The concept of choice acknowledges multiple alternatives, including the consequences of what we choose.
The first version of the Matrix was designed as a utopia, but the humans rejected this simulation. In the Nightmare Matrix there were monsters and the beta operated on a format of causality, but still proved unsuccessful. The Merovingian was a key figure in the Second Matrix . When the Oracle introduced the component of choice in the third version of the Matrix, it was both a solution and a problem for the Architect to keep the Matrix stable.
The human minds connected to the Matrix were not only able to accept the simulation of reality as their only reality, but felt enabled to make decisions that affected palpable changes in their existence, even if their minds were only vaguely aware of their options.
Choice binds both Resistance operatives and the machines alike within the Matrix. Neo is given the choice of two pills to take by Morpheus. The Redpill starts his journey into the reality of the Matrix, and the Bluepill returns him to The Matrix.
In the First film The Oracle tells Neo that he would have to make a choice to save himself or Morpheus from dying. If Neo choose to save Morpheus, he will die instead. Neo chooses to live and not accept his death within the Matrix, enlightening his mind to the inherent powers of The One. Neo seems the only character that existed within the Matrix with the capacity of free will. Other operatives would be stopped by an agent. Programs living in the Matrix cannot execute tasks outside of their assigned purpose.
In the Second film Neo encounters the Architect, at which time presents Neo with two doors: One to the Source to reinsert the Prime Program and reload the Matrix; the second door returns to the Matrix to save Trinity, but includes the possible extinction of the human race. The makeup of the Matrix inherently require the Architect to present Neo with two choices he is forced to select. Neo justifies his reason for returning to the Matrix for a single human. Despite the Architect's efforts with Neo's predecessors, The One chooses to save Trinity. Neo's choice included ramifications which not even the Oracle could foresee.
Some programs, such as the Merovingian believes that the world operates in cause and effect. He attempts to show this basic principle at Le Vrai by presenting a young woman there with a dessert that causes her to experience an orgasm. To demonstrate that we are slaves to our drives. The Merovingian continued existence across versions of the Matrix continues to disdain the Oracle.
The powers of choice embedded within the Matrix that is presented to the One, as the unbalanced equation that causes the simulations' inevitable deterioration. Approximately every 100 years, the Prime Program must be reinserted into the Matrix programming to reload it, to reset the virtual world to stabilize it for another century. The Architect notes that Neo realized this problem faster than his predecessors did and reached his conclusion based on his love for Trinity.
Agent Smith: Why, Mr. Anderson? Why, why? Why do you do it? Why, why get up? Why keep fighting? Do you believe you're fighting for something? For more than your survival? Can you tell me what it is? Do you even know? Is it freedom? Or truth? Perhaps peace? Could it be for love? Illusions, Mr. Anderson. Vagaries of perception. Temporary constructs of a feeble human intellect trying desperately to justify an existence that is without meaning or purpose. And all of them as artificial as the Matrix itself, although only a human mind could invent something as insipid as love. You must be able to see it, Mr. Anderson. You must know it by now. You can't win. It's pointless to keep fighting. Why, Mr. Anderson? Why? Why do you persist? Neo: Because I choose to.”
― The Final Battle