This article critically examines some of the inconsistency objections that have been put forward by John Broome, Larry Temkin and others against the so-called "person-affecting," or "person-based," restriction in normative ethics, including "extra people" problems and a version of the nonidentity problem from Kavka and Parfit. Certain Pareto principles and a version of the "mere addition paradox" are discussed along the way. The inconsistencies at issue can be avoided, it is argued, by situating the person-affecting intuition within a non-additive form (...) of maximizing consequentialism – a theory which then competes with such additive, or aggregative, forms of maximizing consequentialism as "totalism" and "averagism.". (shrink)