Citation
Aircraft in Warfare: The Dawn of the Fourth Arm
TL;DR
Fighting power scales with square of coalition size
Lanchester's Square Law, originally developed for military strategy, provides the mathematical basis for understanding why coalition size matters more than individual quality. The finding that fighting power scales with the square of coalition size (not linearly) explains patterns observed across species and organizations.
The formula demonstrates why three medium-ranked allies consistently defeat two high-ranked opponents: Coalition of 3 (strength 2 each) = 3² × 2 = 18 power vs. Coalition of 2 (strength 4 each) = 2² × 4 = 16 power. This mathematics governs both chimpanzee politics and corporate organizational dynamics.
Key Findings from Lanchester (1916)
- Fighting power scales with square of coalition size
- Larger coalition wins even with weaker individual members
- Three rank-4 individuals defeat two rank-2 individuals
- Applies to any conflict with simultaneous multi-actor engagement
- Explains 77% coalition-based succession in chimps