Hi Dan,
I won't insult you by suggesting that you've never done a long series of rappels and thus don't know why the pulled rope alternates--I'll just say that I forgot the discussion was about ropes of different diameters. I find the very best way of doing long routes (and descending therefrom via rappel), is to lead with two 3/8" ropes: no issues of different diameters to tie or cause troubles with the rappel device; no trail line to manage, and an alternate pull on each successive rappel makes for maximum eficiency in my opinion.
If as you suggest the EDK need be backed up by tying the smaller rope around the larger, we no longer have a perfect bend--we have one that requires a back-up and the extra bulk that that entails.
If you have not seen an EDK roll a little as it is weighted, I congratulate you on having partners who draw it up most carefully as they tie it: not all my partners have been so fortuitous.
I have no idea how long the EDK has been popular in Europe, but in Yosemite I did not begin to see it until the late nineties. Before that I can testify that the popular knot in those parts was the double fisherman.
I would not call all the above-named bends novelty knots: most have existed for longer than climbing has been popular, and the climbing world still has much to learn from the sailing and rigging world. And they've taught us sailors nome neat tricks in their turn.
My favorite bend for rappel ropes is still the Strait Bend, and while I'm indifferent to what other climbers wish to tie, it is the one I will always use. Does a nice job with docklines, too.
Climb safely,
Ben
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