Most a cappella groups will claim they perform the music their fans will most enjoy, and most group will probably, honestly, have the intention of doing so. But do they know that they're hitting the right notes? A group that wants statistical data to back their claims, and that wants to open a true dialogue with fans might consider putting Survey Monkey to work.
Since its inception in 1999, Survey Monkey has evolved into the Internet's predominant mode for collecting feedback, gathering opinions, and organizing such data in useful ways (the company makes charts and tables readily accessible to help process data). So how could an a cappella group make use of this service?
As I alluded to above, one avenue is song selection. Put individual songs, artists, or genres against each other and see what supporters would vote for in terms of what they're most interested in hearing. Leave some free response space available as well to gather fresh, new ideas.
Beyond song selection ask about the venues where you perform, the times and days when you schedule shows, how people learned of your group, what they think of your attire, if they want more or less choreography. You shouldn't necessarily ask questions for areas in which you aren't open to changing (for example, an all-male group probably shouldn't ask if people would prefer that they have women join them, unless they are seriously considering going co-ed), but any areas that are up for debate are worth asking about.
In terms of getting the survey out, a combination of emailing known fans or the groups email list, plus advertising the survey through the group's website, Facebook page, Twitter and other means is as good of a way as any of spreading the word. A small prize incentive (free CD, serenade from the group) from a randomly selected survey responder will only sweeten the deal.