It honestly seems quite evident and factual to me that the ballot screen brought no benefit in competition at all. It brought just more clicks and confusion during installation. Users who knew nothing about browsers did not benefit from it (in ways I can describe if you want, as my personal direct experience), while users who knew about browsers did not need the thing to choose what they liked.
Fun fact: today I spoke with a client of mine about Chrome and Internet Explorer for about 30 minutes, but as soon as I referred to one of them as his "browser," he asked me "what's a browser?" If he had seen that ballot he would have had no idea what he was deciding on, and probably would have gone with the most familiar logo, which most likely would have been the big blue e.
I have had dozens of clients ask me what a browser was.