I don't want to set multiple marks in the same position though.  I just want to be able to know in which buffer I most recently set a mark.  I expected that the first element in global-mark-ring would tell me, but it doesn't, not reliably, because if the mark already happens to be at the place I run set-mark-command, the ring is not updated, and the first element may refer to some other buffer.  That may be the "correct" behavior by some standard, but it doesn't match the documentation.