Robin Ferrier, who leads our Capital Communicators Group, asks this question she hears from skeptics: What if commenters on our blog leave negative comments?
And my answer, largely, is: What would you have done before? Social media platforms only change the game in that they make it easier for people to give you feedback. The fact that some of it is negative hasn't changed--in most cases, the only difference is that you didn't hear the negative feedback before. Now that you can, it's an opportunity to represent yourself. Put another way: When people are talking behind your back, it's tough to respond. When they share their negative feedback with you, the chance to listen, respond and listen again opens up.
I also find that questions like this are common objections put up by skeptical folks unfamiliar with social media. So if you get this question, take the time to orient your questioner. Share an example like Bill Marriott's post about the comments on his controversial decision to make all his hotels smoke-free, worldwide. And take the time to brainstorm internally about how negative comments will be handled--answering them and leaving them up is a better practice to follow.