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In the situation you describe, the paper would probably be singly authored, and the author would write something like "Thanks to my advisor _____ and to my colleagues ____ for many helpful discussions" in an acknowledgments section.
If the contributions were more serious, then possibly the author would invite the others to co-author with him/her, and the others would then either accept (and then help write the paper) or politely decline and say "just mention me in the acknowledgments".
At least in my experience, co-authorship carries responsibilities: to help with the writing, the figures, references, dealing with editors and with submission to journals, speaking about the research at seminars/conferences, etc.
For example: Mike Synder, a brilliant biologist, 'supervises' 36 postdocs, 13 research assistants, 11 research scientists, 9 visiting scientists, and 8 graduate students (http://snyderlab.stanford.edu/members3.html - thanks to Lior Pacter for noticing it).
In 2014, he had 42 published papers. How much scientific input do you think he had on each one?
Is there any research showing this standard to be fair? People pay more attention to the first item of a list than to the middle ones, making me think that one's position on such a list could have a small benefit. Less important if there are overall less multiple name papers, which it seems from the rest of your comment, but still a factor as long as multiple names on a paper do happen.
I don't know of any.
Less important if there are overall less multiple name papers, which it seems from the rest of your comment,
Actually, I think multiple authors is far more common than single authors, though I don't know the numbers to back it up. I was responding to a very specific "what-if" scenario of bouncing ideas off someone else, and describing what would happen in that case.
In math, the group sizes are way smaller. A PI might only have 1 or 2 students.
