Four Maxims of Strategy

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There are four ancient maxims of political behavior, first suggested by the Arthashastra, a 4th century BC Sanskrit treatise on statecraft. These maxims are:

The enemy of my enemy is my friend.
The enemy of my friend is my enemy.
The friend of my enemy is my enemy.
The friend of my friend is my friend.

Though far from iron laws of politics, these principles are generally accepted and common sensical. They also form the basis of a well-known sociological theory called structural balance theory. The questions we want to answer are:

  1. Does quantitative realism provides a justification for these maxims? If so, that would mean that quantitative realism ultimately underpins structural balance theory.
  2. If quantitative realism is not the underlying rationale for the maxims, why not? And is it at least consistent with them?

We first explain structural balance and its relationship to the maxims, and then investigate these questions.

Structural Balance Theory

Structural balance theory looks at agent triads in which all of the relationships are symmetric (and not neutral), and it makes assertions about which triads are balanced and which are not.


Structural balance theory has a variety of implications for larger social networks, predicting phenomena that have been observed among humans and animal communities. Here we explain how SBT is underpinned by certain strategic principles, which are in turn underpinned by quantitative realism.

These maxims explain why two of the triads above are considered balanced, and the other two unbalanced. In the balanced triads, the maxims are satisfied for every agent, and none of the maxims are violated. Conversely, in the unbalanced triads, none of the maxims are satisfied for any of the agents.

Quantitative Realism

Interpretation of the Maxims

Depicted as power structures from the perspective of the focal agent, the four maxims are:


Basis of the Maxims

Does quantitative realism provide the foundation for the four maxims?