The power you all turned down....
You would have been able to do a twist on Exile Island. You would have been able to remove one player from a tribal council vote of your choosing and conversely, select a member of the other tribe to come vote with your tribe. In other words, you could've orchestrated a two vote shift, removing an enemy's key vote and replacing it with the vote of an ally from the other tribe. Such a power, played properly could change the entire course of the game. I would've taken this over immunity any day.
Hype Survivor lesson: Fortune favors the bold.