The Rule of One was a self-affirming doctrine conceived by Darth Sidious to replace the Rule of Two, a long-standing Sith doctrine he considered to be outmoded, it having fulfilled its purpose by placing him in power.
The Rule of One was first articulated in Darth Sidious's political treatise Absolute Power, wherein he stated that the Sith would be embodied by a sole reigning Dark Lord—Sidious himself—who would live forever as Emperor of the galaxy, having no need to train a replacement, and availing himself solely of capable executors of his will, talented in the Force as dark side agents. These agents learned a smattering of Sidious's abilities, but did not assume even a fraction of his authority.
Although officially it resembled Darth Bane's Rule of Two in terms of apprentices and the punishment thereof regarding rule violation, the Rule of One was, in reality, completely different, as there was no chance of succession for his apprentices. Sidious trained apprentices, but betrayed and replaced them, in order to ensure he remained as the sole ruler.
Darth Tenebrous, a Dark Lord of Bane's Order prior to Darth Sidious, calculated that the rise of "One Sith," a Dark Lord so powerful he would have no need of replacement, was inevitable.
- Book of Sith: Secrets from the Dark Side