Little Bighorn is an American event in the Sioux war event chain. It can happen in between to two other events in the event chain, The Sioux Wars and End of the Sioux Wars. It has no other requirements and has a mean time to happen of 12 months.
The event chain is started by the American decision Expedition to The Black Hills.
It removes 5 prestige from 
USA and give all Dakota POPs 10 militancy and consciousness on top of the 8 already given from The Sioux Wars.
Ingame description Sitting Bull and his braves have surrendered, and the Sioux has been defeated. While there will be future battles between the tribes and ourselves, the sharp edge of the Sioux nation has now dulled. Never again will the Sioux be able to muster a force of even comparable size, and the Sioux nation's future will be resigned to the reservations. It is with some sense of mourning that we see the passing of this once great nation into the history books of our young republic.
The description will still say republic even if America has changed its government type. Unlike what the text might hint at, the event will only spark even more Dakota rebels.
The description is exactly the same as the description for the event End of the Sioux Wars.