There Are 360 Candidates by Magnus Hanso

This is kind of a simple concept, but there are 360 candidates. 1 candidate for every bearing that the lighthouse mirror could be set to, as each number had the name of a candidate inscribed beside it.

Did you catch the Easter Egg? Austen was #51 on the lighthouse wheel, and not crossed out.

If we now assume that the cave was the MIBs as some have theorized, this would mean that MIB is unaware of Kate's candidacy as the #51, as he showed Sawyer the remaining candidates and Kate was not one of them listed on his wall.

This must mean one of three things, either the names represent bloodlines, there are several rounds of the “game” that is being played, or there are several "iterations" of a loop going on. Since we recognize the names of so many of these 360 candidates, I think it's fair to assume that there are 15-25 candidates per generation. This makes about 18 generations, which would mean this current “round” or “iteration” has been going on for somewhere around 360 or so years. We have been lead to believe that Jacob and MIB have been on the island for thousands of years, so this is why I think that the 360 is not a complete list of everyone who has ever been a candidate.