In 1948 Hempel and Oppenheim proposed an explicatum for the concept of systematic power 1, pp. 164–167. Since that time some shortcomings have been found in this first attempt. It is the purpose of this paper to show that one can keep the basic approach of the ‘48 paper, and overcome the known disadvantages by means of changes in the details of the definition. In this improvement certain tools will be used that were not available in 1948.

We build a model of the reflective equilibrium method to better understand under what conditions a community of agents would achieve a shared equilibrium. We find that, despite guaranteeing that agents individually reach equilibrium and numerous constraints on how agents deliberate, it is surprisingly difficult for a community to converge on a small number of equilibria. Consequently, the literature on reflective equilibrium has underestimated the challenge of coordinating intrapersonal convergence and interpersonal convergence.