v. To attempt to resolve a problem by taking steps that one believes to be futile but are nevertheless necessary so that others are satisfied that an appropriate degree of effort has been expended.
2006
We are accused of being like the madman on the street corner who is waving a dead chicken around his head. "Why are you doing that?" people ask. "To keep the flying elephants away." "But," people protest, "there are no flying elephants." "See?" he responds in triumph. "It works!"
1992 (earliest)
You've waved a dead chicken when you've gone through motions to satisfy onlookers (suits?), even when you're sure it's all futile.