If someone wants to adopt a known song for a choir, one person wears the arranger's hat and officially gets credit for it. There are people who make a living doing this: arranging music for a genre it wasn't intended to be.
In the rock sense, often most of the arrangement happens by the band: partially as the song is written, and partially as each musician learns how they fit into it as they rehearse. Though during recording, I'm sure the producer has tweaks: perhaps harmony vocals are added, perhaps the drums don't come in until after the first chorus, etc.
For pop, often most of the arrangement is up to the producer (unless he hires an arranger) once he/she starts working with the artist. There is a song, perhaps because the producer hired songwriters on behalf of the artist, and decisions need to be made to know what instruments it consists of.
For electronic music, the arrangement is usually embedded into songwriting and sound design. Each song is a living experiment, and I imagine most electronic artists don't know where a song will take them until it's done.
I suppose an analogy of photographers and painters could fit. Rock is like a photographer who captures whatever is in his environment. Pop is like a photographer who adds and removes things to his environment to take a better picture. And electronic music production is like a painter starting on a blank canvas: he might know where he's going when he starts; he often might just try something to see if it develops into something bigger, and he probably throws away a lot of drafts that didn't turn out as intended.