Re: Updated the FAQ
Edit: Nevermind. I have continued the experiment, and order of construction appears to be the deciding factor. The ship that was built first gets repaired first.
Edit2: Grr. It's a bit more complicated than that apparently. Hold on, this explanation is going to get technical and includes some suppositions about the inner workings of the game. It appears that on construction each ship is assigned a unique ID, possibly an index into an array of ships, that never changes. This ID starts at 1 or 0 for the first ship, and the lowest available ID is assigned to each new ship on construction. When a ship is destroyed (scrapped in my test game), its ID is freed and available for another ship. Repair order of ships appears to be determined exclusively by this ID number, with the lowest ID ship repaired first. In practice, once ships start being destroyed irregularly (i.e. some stay around, others don't; typically happens first when you're regularly building both warships and colony ships), repair order is very difficult to predict or influence with any great degree of accuracy.
Edit: old theory, discredited now. See above. I have just discovered a hidden factor in determining which ships are repaired first: experience. The most experienced damaged ship in a sector will get top priority for repair regardless of what your repair priorities set in the empire status screen are. The repair priorities you set are only used as a tiebreaker when ships have equal experience and to determine the order of components repaired within a single ship.
I discovered this recently when I set repair priorities specifically to repair a damaged minesweeper first (putting Unit Launch at the top, with minesweepers being the only "Unit Launch" components I use right now), only to discover the next turn that the two damaged warships present were repaired first. I then ran a test game with the following series of events: build two ships with just engines; retrofit one with a weapon (moved weapons to bottom of repair priorities) and the other with several extra crew quarters, move both to same sector with inadequate repair ability; the weapon was still not repaired; retrofit both back to base design, send one to ship training center for one turn; retrofit trained ship with weapon (again, weapons are at bottom of list) and other ship with extra crew quarters, send both to repair center; trained ship was repaired first, even though its only damaged component was at the very bottom of the priorities list while the other had six components at the very top of the list (vehicle control).
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