One idea how this formalism can be improved, maybe. Consider a random directed graph, sampled from some “reasonable” (in some sense that needs to be defined) distribution. We can then define “powerful” vertices as vertices from which there are paths to most other vertices. Claim: With high probability over graphs, powerful vertices are connected “robustly” to most vertices. By “robustly” I mean that small changes in the graph don’t disrupt the connection. This is because, if your vertex is connected to everything, then disconnecting some edges should still leave plenty of room for rerouting through other vertices. We can then interpret it as saying, gaining power is more robust to inaccuracies of the model or changes in the circumstances than pursuing more “direct” paths to objectives.
One idea how this formalism can be improved, maybe. Consider a random directed graph, sampled from some “reasonable” (in some sense that needs to be defined) distribution. We can then define “powerful” vertices as vertices from which there are paths to most other vertices. Claim: With high probability over graphs, powerful vertices are connected “robustly” to most vertices. By “robustly” I mean that small changes in the graph don’t disrupt the connection. This is because, if your vertex is connected to everything, then disconnecting some edges should still leave plenty of room for rerouting through other vertices. We can then interpret it as saying, gaining power is more robust to inaccuracies of the model or changes in the circumstances than pursuing more “direct” paths to objectives.