Choice of Elizabeth's pendant??

The ending does not change. However I'm of the belief that the brooch IS significant. Just not in a way that we can be sure about until a DLC. The complete absence of it in the drowning scene is not an oversight I will say that.

Constants. The illusion of choice but ending up with the same outcome.
Lives. Lived. Will live.
Dies. Died. Will die.

Remember?

all the "choice" elements in the game (like at the begining if ur gonna throw the ball at the black couple or at the guy holding a ticket(?) signify one of the core messages/thoughts the game delivers, that is, since there are an infinite number of universes with infinite possibilities, "choice" is just an illusion. since infinity + 1 is still infinity, any "choice" you make is basically insignificant, which is exactly how this game treats "choice" elements.

The game deals with the themes of fate and choice and by the end of the game, you're left with the notion that no matter how many times you choose to go in a specific direction, you inevitably end up going in the other, the one you were destined to go to. Early in the game, it’s established through the Luteces coin flip test that alternate Bookers have been on this mission countless times (at least 122). They have all tried to take Anna either to New York or France many times before, but keep on failing. It just wasn't meant to be.

Regardless of whether Booker says head or tails in the coin flip test, the coin ends up being heads. This is a constant. For some reason it always happens and can’t be changed.

Some things can be changed and these are variables. You can choose to pick the bird pendant instead of the cage one, but the bigger picture remains the same. The characters may choose to say or do something differently, but the play still consists of three acts and ends the same. This is what that pendant scenario is all about.

Can you remember when Anna said something like "You've already made the choice" during the lighthouse part at the end? Sometimes there is a set path and there’s nothing you can do about it.

I understand it to be a theme on the illusion of choice. The game on a few occasions gives us options that, whichever is chosen, result in the same outcome. This is possibly an allegory for how governments, or people in elite power, give the people the illusion of political choice. That is, whichever party one chooses, the political outcome is more or less the same. It creates a sense of freedom and empowerment to placate society, but in the end, it's pure illusion.

Could also be to do with the fact that destiny is preordained. No matter what path we choose, our fate remains the same. Hope this helps.

I also like to think it is a nod to the nature of games themselves. We all play a game differently but we are all steered through the same narrative. We are given choices, we play things different ways, we can have input when we are able to, but ultimately we will travel through the story as it is presented to us and arrive at the end written for us. With the pendant the game has given us a choice that is simply an aesthetic one. It doesn't change any outcome, but it does show that with our choices, our preferences, we have an influence. Even if it is only superficial.

Of course this all plays into the themes of the game.

I think the choice of the pendant is merely to illustrate the theme of being in an infinite loop, aka "Bioshock Infinite." People keep complaining about the game being lazy or non-interactive, but I don't mind a set story that has a plot I can't change as long as I'm invested in it. And boy, did Bioshock Infinite deliver (in my opinion at least).

The first play through I picked the birdcage, and the second play through I picked the bird. Nothing changed, but I think what Elizabeth said was a little different. Is the game being lazy, not in my opinion because there's plenty of other changes that occur which reinforce the theme of constants and variables: things can change, others will stay the same. Another part has Booker choose to wait on Elizabeth or hold a ticket vendor at gunpoint; if you wait, the vendor puts a knife in your hand but if you point a gun at him the scripted shootout happens faster. The only difference is Elizabeth will have to bandage your hand, and you'll have that bandage throughout the game.

These choices represent how ultimately everything that happens is out of Booker's hands. The only reason Booker eventually breaks the cycle is because he eventually gets to a point where Future Elizabeth can teleport him to the future, and then back to 1912 in order to change the future. Before that, Booker kept getting killed before reaching that point; without Elizabeth's interference the cycle would've never been broken.

Even the Luteces aren't totally in control. When Booker acquires his shield, the Luteces remark something like "Wow, it worked that time." Booker responds "Whaddya mean it worked this time?" and the Luteces start discussing how sometimes it works, while other times it kills Booker. It doesn't matter to the Luteces, since they can time travel and are able to keep sending in Bookers until eventually it changes. The ending even reflects this: Booker kills Comstock and decides he doesn't want to be Comstock, but the only way to prevent him from choosing otherwise is to prevent him from choosing at all, which again is where Elizabeth steps in and drowns him. If it wasn't for Elizabeth, Booker would've kept running the loop and if it wasn't for Elizabeth the second time, there would always be a Comstock.

When it comes to the pendant, it's kind of ironic because Booker is making the choice, but Booker's choice doesn't matter. The Luteces can't make a choice, but they'll always be there to provide the variables. Elizabeth is the one who is offering him the choice, and even though the answer doesn't matter in the overall equation it matters to Elizabeth that he even chooses, and Elizabeth is really the one who's choices matter yet she's not the one making it.

Can't be too careful with all those weirdos running around.