The Independence twist originally started in Survivor: The Congo, as the main twist of the season.
ExplanationIndependence: After every two tribal councils, all contestants will be given the choice to declare independence from their tribe. All castaways that choose to declare independence will then form a new tribe. If any of these tribes are diminished to two people or less, then that tribe will be automatically immune from the vote, and the other tribes will compete for immunity.
After the second (or third, or fourth, etc.) time that this twist comes into play, the rules are slightly modified. For the Independents, they will have the option of staying on their tribe, or Surrendering. Surrendering will make the independent contestant join back with one of the two main tribes that started the game, chosen randomly. The other two tribe's members still have the option of declaring independence, but go into the ORIGINAL Independent tribe, instead of a new tribe.
If everyone declares independence, they will be one big tribe, and will be merged until the next oppurtunity, where they may surrender to get out of the merged tribe.
Survivor: The Congo twist: A twist was revealed that for every person that declared independence, idol clues would be sent out to everyone. Idols were hidden at Uhuru, Kupambana, and Tofauti (Indepedent Tribe).
The Independence twist was praised for being unique and tying in with the theme of the season, which was war. It also kept the game from going stale, as a form of a Tribe Switch which would keep contestants on their toes. It also led to the blindside awarded as the best of the season, in the final 10, when the Tofauti Tribal Council led to Maisy's elimination through an idol. All in all, it was seen as a fresh twist to kick the series off with a bang.