In a recent interview by Kotaku, Irrational Games’ Ken Levine stated that the choices taken by the player in Bioshock Infinite will greatly affect the story. By presenting a wide variety of choices to select from, no play-through of the game will ever be the same.
Additionally, Ken Levine mentioned how much influence the player would have on Columbia at the start of the game. While in Bioshock the player entered into a Rapture that was already torn by civil war, Booker (the protagonist of Infinite) would be in Columbia from the start, and his actions and presence would spur most of the changes that occur at the floating city.
“Here, [the player is] really coming in and they’re the ones really getting the party started this time, whether they intend to or not. The world really erupts based upon them being there, not through anything they wanted to do, but as the nature of the situation.”
Although Bioshock had a similar feature where a player’s actions would cause the story to slightly change and determine a good or bad ending, it didn’t really affect the overall plot. Bioshock Infinite looks like it will change this by offering the player a way to mold Columbia in their own way. I guess we’ll find out when the game is released.