It seems like that would reward misinformation. You're saying that people could argue in their small group for a particular position that's not widely-known, but in most of those cases nobody will be there to argue against them, and they can say whatever they want. It would be better if people familiar with the issue voted and people unfamiliar with the issue left that blank on the ballot, instead of making it a lottery of whose supporters end up unopposed more often in small groups.
