hard to make that study work, it presupposes that users (a) understand that their battery life is decreasing and (b) understand that this application is responsible for it (and to what degree). Those are two big if's, it's more likely they'll chalk it up to battery aging than to a malicious application that used to be well-behaved. That doesn't however prove that users don't care - it only takes one article with a headline "Phone draining quickly? Facebook battery usage has increased by XX% the past year and responsible for majority of its users battery drain" to completely swing the pendulum to the other side where more users are deleting your app because of this new reputation, than would proportional to the actual battery drain; but without that trigger the study is not complete.