Let x be all the information available for integration, y in x the integrated information, and C : x -> x' or C(x) = x' a discrete or continuous consciousness respectively st:

• C is self aware when x is different based on the existence of C. Haha. Unprovable
• Consciousness as a noun: the state of being aware
• Conscious as a verb: the act of becoming aware, integrating bits together. Measured in
  • entropy after over before
  • Bits consumed: 2 bits go in, 1 goes out
  • Entropy concerned:
  • Probably most ml metrics are already weakly aligned with the idea

Free will:

• when the external action produced cannot be determined by the external input.
• When there is zero attack surface on a policy's (usually abstract) behavior
• When an agent can (and often naturally does) adaptively act and learn (it has a will) and internal states are readily reachable from any normal point in the internal state trajectory where there is zero attack surface in the agents (usually abstract) behavior (free)
• Agents need to learn, but they need to be able to put up defenses as well. More generally, free will is when the agent is able to maintain a high dynamic range of internal driven control over consciousness (no causal link/mutual information?) ie C(x_in, x_ext)=C(xin, • uniform or random sample of prior trajectories). The previous equation should not be applied at low level dynamics
• The agent's personality (in the sense of, it's probabilistic policy) is a self-organizing system that resists the tendency to erode to outside influence, like all other living systems. - added September 20

Agents with

• Prosocial motivations
• Moral motivations

should display justice

Information economy:

• consciousness consumes information
• free will creates it

Maybe human brains really are special because they employ quantum mechanisms to create information?

Quantum operations without entropy consume zero information

The brain is an entropy maximizing machine - in terms of trying to maximize the number of microstates