This is not how it works. Anyone in the Academy can vote on the nominees. The nominees themselves are decided by the people in their specific category.
Each person belongs to one of 17 branches. Each branch nominates for its own category — e.g., editors nominate editors, actors nominate for the four acting categories. Everyone gets to nominate best picture. For the final voting of the winner, all branches vote for everything.
Source: my family is in the Academy