Deterring unpopular questions in class

Lecture time is a shared resource, but in my experience most professors welcome questions during class.  Once a student (the "questioner") has asked a question, other students are made worse or better off:  if one of these students ("listeners") prefers hearing the answer to the question, he is better off; if a listener prefers that the lecture continue as if the question had not been asked, he is worse off.  Professors rarely have direct information about the preferences of listeners; they know only that the questioner is better off from the answer.  Professors typically answer the question and hope that the questioner constitutes a representative sample; I can attest that this is not always, or even often, the case.

I can think of two methods -- there are certainly more -- by which questions that make listeners generally worse off can be deterred:

• If it is a readily identifiable subset of students asking the preponderance of unpopular questions, other students might take it upon themselves to confront this subset outside of class and request that its member(s) refrain from asking most or all questions that occur to him/them.  Should this "offender" subset not comply with the request, unhappy listeners could go to the professor and request that he act to deter questions from offenders.
• If unpopular questions come from an unpredictable array of students, or if the social cost of confronting the offender subset is high, a technological solution becomes more appealing.  If there were an electronic voting system installed in the classroom (akin to those installed in legislative chambers), students could anonymously and instanteously register their displeasure with a question, and such information could be conveyed privately to the professor.  The professor could then use the count of unhappy listeners as guidance in making a decision to cut short an answer or to explore it at length.

Comments are open (aren't they always?) for other ideas.