Would you rather be free and unaware of all the possible consequences or.? So in the end it begs the question to the player: So it's not whether Elizabeth could be the bird, it's that she is, was and always will be the cage and you will always be the bird guiding the way, unaware of the consequences of your decision. This lead me to believe that even when Elizabeth sees the two brooches, she doesn't make the choice, you as the player make this choice and she has to go with your decision rather than make it herself. With Booker however, he is the one who makes all the choices (albeit minor) in the game's events before it leads up to the ending yet he doesn't know every possible pathway. If you consider Elizabeth as a puppet, she can see all the strings, yet never be able to free herself from the inevitable. Upon further analysis I realised that it wasn't the outcome of the choice they were presenting to us, it was the act of making the choice at all: It's just another of the Luteces' thought experiments. I came to the conclusion that by the end of the game, choosing whichever brooch didn't change the outcome of the ending in any way.

When Elizabeth first discovers the Lutece twins and comes across the two brooches, she is offered one of two brooches and leaves the decision to Booker. I had been thinking about this scene since finishing the game and I came up with a theory.

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