Choice
From The Matrix Wiki
Choice was both solution and problem for the Architect and the keepers of the Matrix.
The first version of the Matrix was designed as a utopia, which human minds connected to this world could not accept. A second version, created with monsters and basic cause and effect, also proved unsuccessful.
When the program later known as the Oracle aided the Matrix by adding to its programming the power of choice, human minds connected to the Matrix were not only able to accept the artificial reality as their only reality, but feel enabled to make decisions that affected palpable changes in their existence, even if the minds were only vaguely aware of their options.
Choice binds both resistance operatives and programs alike while within the Matrix. Neo is given the choice of two pills to take by Morpheus. One pill would continue his journey into the reality of the Matrix. The Oracle tells Neo that he would have to make a choice to save himself or Morpheus from death. Neo saves his mentor and dies instead, but his mind chooses to live and not accept his death within the Matrix, enlightening his mind of his inherent powers as The One.
Some time later, when Neo encounters the Architect, the program presents The One with two doors: One to the Source to reinsert the Prime Program to reload the Matrix; the second door to return to the Matrix and the possible extinction of the entire human race. Given the requirements that the Architect was attempting to force Neo to select, it would seem logical that the Architect would only leave one door available. However, the powers inherent within the Matrix appeared to require even the creator of the Matrix to offer at least two choices. Despite the Architect's efforts and his previous successes with Neo's predecessors, The One chooses to save his love, Trinity. Neo's choice apparently introduced new choices of which not even the Oracle could foresee their ramifications.
Despite the restrictions that choice could bring, Neo appeared to be the only character that existed within the Matrix with the actual capacity of free will. Other operatives, in the course of their duties, would be stopped by the unstoppable agents. Programs living in the Matrix could not generally manage tasks outside of their assigned purpose.
Some programs, such as the Merovingian, eschew choice, believing that existing within the Matrix is merely a matter of cause and effect, believing that knowledge of the effect of something enables the bearer of the cause with power. He attempts to show this basic principle the Le Vrai restaurant by presenting a young woman there with a dessert that causes her to experience a spontaneous orgasm.
Based on the Merovingian's continued disdain for the Oracle as well as his age as implied by the Oracle, it is probable that the Merovingian was a key figure in the second failed Matrix and its basic cause/effect programming.
The powers of choice embedded within the Matrix programming that enabled it to work was also the cause of its slow centennial deterioration. Approximately every 100 years, the Prime Program must be reinserted into the Matrix programming to reload it, presumably resetting the choice-inducing code of the virtual world and stabilizing it for another century. Neo realized this problem faster than his predecessors did, as the Architect noted.
