Tools or Toys?

Table of Contents 
Social sciences in general are characterized by a multitude of different styles of presentation like rich narratives or “thick descriptions”, stylized verbal descriptions, mathematical descriptions. Often explanations in the social sciences work completely without formal models. If an example is seriously needed[10] then Orlando Figes “The Whisperers” could be cited (Figes 2008). In this book Figes describes how the persecution in Stalinist Russia formed the habits of its citizens in everyday's and family life and he explains why it did so. The book is a fine example of “oral history” that rests mainly on interviews with contemporary witnesses. Even though he explains things in his book, Figes does, of course, not have any use for mathematical models or computer simulations whatsoever.
But even in cases where mathematical models might help us to understand social phenomena, they typically operate in a field that is also covered by theories and descriptions of a very different scientific style. To put the content and the results of mathematical models or simulations into relation to theories and descriptions that are rendered in a completely different scientific style requires a considerable interpretative effort.
Getting around these difficulties by confining oneself to a modeling approach and ignoring descriptions and theories that do not fit a mathematical style of research is not recommendable, because it can lead to omitting relevant information. In noneconomical contexts, where the description of the empirical subject matter to which the models are related usually has a narrative form it is not an option at all, anyway.
A good example for this situation is the interpretation of mathematical results in social choice theory. The most famous of these results is Arrow's theorem which shows that a mapping from individual preferences to a collective preference relation is impossible if mild and seemingly selfevident restrictions are placed on the mapping function (such as that it should be “nondictatorial”, guarantee “pairwise independence” and allow any kind of wellformed individual preference relations in its domain) (Mueller 2003, p.\ 583ff.). But what does this abstract mathematical result mean in terms of voting and decision making in a democracy? Does it mean that democratic decision making procedures are unavoidably precarious, as some authors believe (Riker 1982)? In order to answer these questions the mathematical results need to be related to empirical descriptions of democratic elections and democratic decision making as well es philosophical concepts of democracy, liberalism, political participation and the like. Many things can go wrong if the task of interpreting the mathematical results in terms of empirical and philosophical concepts is not done carefully (see Mackie (2003) for a comprehensive portrayel and an acute criticism of misinterpretions of Arrow's theorem). Again, this interpretative task is not the same as the respective task in physics of interpreting the results of a calculation with respect to the physical situation, if only because the hermeneutical gap between the language of the models and the language of the empirical descriptions is much larger in the social sciences than in physics.
The epistemological consequences that the plurality of scientific styles in the social sciences has for modeling can be summarized as follows: 1. Specific attention must be paid to the task of integrating mathematical models with the results obtained by other methods. 2. In some cases mathematical models might not be a reasonable option at all. This should best be evaluated before embarking on the task of constructing models.
[10] It seems that it is, because Epstein (2008) denies that social science without modeling is possible. Epstein's argument that one has only the choice between either implicit or explicit models, wherefore it is better to make explicit models, fails for several resons: 1) An implicit model can be better than an explicit model, if one fails to render one's implicit model in explicit terms properly. Just as the formalization of a verbal theory is a highly non trivial task so is the rendering of implicit assumptions in explicit terms. 2) Implicit assumptions about human behaviour and human nature often work quite well. We use them every day in our life with considerable success. 3) The question that is at stake when discussing social simulations is not whether a model is implicit or explicit but whether it must be mathematical or not. My claim is that for many connections that we can perfectly well describe verbally we do not (yet) have acceptable mathematical equivalents. No formalization is better than poor adhocformalizations. Epstein, however, is right in so far as explicetness is desirable.