How Models Fail
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Several years after Axelrod, Rudolf Schuessler (1990) published a book with game theoretical simulations. One part of this book directly relates to Axelrod. This part of Schüßler's book follows the pattern: Pick a well-known simulation, change the settings or other details of this simulations, produce “surprising” results and publish. If Axelrod had demonstrated with his simulation that the shadow of the future is crucial for the evolution of cooperation, Schüßler demonstrates with a modified simulation that this does not need to mean that the same partners must expect to meet again and again in order to sustain cooperation. In Schüßler's simulation cooperators succeed although cheaters can decide to break off the interaction at any time, thus avoiding punishment.[3]
Given Axelrod's previous simulations and conjectures this can appear surprising. But what is surprising? That a different simulation produces different results is prima facie anything but surprising. Given the almost complete modeling freedom - remember, there are no empirical constraints to be honored - and the volatility of the original model it would be surprising if no surprises could be produced. So why should we be interested in the results of another arbitrary simulation?
At this point Schüßler's narrative steps in. As Schuessler (1990, 91) writes “One of the central, classical assumptions of the normativistic sociology says that in an exchange society of rational egoists no stable cooperation can emerge (see Durkheim 1977, Parsons 1949). Alleged proofs for this thesis try to show that already simple analytical considerations suffice to draw this conclusion. The present simulation should be able to shake this firm conviction.”[4] One may wonder whether this means that the simulation serves more than a purely didactic purpose. But be that as it may. It is in any case questionable whether the premises are correct. Do normativistic sociologists really rely on simple analytical considerations? Sociologists like Durkheim usually argue on the basis of thick narratives supported by empirical research. Highly abstract computer simulations like Rudolf Schüßler's simulations can at best prove logical possibilities. However, it is unlikely that this kind of discourse is vulnerable to proofs of logical possibilities. After all, a normativistic sociologist can easily claim that the seeming possibility of rational egoists to cooperate is an artifact of the simulations that strips away all concrete features of human nature, especially those of a psychological kind which make cooperation of egoists impossible in reality (Arnold 2013b, 128ff.). (Generally, proofs of logical possibilities cannot disprove real impossibilities; e.g. a perpetuum mobile is logically possible but impossible in reality, because it contradicts the laws of nature. See Arnold (2013b) for a detailed discussion of the category of logical possibility.)
Schüßler, who seems to be quite aware of the weaknesses of his argument, follows up with the remark that ultimately it is up to the scientist to decide whether this is sufficient or not (Schuessler 1990, 91). But as we have seen, proofs of logical possibility are simply not sufficient. And then again, it is an indefeasible claim that scientific knowledge is objective and that its validity is independent from the opinions and discretion of any particular person. If it were up to the discretion of the scientist to decide whether some theory or model is sufficient to decide a scientific question, we would not call that science any more.
It is noteworthy that Schüßler criticizes Axelrod quite strongly in the beginning of his book (Schuessler 1990, 33ff.), but then presents computer simulations of exactly the same brand as Axelrod's simulations. The same kind of performative self-contradiction is even more obvious in the following example.
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[3] The details of this simulation are described in Schuessler (1990, 61ff.) and in a simpler form in Arnold (2008, 291ff.). For the curious: Schüßler achieves his effect, because the non-cooperators that break off the interaction are forced to pick a new partner from a pool that mostly contains non-cooperators from which it is impossible to rip a high payoff.
[4] This is my translation. The German original reads: “Eine der zentralen, klassischen Annahmen der normativistischen Soziologie besagt, daß in einer Austauschgesellschaft rationaler Egoisten keine stabilen Kooperationsverhältnisse entstehen können (vgl. Durkheim 1977, Parsons 1949). Angebliche Nachweise für diese These versuchen zu zeigen, daß bereits einfache, analystische Überlegungen zu diesem Schluß ausreichen. Die vorliegende Simulation sollte geeignet sein, diese Sicherheit zu erschüttern.” (Schuessler 1990, 91)
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