I found this paragraph helpful in framing the problem:
The central problem in implementing [the supervenience thesis] has been that of defining a supervenience relation that will fill the twin requirements set forth: first, the relation must be nonreductive, that is, a given domain can be supervenient on another without being reducible to it. Second, the relation must be one of dependence: if a domain supervenes on another, there must be a sturdy sense in which the first is dependent on the second, or the second determines the first. But it has not been easy to find such a relation. The main difficulty has been this: if a relation is weak enough to be nonreductive, it tends to be too weak to serve as a dependence relation; conversely, when a relation is strong enough to give us dependence, it tends to be too strong-strong enough to imply reducibility.