Place potatoes in a saucepan and cover with lightly salted water. Bring to a boil over high heat, then reduce heat to medium-low and simmer until very tender, about 20 minutes. Drain and return to the saucepan.
Mash together the potatoes, garlic, vinegar and olive oil with a potato masher or a large fork. Continue mixing until all ingredients are well blended. Season with salt to taste. This sauce can be served chilled or at room temperature.