Organizations often face moral dilemmas. For example, in 2004 the UN Refugee Agency (UNHCR) needed to decide whether to help refugees in enclosed camps in Pakistan repatriate to Afghanistan. On the one hand, helping with repatriation might have made UNHCR complicit in forced returns, as refugees sought to repatriate just to avoid life without freedom in Pakistan. On the other hand, refusing to help with repatriation would leave refugees stranded in camps: perhaps repatriation was the best option if this was what refugees wanted. When organizations face this and other dilemmas, it is not clear how they should proceed. In other words, it is unclear which policy they should pursue when all feasible policies seem wrong. Some might think that, at least for hard dilemmas, every choice is just wrong, and so no choice is right. But that is not quite true. Even difficult dilemmas can be resolved using certain methods. One method is to ask those affected by potential policies what they think the most justifiable policy is. A second method is to choose what to do randomly. Randomly selecting a course of action can sometimes be the fairest way of determining what to do when every option seems wrong.

We consider a diploid model of random selection. Assuming that the selective fitness is of the SAS–CFF type introduced by Gillespie, we obtain a diffusion approximation. We also discuss the existence of stationary distributions and recurrent properties.