I propose the following desideratum for self-referential doxastic modal agents (agents that can think about their own beliefs), where □A represents “I believe A”, (W|A) represents the agent’s world model conditional on A, and ≻ is the agent’s preference relation:
Positive Placebomancy: For any proposition P, The agent concludes P from □P→P, if (W|P)≻(W|¬P).
In natural English: The agent believes that hyperstitions, that benefit the agent if true, are true.
“The placebo effect works on me when I want it to”.
A real life example: In this sequence post, Eliezer Yudkowsky advocates for using positive placebomancy on “I cannot self-deceive”.
I would also like to formalize a notion of “negative placebomancy” (doesn’t believe hyperstitions that don’t benefit it), “total placebomancy” (believes hypestitions iff they are beneficial), “group placebomancy” (believes group hyperstitions that are good for everyone in the group, conditional on all other group members having group placebomancy or similar), and generalizations to probabilistic self-referential agents (like “ideal fixed-point selection” for logical inductor agents).
I will likely cover all of these in a future top-level post, but I wanted to get this idea out into the open now because I keep finding myself wanting to reference it in conversation.
Edit log:
2024-12-08 rephrased the criterion to be an inference rule rather than an implication. Also made a minor grammar edit.
Formalizing Placebomancy
I propose the following desideratum for self-referential doxastic modal agents (agents that can think about their own beliefs), where □A represents “I believe A”, (W|A) represents the agent’s world model conditional on A, and ≻ is the agent’s preference relation:
Positive Placebomancy: For any proposition P, The agent concludes P from □P→P, if (W|P)≻(W|¬P).
In natural English: The agent believes that hyperstitions, that benefit the agent if true, are true.
“The placebo effect works on me when I want it to”.
A real life example: In this sequence post, Eliezer Yudkowsky advocates for using positive placebomancy on “I cannot self-deceive”.
I would also like to formalize a notion of “negative placebomancy” (doesn’t believe hyperstitions that don’t benefit it), “total placebomancy” (believes hypestitions iff they are beneficial), “group placebomancy” (believes group hyperstitions that are good for everyone in the group, conditional on all other group members having group placebomancy or similar), and generalizations to probabilistic self-referential agents (like “ideal fixed-point selection” for logical inductor agents).
I will likely cover all of these in a future top-level post, but I wanted to get this idea out into the open now because I keep finding myself wanting to reference it in conversation.
Edit log:
2024-12-08 rephrased the criterion to be an inference rule rather than an implication. Also made a minor grammar edit.
Can you clarify the Positive Placebomancy axoim?
Does it bracket as:
or as:
And what is the relationship between P and A? Should A be P?
Oops that was a typo. Fixed now, and added a comma to clarify that I mean the latter.