To hasten cooking time in a busy holiday kitchen I boil the potatoes in their skin in a pressure cooker. You can boil them in a large pot with a lid if you don't have one.
Chill potatoes in the refrigerator, skin, and cube into large bowl.
Pour entire contents of the jar of olives, chopped onions and mayonnaise in with the potatoes.
Stir until the olive juice and mayo are well blended and the olives have begun breaking apart. Cover and chill for 1 hour.
*As Nannan was orating this recipe to me I was shocked at how much mayonnaise she used -- but here in Texas I should have known that most of the old timers seldom consider cholesterol. Unfortunately they usually make the best food so I'll keep using a "tub" of mayo when I make this, and you can feel free to use less if you like.
She does swear the secret is Hellman's brand mayonnaise or a cheap brand which lends more creaminess to the recipe then flavor.