Moral phase space
The question
You cannot show a human right under a microscope. You cannot prove in a mathematical theorem why segregation was wrong, why it was wrong to kill people in the gulag for a better tomorrow. But you can build formal systems that make the wrongness visible, testable, and structurally clear. This playground explores three such systems.
Deontic logic: rights as constraints
Deontic logic formalizes the distinction between what is obligatory, forbidden, and permitted. In this model, rights enter as side-constraints on optimization: some actions are categorically inadmissible regardless of their aggregate welfare consequences.
Optimization happens only inside the admissible set. This is how the mathematics says: “you do not get to solve an equation by deleting the people who make it inconvenient.”
Capability lattice: real freedoms
The capability approach, developed by Amartya Sen and Martha Nussbaum, evaluates social states not by reported satisfaction or resource holdings, but by what persons are actually able to do and be. The seven capabilities measured here — bodily integrity, mobility, speech, participation, education, health, and contestation — form a partial order, not a single scalar. Two states can be incomparable: one may improve education while worsening political voice. The capability floor matters because a society with one collapsed freedom is not redeemed by luxuries elsewhere.
State-space: domination and repair
The third framework models the polity as a dynamical system with two competing forces: domination (coercion, targeted burden, persistence of unjust structures) and repair (courts, participation, accountability). What matters is not just the snapshot but where the institutional dynamics are dragging the system. Domination can become self-reinforcing: coercion erodes repair capacity, which reduces correction, which enables further coercion. The system classifies trajectories into three attractor basins: entrenched domination, contested transition, and repair-and-stabilization.
Naive utility as foil
A crude utilitarian machine compresses moral reality into one scalar: . This playground includes a naive utility score as a deliberate foil — to show how single-number optimization can rate a rights-violating, coercive system as tolerable when future-welfare rhetoric is high. The other three frameworks exist precisely to block this failure mode.
What each framework sees
The point is not to force agreement between the models. Each one notices something the others miss. Deontic logic cleanly captures why “better tomorrow” does not justify arbitrary detention. The capability lattice reveals that formally equal opportunities can coexist with targeted subordination. The state-space model shows that tolerable present indicators can mask a trajectory toward entrenched domination. Together they approximate the “non-crude mathematics” that a single utility function cannot provide.
The limitation
This mathematics is not value-free in the strong sense. It needs axioms: persons count, equal standing matters, some forms of coercion are impermissible, aggregate gain does not automatically justify sacrifice of the few. These are closer to axioms in geometry than to empirical findings. But once chosen, they generate a strong formal system, and many atrocities become demonstrably invalid moves within it.
Model changelog
- Three moral formalisms: deontic logic (rights as side-constraints), capability lattice (Sen/Nussbaum), domination/repair state-space
- Naive utility included as deliberately crude foil
- 4 political scenario presets: fragile democracy, segregation, emergency powers, reparative order
- 13 slider parameters across rights indicators, capabilities, and institutional dynamics
- Framework comparison view, deontic violation panel, capability radar, domination/repair trajectory
- Parameter sweep showing how each framework responds differently to the same parameter change