I have attached a a video and an svg file where I want to arrange a few text objects. The objects are already placed roughly in numerical order across two rows and three columns. When I click arrange, I would intuitively expect it to simply adjust vertical placement of the "3" and "1" while keeping the order intact. However, when I click "arrange" it swaps the places of the "3", "4", and "5". Why does this happen? How can I lay out my objects in a way so that the arrange functionality does not get confused and swap the places of objects, but just arranges them in a tidy grid, as the name implies? Additional clicks keeps swapping tiles for a few rounds until it reaches a steady state where additional click does nothing.

That's interesting. I haven't figured out that logic yet.

Thanks for looking into it @TylerDurden ! One clue I found is that when organizing imported bitmaps, the organization depends on the sort order in the open file dialog of the files that are being imported. I am not sure if that applies here, maybe the creation order of the objects matter? This would still not explain why they are resorted upon pressing arrange a 2nd and 3rd time. 

I did not see the repeated resorting behavior here (92.2), But I don't yet grok why it rearranges at all, rather than spacing and aligning with minimal movement.

Yes, spacing and aligning with minimal movement is what I would expect too. And sorry for not posting the my inkscape version, I'm on Inkscape 1.0 (4035a4fb49, 2020-05-01) with Pango version: 1.44.7,on Arch Linux 5.7.7-arch1-1
 

After raising this in the chat I was encouraged to open an issue, which you can find here https://gitlab.com/inkscape/inbox/-/issues/3243

If you get a response that provides any insight into the algorithm used, please can you post an update here. It would be a useful bit of knowledge for us old-timers to have for when this next comes up ;)