In a large pot, cover the potatoes with water and bring to a boil. Simmer over moderate heat until the potatoes are tender when pierced with a knife, about 20 minutes. Drain and let cool. Peel the potatoes and cut into 1-inch pieces.
In a large bowl, mix the hummus with the yogurt, celery, cornichons, parsley and onion. Fold in the potatoes, season with salt and pepper and serve.