It is well-known that there is a trade-off among the properties of pop
ulation principles that are used to make social evaluations when the n
umber of people in the society under consideration may vary. The commo
nly used principles either lead to the repugnant conclusion (which is
the case for classical utilitarianism), or they violate the Pareto-plu
s principle and related properties (average utilitarianism is an examp
le of such a principle). This paper examines the nature of this trade-
off and shows that the incompatibility between avoiding the repugnant
conclusion and the Pareto-plus principle is fundamental and not restri
cted to the commonly used population principles.