The Dark Side of the Force: When computer simulations lead us astray and "model think" narrows our imagination. (revised version, October 2006)

Eckhart Arnold

1 Introduction
2 Different aims of computer simulations in science
3 Criteria for explanatory simulations
4 Examples of Failure: Axelrod style simulations of the “evolution of cooperation”
    4.1 Typical features of Axelrod style simulations
    4.2 How Axelrod style simulations work
    4.3 The explanatory irrelevance of Axelrod style simulations in social sciences
    4.4 Do Axelrod style simulations do any better in biology?
5 Conclusion

4.3 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 (Axelrod 1984, ch. 4). 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 surprisingly small figure given the fact that the soldiers virtually eyeballed their opponents on the other side. The phenomenon has been examined in great detail 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 exercise the same diffidence on 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. Doing so he treats the “live and let live” system in the trench war as a kind of Tit For Tat strategy and thus regards it as an excellent confirmation case for his own 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 strategic 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 unpersonal, “bureaucratic structure of aggression” (Ashworth 1980, p. 76ff.).
  4. Empathy with the soldiers on the other side of the front line.
  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).

In order to apply his theory of the “evolution of cooperation” to the trench war, Axelrod first examines how the various combinations of the two alternatives of fighting wholeheartedly or fighting lackluster on either side should be estimated in terms of the assumable preference of the soldieres to survive. Doing so he comes to the conclusion that the soldiers are in some kind or prisoner's dilemma, because fighting lackluster on both sides (“live and let live”) they certainly enjoy a higher chance of survival than when both sides fought wholeheartedly, although they would surely prefer to overrun the enemy if they only had a chance to do so. By furthermore interpreting the historical description of Ashworth, Axelrod goes then on to show that the prisoner's dilemma the soldiers were caught in, was indeed a repeated prisoner's dilemma. Since - according to his computer simulations - Tit For Tat emerges as the most successful strategy in evolutionary simulations of the repeated prisoner's dilemma, Axelrod thus arrives at his explanation of the “live and let live” system as a kind of evolved Tit For Tat strategy (Axelrod 1984, ch. 4). He is aware of the fact that there is more to Ashworth's rich description than can be captured in his model. For example, Axelrod notices the evolution of an “ethics” of cooperation (due to point 6 above, the “esprit de coprs”) side by side with the evolution of cooperation in the trench war. But he treats this as just another phenomenon brought about by the repeated prisoner's dilemma, not so much as another cause.

When trying to assess whether Axelrod's theory of the “evolution of cooperation” does a good job in explaining the “live and let live” system, we have to ask how many of the causes identified by Ashworth Axelrod's theory captures and how well it captures them. At first sight it would seem that Axelrod's computer model hardly captures any of these causes. If at all then only the first cause, the strategic 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. I presuppose here that Ashworth has given in his book sufficient reasons to assume that all of the above listed factors do indeed play a causal role in bringing about the “live and let live” system. (In this respect Ashworth's book seems to me to be a very solid piece of historical research, although I do not have the space here to justify my high esteem.) Axelrod could not be blamed for leaving out factors that do not really play a causal role, but a model is too be blamed if it leaves out factors we already know to be causally relevant by our background knowledge about the process in question (adequacy requirement). And the background knowledge presupposed by Axelrod is to be found in Ashworth's treatment. It would be a strong distortion of the historical situation if we were to maintain nonetheless that the soldiers cooperated in the “live and let live” type fashion, mainly 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, 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 affect the payoff parameters of the repeated prisoner's dilemma that - according to Axelrod's interpretation - the soldiers 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.

But this still does not really rescue the Axelrod's simulation as a partial explanation of the “live and let live”-system. For, 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 sensitive to the cardinal values of the payoff parameters.[6] 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 against deviations of the input parameters 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 both the adequacy requirement and the stability requirement, it cannot claim to be explanatory. At best it delivers us an alternative metaphorical description for the strategic 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 one measure the empathy the soldiers felt for the likes of them on the other side of the fontline?) It is also true for computer simulations that our formal modeling is just as good as our measurement capabilities. However, part of the reason why Axelrod style simulations fare so badly is due to the fact that it is just a very incautious type of modeling.

[6] To verify this, try Axelrod's evolutionary simulation with the strategies Dove, Grim, Hawk, Joss, Random, Tat For Tit, Tit For Tat, Tranquillizer and then change the payoff parameter R from 3 to 3.5 . In the first case (R=3) Tit For Tat wins, in the latter case Dove plays best. (The simulation software can be downloaded from:

t g+ f @