Cut away the peel and pith from the grapefruit and remove the fruit segments.
Put 6 segments on one side for garnish.
Cut the remainder into small pieces and put into a bowl.
Halve the avocado, remove the pit, skin and slice the fruit.
Mix with the grapefruit pieces, shrimp and a little mayonnaise.
Arrange a little finely shredded lettuce in individual glasses or on small dishes, top with the avocado and shrimp mixture and garnish with the reserved grapefruit segments.