The Dark Side of the Force: When computer simulations lead us astray and "model think" narrows our imagination
- Preconference draft, Models and Simulations, Paris, June 12-14 -

Eckhart Arnold

1 Introduction
2 Different aims of computer simulations in science
3 Criteria for “explanatory” simulations
4 Simulations that fail to explain
    4.1 Axelrod style simulations of the “evolution of cooperation”
    4.2 Can we simulate the “Social Contract”?
5 Conclusions

4.2 Can we simulate the “Social Contract”?

But it is not just because it leads us scientifically astray that too much indulgence into pure model research is bad. The other problem is that it may prevent us from seeing the most obvious, because our imagination is limited by the narrow lens of our own models. This is what seems to have happened to some of the modern game theoretical interpretations of social contract philosophy.

Such a game theoretical interpretation has been put forward, among others, by Brian Skyrms in two books, “Evolution of the Social Contract” and “The Stag Hunt and the Evolution of Social Structure” (Skyrms 1996) (Skyrms 2004), in both of which he presents computer simulations to deal with classical questions of social contract philosophy. The theory of the social contract is rooted in the philosophy of the 17th and 18th century with Thomas Hobbes' “Leviathan” being the most famous work dedicated to social contract philosophy and Skyrms believes that we can raise the discussion to a higher level by applying the modern tools of game theoretical computer simulations to it. It is as a stag hunt game that Skyrms presents the central question of the social contract in the latter of the two works (though he acknowledges that the prisoner's dilemma usually is the more common candidate): “How do we get from the hunt hare equilibrium to the stag hunt equilibrium? We could approach the problem in two different ways. We could follow Hobbes in asking the question in terms of rational self-interest. Or we could follow Hume by asking the question in a dynamic setting. We can ask these questions using modern tools - which are more than Hobbes and Hume had available, but still less than we need for fully adequate answers.” (Skyrms 2004, p. 10)

Skyrms is by no means alone with his belief in the superiority of the “modern tools” when it comes to social contract philosophy. His belief is shared by many analytic philosophers. Thus we read in a recent introduction to philosophy: “It would be interesting and important if we could make more precise the sort of argument Hobbes offered, so that we could say just why it is that the advantages of civil society over the state of nature ought to appeal to anyone.” (Appiah 2003, p. 232) The author goes then on to introduce the prisoner's as a “modern tool” which - as the reader is to believe - allows to “make more precise the sort of argument Hobbes offered”.

Is it really possible to “make more precise the sort of argument Hobbes offered” by translating the metaphoric language of 17th and 18th century philosophers (e.g. Hobbe's state of nature, Rousseau's stag hunt metaphor) into precise game theoretic models? In order to answer this question, let's first see what kind of problems the social contract theories of the 17th and 18th century philosophers deal with and then examine Skyrm's treatment of these problems. Social contract philosophy is traditionally concerned with two different questions:

  1. social contract philosophy is concerned with justification of political order and, furthermore, with the requirements a political order must fullfill in order to be just.
  2. social contract philosophy tries to answer the question how political order evolves out of anarchy and how just (or democratic) order evolves from authoritarian order.

It is primarily the descriptive question of social contract philosophy that Skyrm's game theoretic discussion is addressed to. For that matter Skyrms presents a number of simple game theoretical models, including his simulation of the stag hunt game. His simulation of the stag hunt game is a territorial simulation, where players on a two dimensional plane play a (one shot) stag hunt game pairwise with their neighbors. They change their strategy (to cooperate or not to cooperate) depending on to the most successful strategy in their neighborhood. Skyrms then examines the effects of the respective sizes of the interaction and reproduction neighborhood. He summarizes his results as follows:

How much progress have we made in addressing the fundamental question of the social contract: “How can you get from the noncooperative hare hunting equilibrium to the cooperative stag hunt equilibrium?” The outlines of a general answer have begun to emerge. Over time there is some low level of experimentation with stag hunting. Eventually a small group of stag hunters comes to interact largely or exclusively with each other. This can come to pass through pure chance and the passage of time in a situation of interaction with neighbors. ... The small group of stag hunters prospers and can spread by reproduction and imitation. The process is facilitated if reproduction or imitation neighborhoods are larger than interaction neighborhoods. (Skyrms 2004, p. 123)

As far as the stag hunt game goes Brian Skyrms is surely right, but if this model is to tell us anything about how political order evolves from anarchy, Brian Skyrms completely misses the point. If Skyrms computer simulations of the stag hunt game really was an adequate model for the evolution of the social contract then we would have to conclude that political order could - if only the neighborhood structure were favorable enough - evolve from anarchy even without the institution of a Leviathan, merely by the gradual propagation of cooperation through neighborhoods. This is of course a most delightful prospect, though, sadly, one for which there exists not a single precedence in history. Other than Skyrm's simulations suggest and as the authors of the 17th and 18th century well knew, there is no way to bring about political order without a Leviathan of some kind. Apart from this lapse, which obviously the “modern tools” could not prevent, there is another omission that must appear striking to anyone who has ever wasted a thought on what the requirements and conditions of political order are: Nowhere in the various game theoretic models Skyrms presents in his two books is the phenomenon of rulership (Herrschaft) and submission (beherrscht werden) reflected, even though this is probably the most basic phenomenon of politics and a condition that surely any serious theory about the evolution of political order must take account of.

Surprisingly, this blunder went largely unnoticed in the lively discussion following the publication of Skyrm's first book. Only Philipp Kitcher points out that dominance hierarchies play an important part in evolution and that the sort of symmetric games Skyrms looks at do not properly reflect these (Kitcher 1999). Kitcher's remark leads in the right direction, but it does not hit the point, because dominance hierarchies as they exist among animals as well as among humans are not the same as rulership, which is an exclusively human phenomenon. The decisive difference is that a ruler can order a subject to do something, while dominance merely means that the others will give way to the dominant person (or animal), which is much less than carrying out orders.

But what caused this rather grave oversight? How come that Skyrms offers an answer to the fundamental question of the social contract that is obviously wrong? What Skyrms and other analytical philosophers seem to forget when they seek to make arguments from 17th and 18th century philosophers more precise by reformulating them in game theoretical terms, is that metaphors (like the state of nature metaphor or the stag hunt metaphor) do not get any better if one makes them more precise only on the side of the metaphorical image without paying due attention to the relation between the metaphor and its object. If the relation between the formal model that is to replace the metaphor and the object of the metaphor is not made more precise (in terms of adequacy, stability and descriptive appropriateness) the epistemological strength of the model is not any greater than that of the metaphor.[5] Or, to put it briefly: A metaphor remains a metaphor even if it employs a formal model as its object of comparison. For this reason it is also a fairly irrelevant question whether the state of nature is better described as a prisoner's dilemma or as a stag hunt game or as some other game. As the failure of Skyrms to provide a sound argument for either of the questions of social contract philosophy shows, the miscarried attempt to translate metaphoric descriptions into formal models may even disrupt the whole argument.

In the case of the Axelrod-style simulations of the “evolution of the social contract” discussed in the previous section it seemed that too much attention was spend on the construction of models and too little attention on whether the models are adequate. But when looking at Skyrms treatment of the social contract one may easily get the impression that he has never thought about the subject matter in question at all. At this point, however, it might be asked if Skyrms really wanted to tell us anything about the social contract, or if he just wanted to show how some of the metaphors from the political philosophy of enlightment could be represented by game theoretical models without any specific claim about their applicability in any (including the original) context. But then, he explicitly relates his models to the social contract. If this is to be taken serious then the severe misunderstandings that result can only be due to the fact that he perceives his subject matter exclusively through the narrow lens of his own models. To give a name to the narrowing of perception or, rather, imagination as a result of the exclusive occupation with the technical aspects of formal modelling, I propose to call it “ model think”. “Model think” occurs when we conceive reality only through one specific brand of models and when we let other possibilities of conceiving reality escape our attention just because they cannot properly be represented with this brand of models.

[5] This is not to say that it is never useful to replace metaphors by models, for the epistemological strength of a model can - if the subject matter in question permitts - be increased, while that of a literal or poetical metaphor cannot.

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