1. GREEN GODDESS DRESSING: In a small mixing bowl, beat into the 3 cups of mayonnaise the vinegar, lemon juice, anchovies, tarragon, scallions, garlic, parsley and cayenne. Taste for seasoning and add a little salt if you think it needs it.
2. In a large mixing bowl combinethe shrimp and 1½ cups of the dressing, stirring them gently until the shrimp are well coated. Fill each artichoke cavity with the mixture, mounding it slightly on the top.
3. Arrange the anchovy, if you are using it, in the center of each shrimp mound and chill the stuffed artichokes until ready to serve. To serve, place the artichokes on chilled plates and surround them with the lemon slices. Pass the remaining Green Goddess dressing separately.
