It’s indeed hard to pull a definite statement from the documentation only. If we try to draw a conclusion from the general description of the “Reduction” process and similar hints of the documentation, it will always feel like we’re possibly doing too much interpretation.
However, there’s an explicit statement regarding this matter from Brian Goetz who’s quite an authority regarding the Stream API:
If the stream is ordered (such as the streams you get from an array or List), it returns the first element that is maximal in the event of multiple maximal elements; only if the stream is unordered is it allowed to pick an arbitrary element.
It’s a pity that such an explicit statement isn’t made right at the documentation of Stream.max, but at least it’s in line with our experience and knowledge of the implementation (those of us who looked at the source code). And not to forget, practical considerations, as it’s easy to say “pick any rather than first” via unordered().max(comparator) with the current state of affairs than saying “pick first rather than any” if max was allowed to pick an arbitrary element in the first place.
