Full Idea
Once you recognise the existence of bottom-up, micro to macro forms of causation, the notion of supervenience no longer does any work in philosophy.
Gist of Idea
Upwards mental causation makes 'supervenience' irrelevant
Source
John Searle (The Rediscovery of the Mind [1992], Ch. 5.V)
Book Reference
Searle,John R.: 'The Rediscovery of the Mind' [MIT 1999], p.126
A Reaction
I'm not sure if the notion of supervenience ever did any work. Davidson only fished up the word because none of the normal relationships between things seemed to apply (and he was wrong about that).