Juice one half, reserve the juice, and discard the rind.
Coarsely chop the remaining half (pulp and rind) and reserve.
Combine sugar and water in a medium saucepan over medium heat.
Stir until sugar dissolves, and let syrup simmer until it thickens slightly, about 2 minutes.
Add chopped grapefruit and cook until the grapefruit releases all its juice, about 5 minutes.
Remove from heat and let cool to room temperature.
Combine cooled grapefruit syrup (including chopped fruit), reserved grapefruit juice, Campari, vodka, and sweet vermouth in a large container with a tightfitting lid.
Stir well, cover, and refrigerate at least 1 hour before using.