1. Place potatoes in a large pot of salted water and bring to a boil. Cook until tender, about 10 minutes. Drain, let cool slightly, cut in halves or quarters; transfer to a bowl. Toss with olive oil and lemon juice. Stir in tuna, tomatoes, olives and parsley. Season with salt and pepper.
2. Arrange arugula on 4 dinner plates. Spoon potato-tuna mixture over arugula and serve.