When the person enters the elevator and it begins to rise, if the balloon does not fall, then the acceleration of the elevator is less then the acceleration of the balloon (due to buoyancy) if it were unrestrained.

While the balloon is restrained by the string, meaning the string is taught, there is a constant buoyancy force lifting the balloon. This causes the acceleration of the balloon to be independent from the elevator. The string of the balloon can not be used to push the balloon upwards. It can only be used to hold it down.

When the balloon is released the only force acting on it will be the buoyancy force, regardless of whether the elevator was rising or still. If the elevator were falling it would be a different situation, because the string of the balloon will pull the balloon down, imparting a downward vertical acceleration, but that is not part of the question.

@downy bill – Why would gravity cease to act? Free fall doesn’t mean gravity is gone, it is a feeling of weightlessness achieved at terminal velocity because the acceleration due to air resistance and gravity are equal with opposite directions.