This paper examines how to satisfy "independence of the utilities of the dead" (Blackorby et al. in Econometrica 63:1303-1320, 1995; Bommier and Zuber in Soc Choice Welf 31:415-434, 2008) in the class of "expected equally distributed equivalent" social orderings (Fleurbaey in J Polit Econ 118:649-680, 2010) and inquires into the possibility to keep some aversion to inequality in this context. It is shown that the social welfare function must either be utilitarian or take a special multiplicative form. The multiplicative form is compatible with any degree of inequality aversion, but only under some constraints on the range of individual utilities.