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Not just the introductory right, there are numerous variation for prayers all through the mass. There are 13 Eucharistic Prayers approved by Holy See for use in the United States.src
Why are there three options?
Because even though all Mass are same in essence, people are invited to meditate upon a certain theme in each mass. Prayers differ depending on the theme of the mass.
Which authority determines which option to use? Is this the presider's choice alone, or does one in authority above the presider make this determination?
Answer is both. Mostly it is the presider's choice. But he has to follow the guidelines in the General Instruction of the Roman Missal Chapter VII. The bishop can make changes but all changes have to be approved by Congregation For Divine Worship And The Discipline of The Sacraments