Econstudentlog

The Origin and Evolution of Cultures (V)

This will be my last post about the book. Go here for a background post and my overall impression of the book – I’ll limit this post to coverage of the ‘Simple Models of Complex Phenomena’-chapter which I mentioned in that post, as well as a few observations from the introduction to part 5 of the book, which talks a little bit about what the chapter is about in general terms. The stuff they write in the chapter is in a way a sort of overview over the kind of approach to things which you may well end up adopting unconsciously if you’re working in a field like economics or ecology and a defence of such an approach; I’ve as mentioned in the previous post about the book talked about these sorts of things before, but there’s some new stuff in here as well. The chapter is written in the context of Boyd and Richerson’s coverage of their ‘Darwinian approach to evolution’, but many of the observations here are of a much more general nature and relate to the application of statistical and mathematical modelling in a much broader context; and some of those observations that do not directly relate to broader contexts still do as far as I can see have what might be termed ‘generalized analogues’. The chapter coverage was actually interesting enough for me to seriously consider reading a book or two on these topics (books such as this one), despite the amount of work I know may well be required to deal with a book like this.

I exclude a lot of stuff from the chapter in this post, and there are a lot of other good chapters in the book. Again, you should read this book.

Here’s the stuff from the introduction:

“Chapter 19 is directed at those in the social sciences unfamiliar with a style of deploying mathematical models that is second nature to economists, evolutionary biologists, engineers, and others. Much science in many disciplines consists of a toolkit of very simple mathematical models. To many not familiar with the subtle art of the simple model, such formal exercises have two seemingly deadly flaws. First, they are not easy to follow. […] Second, motivation to follow the math is often wanting because the model is so cartoonishly simple relative to the real world being analyzed. Critics often level the charge ‘‘reductionism’’ with what they take to be devastating effect. The modeler’s reply is that these two criticisms actually point in opposite directions and sum to nothing. True, the model is quite simple relative to reality, but even so, the analysis is difficult. The real lesson is that complex phenomena like culture require a humble approach. We have to bite off tiny bits of reality to analyze and build up a more global knowledge step by patient step. […] Simple models, simple experiments, and simple observational programs are the best the human mind can do in the face of the awesome complexity of nature. The alternatives to simple models are either complex models or verbal descriptions and analysis. Complex models are sometimes useful for their predictive power, but they have the vice of being difficult or impossible to understand. The heuristic value of simple models in schooling our intuition about natural processes is exceedingly important, even when their predictive power is limited. […] Unaided verbal reasoning can be unreliable […] The lesson, we think, is that all serious students of human behavior need to know enough math to at least appreciate the contributions simple mathematical models make to the understanding of complex phenomena. The idea that social scientists need less math than biologists or other natural scientists is completely mistaken.”

And below I’ve posted the chapter coverage:

“A great deal of the progress in evolutionary biology has resulted from the deployment of relatively simple theoretical models. Staddon’s, Smith’s, and Maynard Smith’s contributions illustrate this point. Despite their success, simple models have been subjected to a steady stream of criticism. The complexity of real social and biological phenomena is compared to the toylike quality of the simple models used to analyze them and their users charged with unwarranted reductionism or plain simplemindedness.
This critique is intuitively appealing—complex phenomena would seem to require complex theories to understand them—but misleading. In this chapter we argue that the study of complex, diverse phenomena like organic evolution requires complex, multilevel theories but that such theories are best built from toolkits made up of a diverse collection of simple models. Because individual models in the toolkit are designed to provide insight into only selected aspects of the more complex whole, they are necessarily incomplete. Nevertheless, students of complex phenomena aim for a reasonably complete theory by studying many related simple models. The neo-Darwinian theory of evolution provides a good example: fitness-optimizing models, one and multiple locus genetic models, and quantitative genetic models all emphasize certain details of the evolutionary process at the expense of others. While any given model is simple, the theory as a whole is much more comprehensive than any one of them.”

“In the last few years, a number of scholars have attempted to understand the processes of cultural evolution in Darwinian terms […] The idea that unifies all this work is that social learning or cultural transmission can be modeled as a system of inheritance; to understand the macroscopic patterns of cultural change we must understand the microscopic processes that increase the frequency of some culturally transmitted variants and reduce the frequency of others. Put another way, to understand cultural evolution we must account for all of the processes by which cultural variation is transmitted and modified. This is the essence of the Darwinian approach to evolution.”

“In the face of the complexity of evolutionary processes, the appropriate strategy may seem obvious: to be useful, models must be realistic; they should incorporate all factors that scientists studying the phenomena know to be important. This reasoning is certainly plausible, and many scientists, particularly in economics […] and ecology […], have constructed such models, despite their complexity. On this view, simple models are primitive, things to be replaced as our sophistication about evolution grows. Nevertheless, theorists in such disciplines as evolutionary biology and economics stubbornly continue to use simple models even though improvements in empirical knowledge, analytical mathematics, and computing now enable them to create extremely elaborate models if they care to do so. Theorists of this persuasion eschew more detailed models because (1) they are hard to understand, (2) they are difficult to analyze, and (3) they are often no more useful for prediction than simple models. […] Detailed models usually require very large amounts of data to determine the various parameter values in the model. Such data are rarely available. Moreover, small inaccuracies or errors in the formulation of the model can produce quite erroneous predictions. The temptation is to ‘‘tune’’ the model, making small changes, perhaps well within the error of available data, so that the model produces reasonable answers. When this is done, any predictive power that the model might have is due more to statistical fitting than to the fact that it accurately represents actual causal processes. It is easy to make large sacrifices of understanding for small gains in predictive power.”

“In the face of these difficulties, the most useful strategy will usually be to build a variety of simple models that can be completely understood but that still capture the important properties of the processes of interest. Liebenstein (1976: ch. 2) calls such simple models ‘‘sample theories.’’ Students of complex and diverse subject matters develop a large body of models from which ‘‘samples’’ can be drawn for the purpose at hand. Useful sample theories result from attempts to satisfy two competing desiderata: they should be simple enough to be clearly and completely grasped, and at the same time they should reflect how real processes actually do work, at least to some approximation. A systematically constructed population of sample theories and combinations of them constitutes the theory of how the whole complex process works. […] If they are well designed, they are like good caricatures, capturing a few essential features of the problem in a recognizable but stylized manner and with no attempt to represent features not of immediate interest. […] The user attempts to discover ‘‘robust’’ results, conclusions that are at least qualitatively correct, at least for some range of situations, despite the complexity and diversity of the phenomena they attempt to describe. […] Note that simple models can often be tested for their scientific content via their predictions even when the situation is too complicated to make practical predictions. Experimental or statistical controls often make it possible to expose the variation due to the processes modeled, against the background of ‘‘noise’’ due to other ones, thus allowing a ceteris paribus prediction for purposes of empirical testing.”

“Generalized sample theories are an important subset of the simple sample theories used to understand complex, diverse problems. They are designed to capture the qualitative properties of the whole class of processes that they are used to represent, while more specialized ones are used for closer approximations to narrower classes of cases. […] One might agree with the case for a diverse toolkit of simple models but still doubt the utility of generalized sample theories. Fitness-maximizing calculations are often used as a simple caricature of how selection ought to work most of the time in most organisms to produce adaptations. Does such a generalized sample theory have any serious scientific purpose? Some might argue that their qualitative kind of understanding is, at best, useful for giving nonspecialists a simplified overview of complicated topics and that real scientific progress still occurs entirely in the construction of specialized sample theories that actually predict. A sterner critic might characterize the attempt to construct generalized models as loose speculation that actually inhibits the real work of discovering predictable relationships in particular systems. These kinds of objections implicitly assume that it is possible to do science without any kind of general model. All scientists have mental models of the world. The part of the model that deals with their disciplinary specialty is more detailed than the parts that represent related areas of science. Many aspects of a scientist’s mental model are likely to be vague and never expressed. The real choice is between an intuitive, perhaps covert, general theory and an explicit, often mathematical, one. […] To insist upon empirical science in the style of physics is to insist upon the impossible. However, to give up on empirical tests and prediction would be to abandon science and retreat to speculative philosophy. Generalized sample theories normally make only limited qualitative predictions. The logistic model of population growth is a good elementary example. At best, it is an accurate model only of microbial growth in the laboratory. However, it captures something of the biology of population growth in more complex cases. Moreover, its simplicity makes it a handy general model to incorporate into models that must also represent other processes such as selection, and intra- and interspecific competition. If some sample theory is consistently at variance with the data, then it must be modified. The accumulation of these kinds of modifications can eventually alter general theory […] A generalized model is useful so long as its predictions are qualitatively correct, roughly conforming to the majority of cases. It is helpful if the inevitable limits of the model are understood. It is not necessarily an embarrassment if more than one alternative formulation of a general theory, built from different sample models, is more or less equally correct. In this case, the comparison of theories that are empirically equivalent makes clearer what is at stake in scientific controversies and may suggest empirical and theoretical steps toward a resolution.”

“The thorough study of simple models includes pressing them to their extreme limits. This is especially useful at the second step of development, where simple models of basic processes are combined into a candidate generalized model of an interesting question. There are two related purposes in this exercise. First, it is helpful to have all the implications of a given simple model exposed for comparative purposes, if nothing else. A well-understood simple sample theory serves as a useful point of comparison for the results of more complex alternatives, even when some conclusions are utterly ridiculous. Second, models do not usually just fail; they fail for particular reasons that are often very informative. Just what kinds of modifications are required to make the initially ridiculous results more nearly reasonable? […]  The exhaustive analysis of many sample models in various combinations is also the main means of seeking robust results (Wimsatt, 1981). One way to gain confidence in simple models is to build several models embodying different characterizations of the problem of interest and different simplifying assumptions. If the results of a model are robust, the same qualitative results ought to obtain for a whole family of related models in which the supposedly extraneous details differ. […] Similarly, as more complex considerations are introduced into the family of models, simple model results can be considered robust only if it seems that the qualitative conclusion holds for some reasonable range of plausible conditions.”

“A plausibility argument is a hypothetical explanation having three features in common with a traditional hypothesis: (1) a claim of deductive soundness, of in-principle logical sufficiency to explain a body of data; (2) sufficient support from the existing body of empirical data to suggest that it might actually be able to explain a body of data as well as or better than competing plausibility arguments; and (3) a program of research that might distinguish between the claims of competing plausibility arguments. The differences are that competing plausibility arguments (1) are seldom mutually exclusive, (2) can seldom be rejected by a single sharp experimental test (or small set of them), and (3) often end up being revised, limited in their generality or domain of applicability, or combined with competing arguments rather than being rejected. In other words, competing plausibility arguments are based on the claims that a different set of submodels is needed to achieve a given degree of realism and generality, that different parameter values of common submodels are required, or that a given model is correct as far as it goes, but applies with less generality, realism, or predictive power than its proponents claim. […] Human sociobiology provides a good example of a plausibility argument. The basic premise of human sociobiology is that fitness-optimizing models drawn from evolutionary biology can be used to understand human behavior. […] We think that the clearest way to address the controversial questions raised by competing plausibility arguments is to try to formulate models with parameters such that for some values of the critical parameters the results approximate one of the polar positions in such debates, while for others the model approximates the other position.”

“A well-developed plausibility argument differs sharply from another common type of argument that we call a programmatic claim. Most generally, a programmatic claim advocates a plan of research for addressing some outstanding problem without, however, attempting to construct a full plausibility argument. […] An attack on an existing, often widely accepted, plausibility argument on the grounds that the plausibility argument is incomplete is a kind of programmatic claim. Critiques of human sociobiology are commonly of this type. […] The criticism of human sociobiology has far too frequently depended on mere programmatic claims (often invalid ones at that, as when sociobiologists are said to ignore the importance of culture and to depend on genetic variation to explain human differences). These claims are generally accompanied by dubious burden-of-proof arguments. […] We have argued that theory about complex-diverse phenomena is necessarily made up of simple models that omit many details of the phenomena under study. It is very easy to criticize theory of this kind on the grounds that it is incomplete (or defend it on the grounds that it one day will be much more complete). Such criticism and defense is not really very useful because all such models are incomplete in many ways and may be flawed because of it. What is required is a plausibility argument that shows that some factor that is omitted could be sufficiently important to require inclusion in the theory of the phenomenon under consideration, or a plausible case that it really can be neglected for most purposes. […] It seems to us that until very recently, ‘‘nature-nurture’’ debates have been badly confused because plausibility arguments have often been taken to have been successfully countered by programmatic claims. It has proved relatively easy to construct reasonable and increasingly sophisticated Darwinian plausibility arguments about human behavior from the prevailing general theory. It is also relatively easy to spot the programmatic flaws in such arguments […] The problem is that programmatic objections have not been taken to imply a promise to deliver a full plausibility claim. Rather, they have been taken as a kind of declaration of independence of the social sciences from biology. Having shown that the biological theory is in principle incomplete, the conclusion is drawn that it can safely be ignored.”

“Scientists should be encouraged to take a sophisticated attitude toward empirical testing of plausibility arguments […] Folk Popperism among scientists has had the very desirable result of reducing the amount of theory-free descriptive empiricism in many complex-diverse disciplines, but it has had the undesirable effect of encouraging a search for simple mutually exclusive hypotheses that can be accepted or rejected by single experiments. By our argument, very few important problems in evolutionary biology or the social sciences can be resolved in this way. Rather, individual empirical investigations should be viewed as weighing marginally for or against plausibility arguments. Often, empirical studies may themselves discover or suggest new plausibility arguments or reconcile old ones.”

“We suspect that most evolutionary biologists and philosophers of biology on both sides of the dispute would pretty much agree with the defense of the simple models strategy presented here. To reject the strategy of building evolutionary theory from collections of simple models is to embrace a kind of scientific nihilism in which there is no hope of achieving an understanding of how evolution works. On the other hand, there is reason to treat any given model skeptically. […] It may be possible to defend the proposition that the complexity and diversity of evolutionary phenomena make any scientific understanding of evolutionary processes impossible. Or, even if we can obtain a satisfactory understanding of particular cases of evolution, any attempt at a general, unified theory may be impossible. Some critics of adaptationism seem to invoke these arguments against adaptationism without fully embracing them. The problem is that alternatives to adaptationism must face the same problem of diversity and complexity that Darwinians use the simple model strategy to finesse. The critics, when they come to construct plausibility arguments, will also have to use relatively simple models that are vulnerable to the same attack. If there is a vulgar sociobiology, there is also a vulgar criticism of sociobiology.”

June 6, 2014 - Posted by | anthropology, biology, books, culture, economics, evolution, mathematics, science

No comments yet.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: