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”
        4.1.1 Typical features of Axelrod style simulations
        4.1.2 How Axelrod style simulations work
        4.1.3 The explanatory irrelevance of Axelrod-style simulations in social sciences
        4.1.4 Do Axelrod-style simulations do any better in biology?
    4.2 Can we simulate the “Social Contract”?
5 Conclusions

4.1.3 The explanatory irrelevance of Axelrod-style simulations in social sciences

The probably most dramatic example for Axelrod's theory of the “evolution of cooperation” is given in his chapter on the trench war on the western front in the First World War. During the long phases when no great battle took place, a rather surprising phenomenon occurred on many parts of the front in this war: Hostilities lost in intensity and the number of casualties was reduced to a figure that is surprisingly small given the fact that the soldiers virtually eyeballed their opponents on the other side. The phenomenon has been extensively studied by the historians of the epoch, among others by the sociologist Tony Ashworth (Ashworth 1980), who found out that it was due to a kind of “live and let live” system that emerged on many (roughly one third) of the quieter parts of the front line: The soldiers hoped that if they weren't taking too hard on their enemies then the enemies would do the like to them. Thus, contrary to standing military orders, a kind of cooperation between the opposing front soldiers emerged on the basis of an unspoken “live and let live” agreement. Axelrod draws heavily on the description of Tony Ashworth as a source and he fully acknowledges Ashworth's achievements. Axelrod treats the “live and let live” system in trench war as an excellent confirmation case for his theory. But would his theory really be able to explain the “live and let live” system? In order to find this out, let us see, whether Axelrod's computer simulations can add anything to the explanation of the “live and let live” system that goes beyond the explanation that is already given in Ashworth's historical narrative. To do so we first have to briefly reconstruct the explanation that is given by Ashworth and then check whether there exist aspects of the phenomenon that Axelrod can explain better.

Ashworth, in his historical treatment, identifies the following causes for the “live and let live” system:

  1. The strategical deadlock. It was virtually impossible to move the frontline for either side.
  2. The natural desire of most soldiers to survive the war.
  3. The impersonal, “bureaucratic structure of aggression” (Ashworth 1980, p. 76ff.).
  4. Empathy with the soldiers on the other side of the front.
  5. Whether elite troops or non elite troops were fighting on either side. “Live and let live” was much less frequent where elite troops were involved. (According to Ashworth this was the most decisive factor of all.)
  6. The “esprit de corps” that can, however, become either conductive or, in the case of elite troops, impedimental to the emergence of the “live and let live” system.
  7. The branch of service. Infantry soldiers had to face a much greater danger and consequently had a greater interest in “live and let live” than artillery soldiers.
  8. The limited means of the military leadership to suppress “live and let live”. (Only later they found an effective way to do so by organizing raids on the enemy trenches.)
  9. Initial causes such as Christmas truces, bad wheather periods when fighting was impossible, coincidental temporary ceasefire due to similar daily routines on both sides (mealtimes).

At first sight it would seem quite obvious that Axelrod's computer model hardly captures any of these causes. If at all then only the first cause, the strategical deadlock situation the soldiers were caught in, could roughly be interpreted as a repeated prisoner's dilemma. But then, this is only one in a long list of causes, which means that Axelrod's model is far from fullfilling the adequacy requirement. It would therefore mean to strongly distort the historical situation if we were to maintain that the soldiers cooperated in the “live and let live” type fashion, because they were caught in a repeated prisoner's dilemma situation and because - as computer simulations demonstrate - “tit for tat” often is a good strategy in such situations.

However, if the model helps to give us a deeper or more precise understanding of one of the different factors that contributed to the “live and let live”-system, Axelrod's model would still have some explanatory value, even if only as a partial explanation. Also, we could still try to link some of the other causes to Axelrod's model by assuming that they determine the preferences of the soldiers and thereby the payoff parameters of the repeated prisoner's dilemma that - according to Axelrod's interpretation - they play with their enemies. For example, it is plausible to assume that the status of the troop (elite troop or non elite troop) had a bearance on how the soldiers valuated the situation they were in. While a non elite soldier would prefer to be a coward and live an elite soldier might prefer to fight and risk death. Consequently, elite soldiers might not even face a prisoner's dilemma. Quite in harmony with Axelrod's model, which suggests that cooperation is the rule and non cooperation the exception, this could help to explain why “live and let live” appeared only in one third of all cases.

The way Axelrod proceeded when determining the payoff parameters was to asses by plausible reasoning the ordinal relations between the different alternatives for soldiers according to their assumed preferences. Unfortunately this is not enough, because the outcome of Axelrod's simulation is strongly sensitive to the cardinal values of the payoff parameters. This violates the stability requirement. Therefore we cannot really know whether the soldiers followed the “live and let live” strategy because of what Axelrod's model suggests.

More generally, the difficulty of applying Axelrod style simulations to political or historical science results from the problem that the values of the required input parameters cannot be found ready made in the historical records. They must be reconstructed through a complicated and error-prone interpretation process. It is therefore hard to see, how the stability requirement can be fullfilled at all for simulations that are not extremely robust right from the beginning. As we shall see later, a similar problem applies for the application of Axelrod-style simulations in biology. Only that there we have more reason to hope that it can be overcome by simulations that are more closely knit to the measurable quantities of the empirical processes.

What then are we left with? Since Axelrod's simulation as applied to the “live and let live” system of the first world war violates the both the adequacy requirement and the stability requirement (the latter is the case even, if we treat it as a merely partial explanation), it cannot claim to be explanatory. At best it delivers us an alternative metaphorical description for the strategical situation the soldiers found themselves in in terms of game theoretical concepts. Offering no more than that it has hardly anything to add to the detailed explanations Ashworth offers within his historical narrative.

The example shows how difficult it is to make any good use of Axelrod style simulations in the social sciences. Partly this has to do with typical difficulties that all formal approaches face in the social sciences outside economics. There are two main reasons for the limited success of formal methods in social sciences. First of all, social processes do often result from an intricate set of interwoven causes (see the example above), for only some of which we have a formal description ready at hand. But if we cannot single out the causes that can be described formally then any accuracy that is gained by the formal description inevitably gets lost when we reintegrate the formally described causes with the other causes in a comprehensive explanation. The second reason is that measurement is difficult in social sciences and that only few quantities can be measured with accuracy. (In the above example, how would you measure the empathy the soldiers felt for the likes of them on the other side of the fontline?) It is not only true for computer simulations that our formal modelling is just as good as our measurement capabilities. Partly, however, the reason why Axelrod style simulations fare so badly is due to the fact that it is just a very incautious type of modelling.

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