection with that of the Moniac: a hydro-mechanical machine created by Bill Phillips in 1949 to model a working economy. The Moniac is clearly a mechanism, yet (like natural selection) what it models lacks many of the defining features of a mechanism. If the comparison is correct, the right thing to say about natural selection is that, whether or not it *is* a mechanism, it can still be usefully represented by a mechanistic model. What remains to be shown is how a mechanistic model can usefully represent something that is not (or not obviously) a mechanism. We enumerate a number of explanatory relationships between models and mechanisms, and briefly outline how this can be done.
Templates vs. Mechanisms? The Lotka-Volterra model reconsidered In a recent attempt to define the nature of modelling Michael Weisberg (2007) and Peter Godfrey-Smith (2006) have suggested that it could be distinguished from other forms of theorizing through the procedures of indirect representation and analysis. According to them the distinguishing feature of modelling is that modellers do not attempt to represent actual systems, but proceed instead by stipulating and studying other more simple hypothetical systems. Weisberg (2007) has explicated this theoretical detour through hypothetical model systems by comparing Vito Volterra’s style of theorizing, which he takes as an example of modelling, to abstract direct representation as exhibited by Dimitri Mendeleev’s Periodic Table. According to Weisberg, Volterra constructed his famous model by “imagining a simple biological system composed of one population of predators and one population of prey” boiling down to a couple of differential equations describing their mutual dynamics. As opposed to this Mendeleev was trying to abstract and identify the key factors of chemical behaviour from data. Much as we appreciate the insight into modelling the idea of indirect representation gives, we find Weisberg’s presentation of Lotka-Volterra model too stylised. Importantly, it does not capture how Volterra himself considered his modelling exercise. Although it may well be the case that what he eventually accomplished agrees rather well with Weisberg’s characterisation of it, looking more closely at Volterra’s opinions on modelling and especially contrasting them to those of Alfred Lotka shows how roughly the same model can be a result of different kinds of modelling strategies. Moreover, this paves the way for considering modelling through a different unit of analysis than the traditional representational focus on the model – target dyad. Whereas Weisberg has suggested expanding the unit of analysis to robustness analysis (e.g. Weisberg 2008), we suggest, instead, considering Lotka-Volterra model using the notion of computational template (Humphreys 2004). It refers to the computational methods and general formalisms that are used across the disciplines providing thus a key to the versatility of computational models as well as to the questions concerning their application to subject-specific domains. The historical trajectory of the Lotka-Volterra model exhibits both these dimensions of modelling already since its inception. For Volterra Newtonian mechanics functioned as an example of how to model biological processes. He aimed at isolating the essential/sufficient components of the predator and prey system and their interaction, distinguishing them from the secondary aspects and perturbations. This he expressed in his Inaugural address delivered at the opening of the academic year at the University of Rome in 1901 in the following way:
Interestingly enough, Volterra thought that economics provided an example of a science successfully shaped after mechanics. In economics the idea of theorizing/ modelling consisting of isolating the workings of some causal factors or mechanisms has lived since the nineteenth century to the present days (e.g. Cartwright 1989, Mäki 1992). Yet, as in the case of economics, the complexity of the biological systems makes the method of isolation difficult to follow as a general modelling heuristic. Thus Volterra had to revert to a hypothetical approach: Making assumptions of what are the essential components of the system and then comparing the predictions of the model with the data. This comes close to what Weisberg claims about modelling in general, but he leaves out Volterra’s reasons for proceeding that way. Moreover, Weisberg bypasses the very different approach to modelling by Lotka, who independently of Volterra arrived at a similar model a year earlier. As opposed to Volterra, Lotka thought that physics, especially statistical mechanics and thermodynamics, did not provide a suitable methodological and conceptual framework for studying biological systems. He started from a very general perspective and applied his model system both to the analysis of biological and chemical systems. Furthermore, his method of proceeding was his main motivation to introduce what he called the “Allgemeine Zustandslehre”, the general method/theory of states. The essential element of this method/theory was a set of differential equations, which describe the evolution of a system in time, being comprised of the interaction between the components of the system and its environment. The components, interactions, and environment had to be specified case by case. Indeed, Lotka’s approach provides a good example of making conscious use of computational templates in modelling. This was also a matter of disagreement between Lotka and Volterra in their subsequent correspondence, since Volterra did not approve of using the Lotka-Volterra model outside of population biology. Volterra’s and Lotka’s different approaches to modelling reveal, we suggest, a more general tension present in modelling: On the one hand the aim for generalizability and tractability, and on the other hand the idea that models should capture the basic mechanisms underlying the phenomena. Weisberg’s philosophically straightforward and neat account of modelling does not capture this tension. One reason for this might be that his account is still tied to the representational paradigm, although he conceives of models as (re)presenting imaginary systems instead of actual systems. Focusing thus on the imaginary entity set up by the model he loses sight of Lotka’s systems approach, which takes the formal features of very general system types to be primary. We claim that Volterra’s and Lotka’s approaches can in fact be seen as reciprocal to one another. Volterra started out in trying to identify what he took as essential components of the system of interest and then went on to generalize his model as he proceeded from the 2-dimensional case to the n-dimensional. Lotka, in turn, began with a general systems approach and on the basis of this general approach looked at specific systems. Consequently, it seems that both the aim of explaining the basic underlying mechanisms and the strive to develop and use general computational templates are simultaneously present in modelling. It is by no means clear that they are pointing at the same direction. This is apparent in the recent discussions on modelling practice in systems and synthetic biology, where identifying the specific mechanisms underlying basic biological functions is accompanied by the question of how general these mechanisms are, and how they fit into the “bigger” picture of spatial and temporal organization of biological systems. This shows that the tension between generalisation and exploring basic mechanisms is a central part of contemporary modelling practice and needs to be addressed in more detail. References Cartwright, N. (1989). Nature’s capacities and their measurement. Oxford: Clarendon Press. Godfrey-Smith, P. (2006). The Strategy of Model-Based Science. Biology and Philosophy, 21, 725-740. Humphreys, P. (2004). Extending Ourselves. Computational Science, Empiricism and Scientific Method. Oxford: Oxford University Press. Mäki, U. (1992). On the method of isolation in economics. In Craig Dilworth (Ed.). Idealization IV: Intelligibility in Science. (pp. 317-351). Amsterdam: Rodopi. Volterra, Vito (1906). Les mathematiques dans les sciences biologiques et socials. La Revue du Mois, 1, 1-20. Weisberg, M. (2007). Who is a Modeler. British Journal for the Philosophy of Science, 58, 207-233. Weisberg, M. and K. Reisman (2008). The Robust Volterra Principle. Philosophy of Science, 75, 106-131.
The Virtue of Simplicity or the Vice of Complexity? – Theoretical and Statistical Modeling in Ecology The Virtue of Simplicity or the Vice of Complexity? – Theoretical and Statistical Modeling in Ecology Jan Sprenger† Science needs to develop and to select mathematical models of real systems. In the scientific as well in the philosophical literature, two general approaches are discussed: First, the “top-down” approach where models are developed by means of theoretical understanding and knowledge about mechanisms. Second, the “bottom-up” approach that is prevalent in statistical model analysis: A large set of candidate models is filtered by means of the data. Both approaches have been dealt with in the literature on models in science, and in particular in biology: Godfrey-Smith (2006) examines modeling strategies in population biology, Weisberg (2007) takes the Volterra model for population ecology as a paradigmatic example of top-down modeling, as opposed to mere empirical generalizations or straightforward descriptions. On the other hand, there is a large amount of literature on bottom-up model selection in statistical ecology (Burnham and Anderson 1998, Taper and Lele 2004). For instance, ecologists would like to predict (and of course, to understand) how populations develop as a result of exogenous influences or how they affect each other in a certain habitat. To this end, mathematical procedures have to discern relevant input variables and to dismiss those variables whose impact is negligible. Since theoretical understanding is scarce, crude data analysis is often the only way to achieve reliable conclusions. In my paper, I focus on an issue that arises for the bottom-up as well as for the top-down approach: namely the role of simplicity in scientific modeling and a particular, statistically motivated attempt to consider simplicity as a scientific virtue. Note first that complex models with a high number of degrees of freedom are often prone to the pitfall of overfitting – they “explain” effects in the data which are just due to random sampling variation. Such an overfitted model will generally have poor predictive performance. Therefore, philosophers often claim that it is important to find models that balance simplicity and data fit (Forster and Sober 1994, Forster 2002). More concretely, they advocate estimators such as the Akaike Information Criterion (AIC) as a means of comparing rivalling models. The idea behind those information criteria consists in penalizing models with a large number of input variables, i.e. overly complexity is punished by assigning a lower estimated predictive accuracy. Forster and Sober argue that AIC can give us a hunch at predictive accuracy and closeness to the truth of a model, identifying both notions with each other. Thus, their Akaike argument apparently vindicates the prevalent preference for simplicity and transparency in the top-down approach from a bottom-up, statistical perspective. However, I doubt the force of their argument. As Caswell (1988) has pointed out in an ecological context, it is often impossible to reach two important goals at once: first, to obtain a model that comes close to truth by capturing the most important mechanisms in a system and second, to obtain a model that makes accurate predictions. Therefore it is awkward to identify closeness to truth and predictive accuracy, as Forster and Sober do in their (1994). Quite often, certain input variables have an impact on the response variables, but the corresponding parameter values might be so hard to estimate that in order to get sound predictions, we better leave them out of the predictive model. Thus, we see the connection between simplicity and predictive success in quite a different light: namely, the increasing danger of estimation error in complex models is a rationale for preferring simpler models from a predictor’s point of view. In other words, the virtue of simplicity in science gets a pragmatic twist – there is no magical connection between truth and simplicity, but there is a robust link between simplicity and predictive success, due to the practical problems of squeeze accurate predictions out of complex models, even if they are approximately true. Thus, the antithesis deserves to be taken seriously: that there is no principled obstacle for data-based models, however complex they be, to get close to the truth and to generate theoretical knowledge about mechanisms, even beyond what top-down approaches may achieve (Breiman 2001). Finally, I explore the scope and limits of my conclusions, in particular with regards to generalization to the simplicity/model interplay in other disciplines, such as econometrics. References Breiman, Leo (2001): “Random Forests”, Machine Learning 45, 10-32. Burnham, Kenneth P. and David R. Anderson (1998): Model Selection and Inference: a Practical Information-Theoretic Approach. Springer, New York. Caswell, Hal (1988): “Theory and Models in Ecology: A Different Perspective”, Ecological Modeling 43, 33-44. Forster, Malcolm (2002): “Predictive Accuracy as an Achievable Goal of Science”, Philosophy of Science 69, S124-S134. Forster, Malcolm and Elliott Sober (1994): “How to Tell When Simpler, More Unified, or Less Ad Hoc Theories will Provide More Accurate Predictions”, British Journal for the Philosophy of Science 45, 1-35. Godfrey-Smith, Peter (2006): “The strategy of model-based science”, Biology and Philosophy 21, 725-740. Taper, Mark and Subhash Lele (eds.) (2004): The Nature of Scientific Evidence. The University of Chicago Press, Chicago & London. Weisberg, Michael (2007): “Who is a Modeler?”, British Journal for the Philosophy of Science 58, 207-233. 2
When idealization goes too far … A realist perspective on the role of assumptions in economic models Behavioral economics has convingly shown that some motivations cannot be framed within the conventional Homo Economicus model, which is characterized by the assumptions of instrumental rationality and self-interest. A well-known phenomenon is that of strong reciprocity, which leads people to act in ways that are neither instrumental nor self-interested. Whereas this kind of criticism implicitly blames conventional economists for the unrealistic character of (the assumptions in) their models, it remains silent on a number of underlying methodological issues. In this paper, I aim to fill in this theoretical gap. To do so, it is important to take a stance in the debate between instrumentalists and realists that has dominated the philosophy of economics since Milton Friedman’s defense of instrumentalism(1). A lot of economists have defended their (clearly unrealistic) models on the basis that models only aim to predict individual behavior rather than give completely adequate accounts of what actually causes people to behave like they do. Every model, instrumentalists argue, is inevitably a highly simplified theoretical construction that in no relevant way resembles the complex world out there. In this respect, models simply cannot be expected to be ‘realistic’ in some meaningful sense of the word. The assumptions that underly economic models do not function as statements about some state of affairs in the real world but allow economists to construct mathematical models on the basis of which they can make predictions. As long as their predictions are empirically confirmed rather than falsified, assumptions and models turn out to be useful. And, instrumentalists argue, it is usefulness (and thus predictive power) that counts in economics, not realisticness. Indeed, it seems quite a task for realists to understand the role of clearly unrealistic assumptions in scientific models. After all, they believe that such models (should) aim to be true in the sense of representing relevant aspects of the world. Here, I want to defend both ontic realism, according to which the world has certain features independently of how scientific models describe it, and theoretical realism, according to which good theories are those that truly describe these features. As such, I aim to answer the fundamental question whether and how theoretical economics relates to the real world. According to Uskali Mäki, good (economic) models redescribe actual events as resulting from specific causal factors and mechanisms in order to explain “the way the world works”(2) . Postulating assumptions is a way of highlighting certain aspects and causal mechanisms from the complex world and abstracting from others. Models are like experiments in that they aim to isolate a number of relevant aspects that characterize the object of study(3). Every model is therefore unrealistic in the sense that it provides an all too simple picture of the physical and social world. No model can ever fully reflect the complex nature of all events. If taken literally as statements about the real world, idealizing assumptions clearly distort the facts and are thus false. Nevertheless, a realist can accommodate these falsehoods by stressing that they serve a strategic purpose. Quite like scientists control for certain variables in laboratory experiments, economists employ the force of assumption in thought experiments. Assuming other factors to be absent (‘ceteris paribus’), they are able to build models that isolate specific features of the world. While this allows one to view models as in some sense resembling the world, one still needs to impose constraints to the degree to which scientists can abstract from – and thus leave out of consideration –aspects of reality. In this respect, I believe conventional economic assumptions break these boundaries. Empirical research convincingly shows that only a minority of people is actually motivated by the instrumental and self-interested considerations that characterize the conventional Homo Economicus model. Its highly idealizing assumptions make the model a limited one that lacks both explanatory and predictive force in quite a lot of cases and situations. A model world populated by Homines Economici does not necessarily learn us anything about the behavior of real people in the real world. Most orthodox economists attempt to incorporate the empirical insights surrounding motivations like duties, principles, commitments and strong reciprocity by reducing them to instrumental and self-regarding behavior. In my view, however, these reductionist strategies have failed. In a number of instances, actions are clearly motivated by considerations that simply do not fit conventional economic vocabulary. Here, I believe a number of alternative models should complement – rather than replace – the conventional Homo Economicus model. In order to focus on motivations and avoid generalizing and stigmatizing economists, I would like to speak of Homo Egoisticus rather than Homo Economicus when modeling instrumental, self-interested behavior. Second, there is Homo Deonticus, which is characterized by principled, non-instrumental behavior. Third, there is Homo Altruisiticus whose behavior is instrumental and other-regarding. Fourth, there is Homo Reciprocans whose behavior is both non-instrumental and other-regarding. In my view, each of these models highlights certain motivations that cannot be reduced to each other. Such a plurality of models is a desirable way of capturing the wide motivational array that characterizes most actual individuals. It also helps understand that non-instrumental and counterpreferential choice is more widespread than conventional economists would have it. The basic thrust of my criticism is thus that conventional economic models are unrealistic in that they unduly exclude from consideration certain aspects of individual motivation. Their strategy of abstraction, isolation and idealization indeed goes so far that it inhibits a proper understanding of the majority of real-life people. In this respect, one needs to de-isolate and relax the narrowing assumptions and incorporate neglected elements in order to broaden its field of study. In a minimal conception of rationality, which is essentially a stripped down version of what I label the economic conception of rationality, most problematic assumptions (like instrumentality and self-interest) can and should be dropped. In this paper, I hope to answer a number of crucial questions. What are the respective realms that the alternative models can be said to delineate and where are they situated? How to understand the relation between these models? Is it possible to construct a meta-theory which stipulates the circumstances under which each of the respective models gains relevance? All this is of fundamental interest to philosophers, economists and other social scientists. As such, it shows the need for interdisciplinary attempts to understand individual motivation and behavior. Whereas experimental economics has gained a lot of empirical insight in this respect, further theoretical reflection is needed to achieve a more integrated and complete understanding of people’s motivation and behavior. (1) Friedman, M. Essays in Positive Economics, Chicago: The University of Chicago Press, 1953: 3-43. (2) Mäki, U., ‘The Way the World Works (www)’, in: Mäki, U. (ed.), The Economic World View: Studies in the Ontology of Economics, Cambridge: Cambridge University Press, 2005: 369-389. (3) Mäki, U., ‘Models Are Experiments, Experiments Are Models’, Journal of Economic Methodology, 12, 2005: 303-315.
Trading off explanatory virtues in economics This paper draws on Richard Levins’ classic (1966) paper which scrutinizes three different models in population biology. Levins argues for the existence of a three-way tradeoff between generality, realism and precision. The existence of this tradeoff renders it impossible to construct a single model in which all of these theoretical virtues are maximized simultaneously. Interestingly, more or less implicit references to this tradeoff in the context of explanation appears in the work of philosophers of science such as Alan Garfinkel, Philip Pettit and Nancy Cartwright. Explanation is caught, and lives, in a tension between these two requirements. On the one hand, explanations are about the world and so must refer to real things. On the other hand, every explanation must have some generality, and so its objects must in some sense be abstract. (Garfinkel, 1981, p.174) I t is true that going micro and getting at smaller levels of causal grain involves getting better and better contrastive information – greater and greater detail – on causal history. But it does not follow that it involves getting better and better information tout court. On the contrary, the obvious thing to say is that while it means getting better and better contrastive information, it means losing information of a comparative kind. (Jackson & Pettit, 1992, p.15) In modern physics, and I think in other exact sciences as well, phenomenological laws are meant to describe, and they often succeed reasonably well. But fundamental equations are meant to explain, and paradoxically enough the cost of explanatory power is descriptive adequacy. (Cartwright, 1983, p.3) In a bid to render this connection between tradeoffs in model building and the philosophy of explanation more explicit, I will outline a framework consisting of a tradeoff between generality and precision in which the erotetic model of explanation is used to position explanations according to their respective levels of generality and precision. This framework, with its roots in biology, will then be applied to economics. Using the Cobb-Douglass production function as a case, attention will be paid to the topic of microfoundations in economics (Hoover 2001, esp. chapter 3), the issue of the complementarity of models (Marchionni 2008) and idealization (Weisberg, unpublished; Mäki, 1994; Hoover, 1994; Hartmann 2005). The aim is to show, both practically and theoretically, the way in which different models answer different questions and have an irreducible role to play in explanatory practice. A view on models is proposed which holds that a model is one possible answer to the question of how to trade off precision and generality. A model strives to optimize the combination of precision and generality for a given (cluster of) question(s). References Cartwright, Nancy (1983). How the laws of physics lie. Oxford: Oxford University Press Garfinkel, Alan (1981). Forms of explanation. New Haven and London: Yale University Press Hartmann, Stephan (2005), “Idealization in quantum field theory” http://philsci-archive.pitt.edu/archive/00002411/ Hoover, Kevin (1994), “Six Queries on Idealization in an Empirical Context” in: Idealization VI: Poznan Studies in the Philosophy of Science and the Humanities. Bert Hamminga and Neil De Marchi, (eds.). Amsterdam: Rodopi Hoover, Kevin (2001). The methodology of empirical macroeconomics. (Cambridge: Cambridge University Press) Jackson, Frank & Pettit, Philip (1992), “In defense of explanatory ecumenism”, Economics and Philosophy, 8, 1-21 Levins, Richard (1966), “The strategy of model building in population biology”, American Scientist, 54, 421-431 Mäki, Uskali (1994), "Isolation, idealization and truth in economics" in: Idealization in Economics, Bert Hamminga and Neil de Marchi (eds.), special issue of Poznan Studies in the Philosophy of the Sciences and the Humanities, 38, 147-168 Marchionni, Caterina (2008), “Explanatory Pluralism and Complementarity: From Autonomy to Integration”, Philosophy of the Social Sciences, 38(3), 314-333 Weisberg, Michael (2008), "Three Kinds of Idealization”, Journal of Philosophy, CIV: 639-659
Modelling and the Epistemic Import of How-Possibly Explanations Both in biology and economics highly abstract models are used to provide explanations. Quite often these models are treated as how-possible explanations (HPEs). They tell how the phenomenon could have arisen. In philosophy of science, the nature of HPE’s is not well understood. They are often treated as merely potential explanations – explanations that might be actual explanations. We will argue that there is more to their epistemic import than that, and that this simplistic account is a hindrance to proper understanding of the use and development of models in science. For example, it does not help us to understand why the models scientists find most interesting are very simple and quite detached from real empirical explananda. These highly abstract models and their extremely stylized explananda are highly valued by the scientists, and philosophers should be able to say why. Our account of HPEs builds upon the idea that the aim of scientific enquiry is understanding: the ability to make correct what if -inferences about phenomenon. In this account the explanatory knowledge consists of knowledge about dependencies that characterize the phenomenon. The point of (explanatory) models is to represent these dependencies. This account is useful for making sense of models that abstract away or idealize heavily. The intended explananda of these models are much more selective than their critics recognize. These explananda can be articulated naturally reconstructing them contrastively: the models are not intended to explain the phenomenon as a whole, but to explain why it has some properties rather than some others. However, representing an explanatory dependency related to some particular empirical phenomenon is not the only way in which a model can contribute to understanding. Much of the work related to models is theoretical in the sense that the model is not intended to represent any particular phenomenon. Making sense of epistemic import of these activities is a major challenge to philosophical accounts of models. They should be able to say what are the explananda of these models and how they are related to real world phenomena that are the ultimate target of scientific enquiry. In our account the epistemic import of theoretical models is based on the idea of developing a menu of HPEs. A model might not provide a representation of crucial explanatory relationship for any particular real world phenomenon, but it might still make an important contribution by expanding the menu of possible explanations. The expansion of the menu contributes to understanding by increasing the ability to construct explanations for phenomena we might encounter in the future. In this account, a model’s epistemic import is evaluated not only by its ability to represent some particular phenomenon, but also by the changes it brings about in the menu of possible explanations. The latter criterion helps us to make sense of highly abstract theoretical models: their point is to expand or to systematize the menu. This gives us a nice way of thinking about advancement of knowledge and relieves us from the need to invent some special explananda for the theoretical explanations. They are not explanations of ideal or imaginary objects – their explanatory import is based on their contribution to our ability construct explanations for novel phenomena. This account of HPE’s also helps us to understand why it is mistaken to analyze models in isolation as is often done in philosophical studies. Models come in clusters and this is a crucial feature of modeling enterprise that can be explained with our approach. The HPE’s have also an interesting evidential contribution to make. The search for causal explanations in economics and evolutionary biology has often the structure of the inference to the best – or, more properly, to the only – explanation. In this context the knowledge about the range of possible explanations is crucial: we can only be confident in the results of our inquiry if we are confident that our list of alternatives is comprehensive. The remaining alternative does not have much value if we suspect that there are viable alternatives that have not been considered. Furthermore, as the evaluation of the alternatives is comparative, each added alternative increases the challenge for other alternative under consideration. This increases the stringency of the selection process. The paper will illustrate these philosophical ideas with examples from both economics and evolutionary biology. The examples will highlight how individual models contribute to the menu of possible explanations, how the observation that models come in clusters is crucial for their understanding, and how there is a number of different ways in which a model can fail.
Models as a Product of Interdisciplinary Exchange: The Case of Evolutionary Game Theory Models as a Product of Interdisciplinary Exchange: The Case of Evolutionary Game Theory Extended Abstract Evolutionary game theory is (i) a theory of certain causal factors in the world, (ii) a toolbox for construction, and (iii) for solving highly idealized models. Structurally, it is thus similar to standard game theory (Grüne-Yanoff and Schweinzer 2008), but it differs in the ways it allows model construction and solution. Interestingly, evolutionary game theory is the product of two interdisciplinary transfers. First biologists adopted economists’ game theory for the purpose of modeling frequency- dependent selection. Then, roughly twenty years later, economists adopted what biologists had made of game theory and labeled it evolutionary game theory. In this paper, I investigate what exactly was transferred between the sciences, and how it affected model use both in biology and economics. In the first section, I discuss three cases in order to show that biologist imported only rudimentary elements of game theory, always prioritizing their own theoretical ideas, related to the concept of frequency-dependent fitness. First, I show how authors like Fisher (1958), Lewontin (1961), Verner (1965) suggested the use of game theory in ways that is at odds with the form evolutionary game theory would eventually assume. In particular, they suggested games of a species against nature, instead of applying it to competition of individuals within a population. I argue that this at least partly is due to the fact that these authors lacked a full understanding of contemporary game theory, and hence lacked the tools to formulate such an application. Second, I investigate Hamilton (1967), who was the first to employ game theory to model competition of individuals within a population. His development and discussion of his ‘unbeatable strategy’ concept raises some interesting questions about how much he knew about game theory. Clearly, he had some understanding of the equilibrium concept, yet his paper goes without reference to the more contemporary literature, instead using terminology dating back to von Neumann’s and Morgenstern’s 1944 book. Finally, I will focus on John Maynard Smith who in 1972 argued for the ‘logical similarity between the role of human reason in optimizing the outcome of a conflict between men, and the role of natural selection in optimizing the outcome of a fight between two animals’. Again, there is little explicit reference to the game theoretic literature here, although his discussion clearly shows knowledge of it, and Sigmund (2005) assures us that he owned a copy Luce and Raiffa's (1956) Games and Decisions. Curiously, in a follow-up paper (1973), he and Price even devised a simulation solution - something that game theorists had never done before, oddly ignoring the solution techniques available that time. Their unorthodox means of analysis let them miss the unique solution (Gintis 2000, 155-157). Only in later papers (MS 1974) and in a first popular article (MS 1976) did Maynard Smith adopt the more standard analytic means known from game theory, and with those, managed to find the unique solution. These cases show that the transfer from economics to biology was one of basic ideas, not full theory structures or even ontological frameworks. Biologists took structural elements like the payoff matrix and the dependency of the outcome of a behavior on all behaviors involved, and gave these structural features a new interpretation in the light of their own theories. Economists’ game theory thus became an inspiration to formally model a biological theory. As a consequence, biology became more ’mathematised’ – i.e. increased its use of formal models in the way economist were used to. Yet because the biological theory was considerably different from the economic theory, it would be wrong to speak of a transfer of models. Rather, after biologists were inspired by game theorists, they developed their own toolbox for building and solving models. This led to the creation of new types of models, different from those used in standard game theory and ready to be rediscovered by economists. In the second section, I show that economist became interested in evolutionary game theory in the early 1980s. In contrast to the transfer described in section 1, I argue that the ‘re-import’ into economics consisted in a more complete modelling toolbox transfer. I will focus on three cases here. First, I show how Robert Axelrod’s work on the Prisoners’ Dilemma introduced crucial elements of evolutionary game theory into the social sciences. At the hand of early reviews in economic journals, I show that Axelrod’s consecutive book influenced economists into taking evolutionary game theory serious as a new approach to equilibrium refinement. This inspired the formal identity proofs of Bomze (1986) and their popularisation through van Damme (1987 and 1991), leading to the most mainstream application of evolutionary game theory in economics today. Second, I look at Robert Sugden’s (1986) use of evolutionary game theory to model evolution of social institutions. Sugden, in his words, chose biologists’ games because it offered the basis for ‘a theory how people actually play games’ (Sugden 1986, 16). Sugden’s book The Economics of Rights, Co-operation and Welfare thus became an attempt to increase the realism of social theory by borrowing theory from biology. The underlying forces that governed social dynamics, so the claim goes, were mutatis mutandis adequately represented by the biological theory. Finally, I revisit Ken Binmore’s (1988) argument for the adoption of an evolutive account of equilibrium attainment, which focuses on processes driven by evolutionary mechanisms. The result of this effort, (Bimore 1994) are an unchanged standard game theoretic framework with a new interpretation of the game equilibrium at its core, leading to a subtle but significant shift in the justificatory practices of many applied game theorists (Sugden 2005). Thus, in contrast to the transfer from economics to biology, the transfer of evolutionary game theory to economics consisted in more than an inspiration. For the purpose of equilibrium selection, the central model building and model solution concepts (ESS and asymptotic stability) were transferred whole. However, their use is restricted to formal similarities: when looking at the details of interpretation, we find important differences between biology and economics. What was transferred was thus a formal element, a computational template (Humphreys 2004), filled with different meanings in each discipline. The resulting derivational unification (Mäki 2009) must then be investigated for the usefulness of the inferential patterns that can be derived from one theory. A possible angle of criticism, for example, would be the question whether it is useful that models in both disciplines share the formal property of inter-agent payoff comparisons (Kuhn 2004, Grüne-Yanoff 2008). Finally, in Sugden’s or Binmore’s case, the import of evolutionary game theory brings with it the claim that the phenomena organized under these sets of models also manifest common entities, causes, or mechanisms. The models are transferred, so the underlying assertion, because it represents these common entities, causes, or mechanisms for the phenomena of both disciplines. The resulting ontological unification must then be investigated for the truth of its causal claims. A possible angle of criticism, for example, would be to investigate whether biological and social inheritance have any causal properties in common, or whether they are governed by completely different forces. References Axelrod, R. (1980) "More Effective Choice in the Prisoner's Dilemma," Journal of Conflict Resolution, 24: 379-403. Axelrod, R. (1984) The Evolution of Cooperation. New York: Basic Books. Binmore, Ken. 1988a. "Modelling Rational Players I", Economics and Philosophy, 3: 179-241. Binmore, K. (1994). Game Theory and the Social Contract (v. 1): Playing Fair. Cambridge, MA: MIT Press. Bomze (1986) ‘Non-cooperative two-person games in biology: a classification’, Int. J. Game Theory 15, 31-57 (1986). Fisher, R.A., 1958. Polymorphism and Natural Selection. J. Ecol., 289–293. Gintis, Herbert (2000) "Classical Versus Evolutionary Game Theory," Journal of Consciousness Studies 7, 1-2: 300-304. Grüne-Yanoff, Till (2008) Evolutionary Game Theory, Interpersonal Comparisons and Natural Selection. Mimeo. Grüne-Yanoff, Till;Schweinzer, Paul. Journal of Economic Methodology, Volume 15, Number 2, June 2008 , pp. 131-146(16) Hamilton, W.D., 1967. Extraordinary sex ratios. Science 156, 477–488. Humphreys Paul, 2004 Extending Ourselves: Computational Science, Empiricism, and Scientific Method, Oxford University Press. Kuhn, Steven T. (2004) ‘Reflections on Ethics and Game Theory’ Synthese 141: 1-44. Lewontin, R.C., 1960. Evolution and the theory of games. J. Theor. Biol. 1, 382–403. Luce, R.D., Raiffa, H., 1956. Games and Decisions. Wiley, New York. Mäki, Uskali. 2009 Economics imperialism: Concept and constraints" , forthcoming in Philosophy of the Social Sciences. Maynard Smith, , J. (1972) On Evolution. Edinburgh University Press. Maynard Smith, J. (2004) The theory of games and the evolution of animal conflicts. J. Theor. Biol. 47: 209-21. Maynard Smith J. Evolution and the theory of games. American Scientist 64: 41-5. Maynard Smith, John and George Price (1973) "The Logic of Animal Conflict" Nature:146, pp. 15-18. Milgrom, P. (1984) Review of Axelrod's The Evolution of Cooperation, Rand Journal of Economics, 15, 1984, 305-9. Sigmund, K. (2005) ‘John Maynard Smith and evolutionary game theory’ Theoretical Population Biology 68 (2005) 7–10. Sugden, Robert (1986) The Evolution of Rights, Cooperation, and Welfare, Oxford: Basil Blackwell. Sugden R. (2005). ‘The evolutionary turn in game theory’, Journal of Economic Methodology, 8, 113-130 Van Damme Stability and Perfection of Nash Equilibria, Springer Verlag, Berlin, 1987. Second edition 1991. Verner, J., 1965. Natural selection for the sex-ratio. Am. Nat. 99, 419–421. Von Neumann, J., Morgenstern, O., 1944. The Theory of Games and Economic Behavior. Princeton University Press, Princeton, NJ.
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