Why does the V-22 Osprey have twin stabilizers?
The V-22 was designed to be operated by the US Marine Corps on-board US aircraft carriers. Any airplane that operates off of a carrier has to be relatively compact in order to be able to fit onto the carrier's elevators and short enough to fit into the hangar deck. A twin tail spreads the elevator authority over 2 smaller control surfaces instead of 1 big surface, making the aircraft shorter, and the placement at the ends of the elevator reduces its overall size footprint. 

The other benefits of a twin tail are a reduced radar cross section (the V-22 needs all the help it can get there) and increased redundancy as if one tail is damaged there is another one available. The wide placement of the stabilizers reduces the chance that enemy fire will take out both at once.