Why did Ye Wenjie give Luo Ji the axioms of cosmic sociology?

Question

In the prologue of The Dark Forest, Ye Wenjie has a conversation with Luo Ji in which she reveals the "axioms of cosmic sociology" as well as the concepts of "chains of suspicion" and the "technological explosion". With these clues, Luo Ji eventually developed cosmic sociology to

discover the "dark forest" state of the universe and that the Trisolarans could be deterred from conquering Earth by threatening to broadcast Trisolaris' coordinates for destruction by hostile civilizations elsewhere in the universe.

She evidently felt she needed to give this information to Luo Ji since her parting words to him were that she'd "fulfilled [her] duty".

However, Ye Wenjie's decision to seek out Luo Ji and give him this information seems counter to her goals since she

deliberately betrayed the Earth's location to the Trisolarans when she answered the Trisolaran transmission. She wanted to "end human tyranny" as the "spiritual leader" and "commander in chief" of the rebel Earth-Trisolaran Organization (ETO).

Furthermore, Ye Wenjie put both herself and Luo Ji in danger by revealing this information to him despite knowing that

the Trisolarans could know about the conversation due to the sophons. Indeed, the Trisolarans were undoubtedly aware of the conversation since they tried to have Luo Ji killed by the ETO.

Why did Ye Wenjie reveal these clues to Luo Ji?

Answer 1

Ye Wenjie regretted inviting the Trisolarans to invade Earth, but that is almost beside the point. If she never revealed the axioms of Dark Forest theory, then it might not be developed at all. She points out that "no one's done it before. The opportunity is left to you." Later she says, "I've been thinking about this for most of my life, but I've never spoken about it with anyone before." She does know how to keep a secret, but as she grew older and no one else came up with the idea independently, she may have realized that she had to share the knowledge if it were not to be lost. She didn't reveal everything she knew. "But you're clever enough to figure them out. Use these two axioms as a starting point for your discipline, and you might end up becoming the Euclid of cosmic sociology."

It might not matter that the Trisolarans were aware of her conversation, because at some point they had to be told anyway; a threat doesn't work without communication. Yes, it did place Luo Ji in danger, but she evidently had no other choice. She gave him enough to get started.