The Noon Position and the absence of Democracy

Decades ago around noon, you could take this picture every day on all ships at sea. When the sun reaches her zenith, she will do this in the south or north (depending on your latitude). Shooting the sun at meridian passage gives a fast and reliable update on your latitude (not on your longitude). You have to calculate at what time the sun passes the meridian, then you shoot the sun and when you see her lowering in your sextant mirror, you know that she had reached her highest point, thus exactly south (or north). Most of the time, the captain and a third mate were shooting the sun simultaneously, sometimes even the chief mate joined them. The biggest question was always: who has the most accurate and correct reading? Democracy is not working on board of a ship, so the captain's readings were always regarded as the most accurate and reliable. Is this still the case today? How about democracy on board ships today? Let's say it this way: all input is welcome, but one man has to make the final decision.
You see the coordinates 53 North 05 East on my T-Shirt? Thats where I live and my noonposition was exactly 6310 nautical miles away from that position where the position of our apprentice Henno was about 9 miles more to the northeast. There is that same old question again: who is right?