As revealed by Ilana, a candidate is a person who is capable of replacing Jacob as the protector of The Island and, in particular, The Source. The exact criteria of what constitutes a candidate has not been revealed, however, they seem to have a special protected status among The Others, as evinced by Dogan's insistence that the remaining candidates remain inside The Temple where they will be safe. Ilana notes that there are only six candidates remaining in the episode "Ab Aeterno", however, since that revelation two candidates, Sayid and either Sun or Jin, have died, bringing the total number of remaining candidates to three. They are Hugo "Hurley" Reyes, James "Sawyer" Ford and Jack Shephard.
All the currently surviving candidates (and several past candidates) have made physical contact with Jacob while off the Island. He put his hand on Hurley's shoulder in a taxi-cab outside of prison after he was released. He touched Sawyer's hand when he gave him a pen at his parents' funeral. He touched Jack's hand by a vending machine when he gave him a candy-bar after his first solo surgery.
It is unknown if Jacob's touch is the criteria for assigning a candidate, marking the candidate, protecting the candidate, or if there is another reason for the physical contact.
Candidates' names often appear in lists. Charles Widmore indicates that he has a list of candidates' names when he takes them prisoner on Hydra Island. Dogan extracts a list from an ankh that Hurley had in a guitar case given to him by Jacob. The candidates' names are written on the wall of a Cliffside Cave, and the names of the candidates are written on a rotational dial in the lighthouse.
According to the lists that the viewers are shown, no first names have been used. This causes ambiguity about a character's status when the character shares a surname with another character. For instance, the name Kwon can refer to either Sun or Jin. The name Linus could be either Ben or Roger, and the name Rousseau could be either Danielle or Alex.
In the episode "Lighthouse", Hurley and Jack visit a lighthouse, in which a dial that indicates the rotation of the beacon has a list of names written upon it, each name corresponding to a degree value. If the list completely corresponds to the rotation of the dial, then there were originally 360 names on the list of candidates. However, this cannot be verified, because the entire dial was never shown, and Jack destroyed the dial in a fit of confused anger. In the episode "The Substitute", Sawyer and The Man in Black visit a cave, in which the names are written on the wall, along with a number.
It has been observed that there is a correlation between the names and their number in the cave and the names and degree numbers in the lighthouse. For instance, the name Shephard is written at 23 degrees in the lighthouse, and is written as 23-SHEPHARD on the wall of the cave.
In both the cave and the lighthouse, names are crossed off the list to indicate that a particular individual is no longer considered a candidate. Candidates are crossed off the list when they die, or achieve another purpose in life. For instance, Kate's name was crossed off the list when she adopted Aaron Littleton. Jacob is the one who decides who are candidates, and terminates their candidacy when it becomes unlikely they'd accept the mantle of protecting the Island. Although The Man in Black was shown to cross off John Locke's name after his death. (The Substitute)
As Jacob told Kate, however, crossing a candidate's name is not permanent. "It's just a line of chalk in a cave. The job is still yours if you want it". (The Candidate). So apparently crossing off names is more of an organizational tool for Jacob rather than actually symbolic of candidacy termination, unless the Candidate has died.
A partial list of candidates can be gleaned from the wall of the cave from "The Substitute" and the dial from "Lighthouse". The following tables contains the information currently available. It should be noted for the sake of honesty and objectivity the characters specified in the comments section of the following table are only the most likely matches to the names, although in many cases (as with Shephard, Reyes, Sawyer, Locke, et. al.), it's so extremely likely, that it's almost a certainty. However, the only conclusive match will be when Jacob's replacement is finally selected.
There does not appear to be any reason for the order in which the names appear, with the exception that the most likely candidates were attached to numbers which have played a significant role in the overall story arc.
|2||LaCombe||Member of Danielle Rousseau's science expidition|
|4||Locke||John Locke - Survivor of Flight 815|
|8||Reyes||Hugo "Hurley" Reyes - Survivor of Flight 815 (Became a Protector of the Island)|
|14||Pryce||One of The Others|
|15||Ford||James "Sawyer" Ford - Survivor of Flight 815|
|16||Jarrah||Sayid Jarrah - Survivor of Flight 815|
|20||Rousseau||Either Alex or Danielle|
|23||Shephard||Dr. Jack Shephard - Survivor of Flight 815 (Became a Protector of the Island)|
|29||Brennan (Lighthouse)||Appears as number 35 in the cave. A member of Rousseau's science expedition|
|32||Rutherford||Shannon Rutherford - Survivor of Flight 815|
|35||Brennan (Cave)||Appears as number 29 in the lighthouse. A member of Rousseau's science expedition|
|42||Kwon||Sun-Hwa Kwon or Jin-Soo Kwon - Survivors of Flight 815|
|48||Stanhope||Either Harper Stanhope or Goodwin Stanhope. Members of The Others.|
|51||Austen||Kate Austen - Survivor of Flight 815|
|58||Burke||Juliet Burke - One of The Others|
|62||Inman||Kelvin Inman - Member of the DHARMA Initiative|
|90||Troup||Gary Troup - Survivor of Flight 815|
|101||Faraday||Daniel Faraday - Member of the Kahana Crew|
|102||Montand||Member of Rousseau's science expedition|
|104||Lewis||Charlotte Lewis or one of her parents: either David or Jeanette - Members of the DHARMA Initiative|
|108||Wallace||Unknown character. This is the only significant number that doesn't correspond to a main character.|
|109||Friendly||Tom Friendly - Member of The Others|
|117||Linus||Either Roger or Ben (DHARMA & The Others, respectively)|
|124||Dawson||Michael Dawson - Survivor of Flight 815|
|131||Jackson||Scott Jackson not to be confused with Steve Jenkins - Survivor of Flight 815|
|140||Lewis||Charlotte Lewis or one of her parents: either David or Jeanette - Member of the DHARMA Initiative|
|171||Straume||Miles Straume - Member of the Kahana Crew|
|195||Pace||Charlie Pace - Survivor of Flight 815|
|226||Carlyle||Boone Carlyle - Survivor of Flight 815|
|233||Jones||American Solidier who brought Jughead to the Island.|
|285||Jenkins||Steve Jenkins, not to be confused with Scott Jackson - Survivor of Flight 815|
|301||Mars||Edward Mars - Survivor of Flight 815|
|313||Littleton||Claire Littleton or Aaron Littleton - Survivor of Flight 815 and her son born on the Island.|
|317||Cunningham||American Solidier who brought Jughead to the Island.|
|321||Fernandez||Nikki Fernandez - Survivor of Flight 815|
|335||Henderson||Rose Nadler nee Henderson - Survivor of Flight 815|
|337||Martin||Karl Martin - member of The Others|
|?||Chang||Pierre Chang or Lara Chang - Member of the DHARMA Initiative|
|?||Goodspeed||Either Horace, Amy, Olivia Goodspeed or Ethan Rom nee Goodspeed. Members of the DHARMA Initiative & The Others|
|?||Pickett||Danny Pickett - Member of The Others|
|?||Sullivan||Survivor of Flight 815|
It should be noted that Frank Lapidus was identified as a possible candidate by Bram, although his name was not seen in either the lighthouse or the cliffiside cave. However, there are many numbers that are unaccounted for, it's possible that his name appeared in both the lighthouse and the cliffside cave, but simply never made it to the camera.