There are unspecified details in this question. Here's one way to do it, chosen because it is quick to set up for any number of affected bones and allows for easy manipulation of the falloff:
The bones damped track a marker bone which is parented to the control, and then we limit their rotation to local X axis rotation only. As the bones become more distant, less of their rotation from a damped track is in their X axis, and so they rotate less and less.
We can easily do this with any number of affected bones; we can select as many bones as we want, then select a bone with the appropriate constraints, and use "copy constraints to selected bones" operation. Alternatively, we can just duplicate constrained bones; the duplicates will keep the constraints. None of the bones need individually tuned parameters.
If we want to change the falloff, we can scale the control in its Z axis to bring the target closer or further from the line of bones, which will change the axes those bones rotate in:
Scaled up and moved along the chain:
However, it's not inconceivable that this doesn't meet your needs because of unspecified details.