The iron law of oligarchy claims that the complex organisation will always end up in an oligarchy, no matter it was constituted originally. In that sense, the oligarchy should also happen in the Community Energy System (CES) as a complex self-govern common-pool resource system. The oligarchy situation raises the issue of the fairness and the health in the community since that subgroup of the member may steer the future decisions to be more favourable on one side than the others or may drive the rules to limit the active participation of others, or decrease the community cohesion. This paper specially concerned with the emergence of oligarchy in the CES and the effect of the iron law of oligarchy on the health and the fairness in the CES. The result shows that the iron law of oligarchy occurs in CES, but it is needed to make CES has the level of fairness and health required to support its continuity