Electronic – Should cable shields be connected to earth ground, or to power supply negative

What you have here is this:

^{simulate this circuit – Schematic created using CircuitLab}

It may be most advantageous to tie the shield to the case, the goal of a shielded cable is to take electric fields that might capacitively couple into the signals you wish to shield and shunt them someplace else. Since the isolated supply is most likely capacitively coupled (isolated) to the box tying the shield to the isolated supply is not going to provide a good pathway to shunt currents away from your signal, it could also create common mode problems if a large current is moving down the shield. If you tie the shield to the chassis ground, the currents that impinge across the will flow down to ground away from the signals you want to protect.

It really depends on which is the lesser of two evils, there are circumstances where one would be better than the other, I'm talking about the general case. Cable shielding is about controlling currents on the shield. Typically in my experience tying the shield to the case is best, but I've also seen a few cases where it isn't.

If your requirement is also having the shield isolated then tie it to the powersupply ground.

A second thing to note is what is tied on the other end of the shield, because if the shield is tied on both ends, there can be currents that flow from ground loops and if you get that, the current can inductively couple and create noise in your signals inside of the cable. In a general sense, tying the shield on both ends to ground is bad for this reason.