Causal Sufficiency and Actual Causation
  Pearl opened the door to formally defining actual causation using causal
models. His approach rests on two strategies: first, capturing the widespread
intuition that X=x causes Y=y iff X=x is a Necessary Element of a Sufficient
Set for Y=y, and second, showing that his definition gives intuitive answers on
a wide set of problem cases. This inspired dozens of variations of his
definition of actual causation, the most prominent of which are due to Halpern
& Pearl. Yet all of them ignore Pearl's first strategy, and the second strategy
taken by itself is unable to deliver a consensus. This paper offers a way out
by going back to the first strategy: it offers six formal definitions of causal
sufficiency and two interpretations of necessity. Combining the two gives
twelve new definitions of actual causation. Several interesting results about
these definitions and their relation to the various Halpern & Pearl definitions
are presented. Afterwards the second strategy is evaluated as well. In order to
maximize neutrality, the paper relies mostly on the examples and intuitions of
Halpern & Pearl. One definition comes out as being superior to all others, and
is therefore suggested as a new definition of actual causation.
