Score skin in a crosshatch pattern just through fat of ducks, making sure not to cut into meat. (This will release fat while cooking, and keep the skin crispy.) Rub with 2 teaspoons of the salt, and chill, uncovered, 8 hours or overnight in the refrigerator.
Place potatoes and cold water to cover in a large saucepan; bring to a boil over high. Reduce heat to medium, and simmer until fork-tender, about 10 minutes. Drain and spread onto a baking sheet to dry.
Let ducks stand at room temperature 20 minutes. Preheat oven to 450°F.
Place ducks, breast side up, on a wire rack in a rimmed baking sheet lined with aluminum foil. Roast in preheated oven 45 minutes.
Remove from oven, and lift rack from baking sheet, and set aside. Carefully skim fat from juices in baking sheet, and discard. Spread potatoes in a single layer in juices on baking sheet. Place ducks, breast side up, on potatoes. Reduce oven temperature to 350°F, and roast until a thermometer inserted in thickest portion of duck registers 180°F, and potatoes are crisp and tender, 30 to 35 minutes. Let ducks stand 15 minutes before serving.
Combine potatoes, parsley, capers, and remaining 1 teaspoon salt in a large bowl, and gently stir together. Let guests slice their own duck with crispy skin. Serve warm with potatoes.
The Walrus and the Carpenter, plus others, Seattle