Cook potatoes in boiling water just until they yield to a sharp knife, about 12-15 minutes once they have started boiling.
In the meantime put another pot of water on medium high heat. Once this pot has started boiling add the eggs and boil for 8 minutes for a slightly soft yellow. Once done place the eggs in ice water bath.
Remove the potatoes to a cutting board and let cool. Slice in half and place in the bottom of a shallow bowl. Mix vinegar, oil and pepper, shake well. Spoon about 4 teaspoons over the potatoes.
In a bowl combine the beans, onion, capers and olives and tarragon with the remainder of the dressing. Spoon this mixture over the potatoes. Peel the eggs and slice them in half. Add them around the perimeter of the bowl. Italian tuna may be added as well in chunks.