There are many competing theories in normative ethics. Some people say the right thing to do is what would lead to the most happiness. Others say that it is what the virtuous person would do, or what is done on a maxim that we could rationally will all others to follow, or what we are told to do in a particular religious text. There is much disagreement by intelligent people over what it is right to do, and while we each have our own beliefs about the matter, it would be foolish to be 100% certain that we are correct while all these others are not. Until further evidence is in, or until much wider consensus is reached, the only rational approach is to spread your degrees of belief between different ethical theories. For example, I think that the true ethical theory is likely to be some form of utilitarianism, but I'm not sure which form, and I also accept that there is some possibility that it will be something quite different.
However, what are we to do in situations where the different theories that we have some credence in urge us to do different things? In such situations, we suffer from what is called moral uncertainty. This is not to be confused with everyday uncertainty in moral situations: such as where you don't know which charity you should donate to because you don't know which one will best help the poor. The moral theories themselves should tell you how to deal with such a situation (for example, by looking at the expected benefits). Instead, these are cases where even if you had all the empirical evidence, you would still not know what to do. What you still need to know are the moral facts of the matter. Perhaps the philosophical community will eventually work out what these are: normative ethics will be settled once and for all. But what are you to do now, when you need to act?
I believe that this is a very important question, and one that has been overlooked in the study of ethics. There is a lot of focus on what each ethical theory tells you to do, but almost none on what to do when you are uncertain of which theory is correct (as we all are, or should rationally be). I have been working on this topic for a while with Nick Bostrom, and we have reached a few conclusions. For example we have shown that the following two principles of moral uncertainty are both false:
1) Always do what the theory in which you hold the most credence tells you to do.
2) Always do the act that you most believe is right.
For (1), consider a case in which you have a 2% degree of belief in a theory which tells you to do A and a 1% degree of belief in 98 other theories which each tell you to do B (and which say that this is very important). It is not plausible that the appropriate act must be A.
This type of example, makes (2) look very plausible, but consider a case in which you have a 51% degree of belief in a theory which tells you to do A, but says the benefit is only marginally more than doing B, and that you have a 49% degree of belief in a theory which tells you to do B and says that this is critically important. It seems that in such a case you need to morally hedge your bets by doing B. Thus neither of these principles seems to be correct.
We are in the process of writing a paper in which we discuss these and other results concerning this very interesting issue. We will not present a full theory of moral uncertainty, but have quite a few surprising results and promising ideas.