if you put a survey on your site, or send people a survey via email, asking them do you think we should do this, probably very few people will respond.

But let us suppose that you have developed a reputation for not being nice, if you propose something nice people will think you are being devious, if you send a survey you won't know how many people actually want you to be nice. But if you can get a petition out there then people will think hey, I can force those not nice people to be nice by putting in my two cents. Now you find out how many people really want you to be nice, furthermore then you can market it later - we heard, we responded, and those people all think hey my voice is important and feel good about themselves and maybe feel good about you and think maybe they really are nice after all?

It is a brilliant piece of marketing really, that will of course be taken over by everyone and ran into the ground and poisoned as a method to the point where nobody will believe honest petitions anymore either - but that is years away.