With respect to cognitive empathy (CE) versus emotional empathy (EE) and Asperger's, Autism, Williams syndrome, schizoid and antisocial personality disorder here's one view:
4 developmental empathy disorders:
1. CE deficit disorder (low CE ability combined with high EE sensitivity): autism
2. EE deficit disorder (low EE sensitivity combined with high CE ability): antisocial personality disorder
3. general empathy deficit disorder (low CE ability and low EE sensitivity): schizoid personality disorder ( (and some cases of autism spectrum disorder)
4. general empathy surfeit disorder (high CE ability and high EE sensitivity): Williams syndrome
http://cogprints.org/6799/1/TPRVol59No3-SMITH.pdfSo based on this scheme antisocial personality and Williams syndrome do have empathy characteristics opposite to some ASDs.
Interesting. Especially the first two.