When Arbiter of Knollridge enters the battlefield, each player's life total becomes the highest life total among all players.
In a Two-Headed Giant game, each team chooses one person on that team to gain the appropriate amount of life. This basically means that the triggered ability will set the life total of each team to that of the team with the highest life total.
Abilities that trigger when a player gains life may trigger as a result of this ability.
In other multiplayer formats, each player’s life total is set to the highest life total within their range of influence. These changes happen at the same time. For example, if each player has a range of influence of one, and the players in the game are Alice (4 life), Barry (8 life), Carrie (11 life), and Doug (7 life), in that order, then Alice’s life total will become 8 and Barry and Doug’s life totals will each become 11.