Place the scallops in a small bowl. Add the lime and orange juice and stir. Cover and refrigerate for 5-6 hours, stirring every 20-30 minutes.
Drain most of the excess liquid. Toss scallops with the peppers, avocado, basil and shallots.
Season with salt if desired.
Notes
The avocado should be ripe enough to easily cut but not soft enough that it will become mushy. For best results it should hold its shape when stirred with the other ingredients.