In a 12- to 14-quart pan (see notes), combine about 6 quarts water, vinegar, olive oil, peppercorns, bay leaves, and allspice. Cover and bring to a boil over high heat.
Meanwhile, rinse artichokes well. Slice off and discard about 1 inch from tops; trim off stems. With scissors, cut off and discard remaining thorny tips from outer leaves.
Add artichokes to boiling water. Return to a boil, cover, and simmer until bottoms are tender when pierced with a fork, 25 to 30 minutes. Drain and let cool. Serve cool or cold.
Nutritional analysis per artichoke.