Place potatoes in a saucepan with enough water to cover entirely. Bring to a boil and cook over medium high heat for 30 minutes or until tender. Drain, peel and dice while still hot. This is what will make the salad fluffy. Cover and refrigerate until cold.
In a large serving bowl, toss together potatoes, eggs, crabmeat, black olives and carrot. Sprinkle with sugar and stir in enough mayonnaise to moisten. Season with salt and pepper to taste and garnish with chopped parsley. Chill until ready to serve.