Appendix III: Report on the Bene Gesserit Motives and Purposes
On the surface it would seem that the Golden Path of Leto II was that plan and he was in charge, but he was not alive during the Arrakis Affair. Also one might think that it's Paul himself but Mr Herbert seems to indicate that it started before even Paul's birth.
The Lady Jessica was ordered to produce an Atreides daughter. The plan was to inbreed this daughter with Feyd-Rautha Harkonnen, a nephew of the Baron Vladimir, with the high probability of a Kwisatz Haderach from that union. Instead, for reasons she confesses have never been completely clear to her, the concubine Lady Jessica defied her orders and bore a son.
This alone should have alerted the Bene Gesserit to the possibility that a wild variable had entered their scheme. But there were other far more important indications that they virtually ignored:
The Report is a scathing criticism of the Gesserit multi-generational plan and ends the book with the hair raising:
In the face of these facts, one is led to the inescapable conclusion that the inefficient Bene Gesserit behavior in this affair was a product of an even higher plan of which they were completely unaware!
In many years of (re)reading the original books I don't see an answer, did I miss it, or is there an answer in the subsequent works not written by Mr Frank Herbert?