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Utility functions or their equivalents (value functions, objective functions,loss functions, reward functions, preference orderings) are a central tool inmost current machine learning systems. These mechanisms for defining goals andguiding optimization run into practical and conceptual difficulty when thereare independent, multi-dimensional objectives that need to be pursuedsimultaneously and cannot be reduced to each other. Ethicists have provedseveral impossibility theorems that stem from this origin; those results appearto show that there is no way of formally specifying what it means for anoutcome to be good for a population without violating strong human ethicalintuitions (in such cases, the objective function is a social welfarefunction). We argue that this is a practical problem for any machine learningsystem (such as medical decision support systems or autonomous weapons) orrigidly rule-based bureaucracy that will make high stakes decisions about humanlives: such systems should not use objective functions in the strictmathematical sense.  We explore the alternative of using uncertain objectives, represented forinstance as partially ordered preferences, or as probability distributions overtotal orders. We show that previously known impossibility theorems can betransformed into uncertainty theorems in both of those settings, and provelower bounds on how much uncertainty is implied by the impossibility results.We close by proposing two conjectures about the relationship betweenuncertainty in objectives and severe unintended consequences from AI systems.

Impossibility and Uncertainty Theorems in AI Value Alignment (or why your AGI should not have a utility function)