Would be a nice new idea for Civ to be able to push bad great people on other civs.
Great Populist: +1 happiness in your 5 unhappiest cities, -15 relationship with three random civs.
Great Chickenhawk: Declare war on a random civ, -25% war weariness, +100% unit maintenance for 20 turns.
Great Deregulator: -25% on all maintenance, +5 health and happiness in every city.
Great Deficit Hawk: + 10% income, can't buy units or buildings with gold, can't build wonders.
Great Patent Troll: Gain a free technology, unable to use anything that tech unlocks for 50 turns.