How to Make It
Using a mandoline or sharp knife, slice the potatoes 1\8 inch thick. Put each kind of potato in a separate bowl of cold water.
In a small bowl, whisk the oil with the vinegar and season with salt and pepper. In a medium saucepan, cook the red potatoes in boiling salted water until just tender, about 5 minutes. Using a slotted spoon, transfer the potatoes to a bowl of ice water to stop the cooking; remove and pat thoroughly dry. Put the potatoes in a medium bowl, add 2 tablespoons of the vinaigrette and toss. Repeat the process first with the white potatoes, then with the blue.
Arrange the potatoes on a large platter, keeping the 3 kinds separate. Drizzle with some of the remaining vinaigrette and serve.