We are sometimes uncertain about empirical facts, such as whether it will rain tomorrow. But we can also be uncertain about moral facts, such as whether it's wrong to steal, or how we should value the well-being of animals. Uncertainty about whether it's wrong to steal is uncertainty about moral or normative facts, while uncertainty about how we should value the well-being of animals is uncertainty about axiological or value facts.
Can moral uncertainty be rational, and what should we do in response to it? We might think that it can never be rational to be uncertain about normative or axiological facts, because such facts are, like mathematical facts, knowable a priori. Nevertheless it seems that agents like ourselves are uncertain about non-trivial mathematical facts, and that we are also uncertain about normative and axiological facts. Given this, it seems necessary to develop some account of how we ought to act under moral uncertainty.
Several such accounts have been formulated in recent years:
Normative externalism: We can be required to act in accordance with norms, even if we are not in a position to know what they are (Weatherson 2014)
My favorite theory: We should act in accordance with the moral theory that we are most confident in (Gustafsson & Torpman 2014).
Maximize expected choiceworthiness: Moral theories rank actions, and we should act so as to maximize the overall choiceworthiness of our actions relative to the theories we are uncertain over (MacAskill 2014).
The parliamentary model: Moral theories should be given weight in accordance with our credences in them, and trades can be made between them to determine the optimal set of actions under uncertainty (Bostrom 2009).
Two important problems facing the view that moral uncertainty can affect how we ought to act are the regress problem - the problem that we will be uncertain not only about typical moral questions, but also about which approach to moral uncertainty is correct, and so on ad infinitum (Sepielli 2013) - and the problem of intertheoretic comparisons - the problem that there seems to be no principled ways to make comparisons between different moral theories (Nissan-Rozen 2015).
Bostrom, Nick. 2009. Moral uncertainty - towards a solution?.
Gustafsson, Johan E. & Olle Torpman. 2014. In defence of my favourite theory. Pacific Philosophical Quarterly 95(2):159-174.
MacAskill, William. 2014. Normative uncertainty. Doctoral dissertation, University of Oxford.
Nissan-Rozen, Ittay. 2015. Against moral hedging. Economics and Philosophy 31(3): 349-369.
Sepielli, Andrew (2013). What to Do When You Don't Know What to Do When You Don't Know What to Do…. Nous 47 (1):521-544.
Weatherson, Brian 2014. Running Risks Morally. Philosophical Studies 167, 141–63.