Remove the orange part of the orange skin using a vegetable peeler. Cut these strips into julienne, (small strips 1/16 inch wide and 1 1/12 inches long). Simmer for 15 minutes in a quart of water. Drain. Pat dry in paper towels.
Season the duck cavity with salt and pepper, add a third of the prepared orange peel, and truss the duck. (Roast according to the master recipe in Mastering the Art of French Cooking p. 274)
While duck is roasting, make a sweet and sour caramel coloring as follows: Boil the sugar and vinegar over moderately high heat for several minutes until the mixture has turned into a mahogany-brown syrup. Immediately remove from heat and pour in 1/2 cup of the duck stock. Simmer for a minute, stirring to dissolve caramel. Then add the rest of the stock, beat in the arrowroot micture, and stir in the orange peel. Simmer for 3 to 4 minutes or until the sauce is clear, limpid, and lightly thickened. Correct seasoning and set aside.
Cut the 4 oranges into neat, skinless segments (or supremes) and place in a covered dish.
When the duck is done, discard trussing strings, and set it on a platter. Place it in the turned-off hot oven, leaving the door ajar.
Remove as much fat as you can from the roasting pan. Add the wine and boil it down rapidly, scraping up coagulated roasting juices and reducing the liquid to 2 or 3 tablespoons.
Strain the wine reduction into the sauce base and bring to the simmer. Stir in the orange liqueur by spoonfuls, tasting. The sauce should have a pleasant orange flavor but not be too sweet. Add drops of orange bitters or lemon juice as a corrective.
Just before serving, and off heat, swirl in the butter and pour the sauce into a warmed sauce boat.
Place a line of orange segments over the length of the duck and heap the rest at the two ends of the platter. Spoon a bit of sauce with peel over the duck, and serve.