Place the potatoes in a large pot and cover with cold water by about 1 inch. Stir in 1 teaspoon of salt. Bring to a boil, then reduce the heat and simmer, uncovered, until fork-tender, 10 to 15 minutes. Drain the potatoes and when cool enough to handle, slice in half or quarters.
Refill the pot with water, bring it to a boil, and set a bowl of ice water nearby. Drop the green beans into the boiling water and blanch for 2 minutes. Drain and immediately immerse in the ice water. After 1 minute, drain and place on a kitchen towel to dry.
Assemble salad with the potatoes, green beans, white beans, eggs, artichokes, radishes, tomatoes, olives, and capers. Drizzle generously with the lemon vinaigrette. Sprinkle with parsley and season to taste with salt and pepper.