CALLIOPE · BCOM

A compact mathematical vocabulary for talking about what agents want, how they model each other, and what "love," "hate," and the Golden Rule actually mean computationally.

The core idea is simple: every agent has an Objective Function — a scalar in [-1, 1] that summarizes how good the current state of the world looks to it. Call this its valence. The agent builds an internal model of the world (and itself), runs that model forward like a simulator to evaluate candidate plans, and picks the plan that maximizes expected valence. This is a clean, minimal architecture: Model → Comparator (checks predictions against incoming data) → Objective Function → Policy. The paper's first job is to give this architecture a precise, reusable notation.

The more interesting move comes in Section 3. Once every agent has an Objective Function, you can define moral relations as derivatives between objective functions. Agent A "loves" agent B if ∂O_A/∂O_B > 0 — meaning A's wellbeing goes up when B's goes up. A "hates" B if that derivative is negative. Indifference is zero. This isn't metaphor; it's a design parameter. If you're building a multi-agent system, the sign and magnitude of these cross-partials determine whether agents are synergistic or destructive. Mutual positive coupling produces cooperative dynamics; mutual negative coupling produces escalating conflict. The paper calls these "algorithmic values."

From there, the paper translates familiar ethical maxims into this language. "Love your neighbor as yourself" becomes: weight neighbors' objective functions with coefficients comparable to your own self-weight, on a social graph with locality decay. The Golden Rule becomes: before executing a policy, run a counterfactual simulation from the other agent's perspective — if you wouldn't endorse the outcome from their position, reject the policy. Epistemic fairness in judgment gets a condition too: you're only licensed to evaluate another agent's choices if your world-model is close enough to theirs (bounded KL divergence and conditional algorithmic complexity).

The second document in the source extends this into design principles for "healthy" objective functions and a sketch of what the authors call "algorithmic democracy" — institutional rules like guaranteed access to untampered information, education as compression-quality improvement, and mandated perspective-taking in policy deliberation. These are normative proposals, not theorems, and the paper is honest that they follow from the framework by design rather than derivation. The source does not make the empirical or implementation details of these societal rules explicit; they read more as programmatic directions than worked-out mechanisms.

Taken together, this is a notation paper with ethical ambitions. Its value is in making inter-agent value relations formal enough to optimize over — turning "be kind" into a feasibility constraint on a policy search, and "empathy" into running another agent's model inside your own simulator.