EDS:
thanks to WillowJ
The Beighton criteria for Ehlers-Danlos Syndrome, joint hypermobility type (current version) was written by 5 EDS specialists (geneticists) and 2 disease orgs http://www.ncbi.nlm.nih.gov/books/NBK1279/
The other criteria, the Brighton criteria (not a typo, the two definitions are called Beighton and Brighton), was written by three rheumatologists (current version). These are cited by the US Army Health Clinic in Germany http://www.jaoa.org/content/106/9/531.full
Fibromyalgia:
thanks to WillowJ
"The two criteria for fibromyalgia were written by 1) three doctors and 2) ten doctors and the professional college (American College of Rheumatology)."