It does seem odd that such an iconic,historic, sport as wrestling gets dropped but from the news story it looks like a popularity contest and if enough of the IOC board members think badmitten is a better draw than wrestling they vote to keep the olympic games competitive from a marketing standpoint. Hard to imagine that curling gets to be an Olympic sport but not wrestling.
I'm sure the most influential wrestling supporters are working behind the scenes to figure out what,if anything, can be done. Signing a petition or wearing a singlet to work in support can't hurt, but the US Olympic Committee is probably working very hard to do what is possible.
