Drain yogurt in a cheesecloth-lined sieve for 30 minutes. Place potatoes in a medium pot, and cover with cold water; bring to a boil over high heat. Boil until tender, about 20 minutes. Remove from heat. Drain; run under cold water to stop cooking. Set aside until completely cool.
Cut potatoes into 1-inch pieces; place in a bowl. Add cucumber, olives, onion, and chervil; set aside.
Place drained yogurt (about 1 1/2 cups) in a bowl. Add red-wine vinegar, cinnamon, nutmeg, salt, and paprika; stir until well combined. Pour over potato mixture; stir until potatoes are well coated. Transfer to a serving bowl; serve immediately.