Cook the potatoes, unpeeled, in a large pot of boiling salted water until tender, about 20-25 minutes. Drain and let stand 15 minutes or until cool enough to handle.
Meanwhile, prepare the hard-boiled eggs.
In a separate small pot, bring salted water to a boil, then add the shrimp and boil until they are just cooked through and pink, about 2-3 min. With a slotted spoon, transfer the shrimp to a sieve and set aside.
Finely chop the capers and scallions, then put them in a salad bowl. Pour in the olive oil, lemon juice, and mayonnaise, then mix well.
Peel the potatoes and cut them into 1 cm cubes. Add them to the bowl with the dressing and toss to blend. Let stand 10 minutes. Season to taste with salt and pepper. Add the shrimp and chopped boiled eggs. Serve at room temperature