Clip first quick draw with both rope strands when using half rope technique

Thank you very much for your academic  paper Richard!

So a little hop for a soft catch should or shouldn’t be done with one or both strands? What ever happened to the dynamic belay? I am so confused.

Hopping for a dynamic belay is necessary only when using a static belay device like a GriGri. When using an ATC-type belay device you can control the rope passing through the device and thus brake dynamically. More over, hopping is nearly impossible when tethered to the belay station on multi-pitch climbs. So, if you want to be able to perform a dynamic belay in that situation, you can’t use a GriGri. 

climbs sometimes wrote:

always hop, always give a soft catch 

There are several things in climbing you should ALWAYS do.

This is not one of them.