Place potatoes in a large pot, and cover with water; bring to a boil. Reduce to a simmer, and cook until soft when pierced with the tip of a knife, about 30 minutes. Drain, and allow to cool slightly. Peel potatoes, and slice into 1/4-inch-thick slices.
Combine potatoes, onion, water, vinegar, sugar, and salt in a large bowl. Toss gently between two large bowls, trying not to break up potato slices. Let stand for 10 minutes. Add mayonnaise; mix gently between two large bowls until well combined and creamy. Refrigerate for at least 2 hours; the mixture will thicken as it stands. Garnish with parsley and/or sliced hard-boiled eggs, if desired.