Before revision:   We discuss the importance of actuarial fairness, defined as the expected benefits equalling the contributions for each member, and whether actuarial unfairness can be seen as solidarity between members.
After revision:  Collectively, the structures are called pooled annuity funds. Since the pooled annuity funds propose different methods of pooling mortality risk, we investigate the connections between them and find that they are genuinely different for a finite heterogeneous membership profile. We discuss the importance of actuarial fairness, defined as the expected benefits equalling the contributions for each member, and whether actuarial unfairness can be seen as solidarity between members.