<aside> ℹ️ Epistemic status: The best single-word term we have found is mana; the definition is the Polynesian term.
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The term “independence compensation” defies description. Here are some descriptions of what it isn’t.
The term "independence compensation" is used in certain communications. It refers, vaguely, to pre-commitments used to allow for certain types of actions to occur before they occur.
TLDR - Independence Compensation is the quota system that prevents paradoxes in a system with multiple pre-commitments and timemachines.
You get independence compensation by binding your will to the future, and spend it to change the probabilities of future events.
Such as our example with the Predictor. Once we acknowledge that there are no Perfect Oracles, the situation is simple. You spend independence compensation to control the time machine, and that largely cancels out with by binding your future actions regarding the Predictor.
At larger quantities, this system can produce:
Our probability array $A = \begin{bmatrix} P + L & !P + L \\ P + !L & !P + !L \end{bmatrix}$is the "convolution" (not matrix multiplication, we must use a 4x4 matrix for that to be the correct operation) of other matrices. Two of these are $B = \begin{bmatrix} Y & 1-Y \\ Y & 1-Y \end{bmatrix}$and $C = \begin{bmatrix} Z & 1-Z \\ 1-Z & Z \end{bmatrix}$. Matrix B represents the pre-commitment to either push the button or not push the button, independent of the light. Matrix C represents the pre-commitment to either treat the Predictor as a valid oracle or an invalid oracle. A third matrix is $D = \begin{bmatrix} W & 1-W \\ 1-W & W \end{bmatrix}$ where W is the accuracy of the timemachine.
Except that's not useful at all. There is an interesting correlation between the pre-commitments you can make; you cannot make both at once. The rest is just needless formalism.
The problem arisen is that you have one force (C, the agent's pre-commitment) and another force (D, the timemachine) in opposition. In a classical model, the forces might cancel each other out, and you have an equilibrium. Here, we must have one of the systems win. And the Independence Compensation term will cancel out.
Discussion of multi-timemachine systems is withheld at the current time.
A person has a Predictor time machine. If functions at 50% effectiveness. In other words, a light blinks randomly whether you push a button it not. It is easy to build something that appears to act this way; it need not actually use a time machine so far.
You then spend Independence Compensation on your actions. You commit to either confirming the prediction, or rebutting it. As a result, the time machine becomes more likely to agree (or disagree) with your predictions. This still doesn't need a time machine as the situation is symmetric regarding whether a light or a lack of light starts the procedure.
The situation becomes less trivial once the proper rituals are conducted. It starts to matter whether The System is Measured as whole or as parts.