Fill a large pan with water and bring to a boil. Add the artichokes and half of the lemon to the pan. Cover and cook the artichokes until they are barely tender, about 20 to 25 minutes. Drain and set aside to cool.
When artichokes are cool enough to handle pull off the leaves and cut out the fuzzy chokes. Slice the hearts into bite size wedges and squeeze the other half of lemon over the hearts, set aside. Peel and section the oranges discarding the seeds and white pith in a large bowl.
When ready to serve, alternate orange sections and artichoke wedges on individual plates. Garnish with radish slices, olives and a mixture of the olive oil and lemon juice that will be drizzled over the salad. Sprinkle with paprika and salt, serve immediately.