Full Idea
For Parfit all personal identity really amounts to is a chain of experiences and other psychological features causally related to each other in 'direct' sorts of ways.
Gist of Idea
Personal identity is just causally related mental states
Source
report of Derek Parfit (Personal Identity [1971]) by Keith T. Maslin - Introduction to the Philosophy of Mind 10.5
Book Reference
Maslin,Keith: 'An Introduction to the Philosophy of Mind' [Polity 2001], p.269
A Reaction
When summarised like this, it strikes me that Parfit is just false to our experience, whatever Hume may say. I suspect that Parfit (and those like him) concentrate too much on rather passive perceptual experience, and neglect the will.