This article defends a new account: Rank-Matching Theory. Unlike ‘partial’ or ‘limited’ aggregation, it wholly rejects the idea that the interests of separate people sum. Unlike traditional ‘anti-aggregative’ theories, it is nonetheless sensitive to the numbers.

We argue that the commitments underlying this theory make better sense of our intuitive reactions than competitors, and we prove that the theory follows from some natural principles. We also use simulations to show how, given certain empirical claims, it may be able to explain the distinction between ‘relevant’ and ‘irrelevant’ interests.

When each affected party has equally strong interests, we ought to help the greater number. I defend an extension: when every affected party has nearly equal interests, we ought to help the greater number. This slight strengthening turns out to conflict with many otherwise attractive views.

Joe Horton argues that partial aggregation yields unacceptable verdicts in cases with risk and multiple decisions. I begin by showing that Horton's challenge does not depend on risk, since exactly similar arguments apply to riskless cases. The underlying conflict Horton exposes is between partial aggregation and certain principles of diachronic choice.

I then provide two arguments against these diachronic principles: (i) they conflict with intuitions about parity, prerogatives, and cyclical preferences, and (ii) they rely on an odd assumption about diachronic choice. Finally, I offer an explanation, on behalf of partial aggregation, for why these diachronic principles fail.