 In the sixty years since Arrow wrote, there has been a plethora of work in social choice theory, a good deal of which is arguably of great importance to ethics. For example, John Harsanyi proved that if individual preferences and social evaluations both satisfy the axioms of expected utility theory (with shared or objective probabilities) and that social preferences conform to unanimous individual preferences, then social evaluations are determined by a weighted sum of individual utilities (1955, 1977a). Matthew Adler (2012) has extended an approach like Harsanyi’s to demonstrate that a form of weighted utilitarianism, which prioritizes the interests of those who are worse off, uniquely satisfies a longer list of rational and ethical constraints. When there are instead disagreements in probability assignments, there is an impossibility result: the unanimity condition implies that for some profiles of individual preferences, social evaluations will not satisfy the axioms of expected utility theory (Hammond 1983, Seidenfeld, et al. 1989, Mongin 1995). For further discussion of social choice theory and the relevance of utility theory to social evaluation, see the entry on  social choice theory, Sen (1970) and for recent reappraisals Fleurbaey (2007) and Adler (2012).