Does Cheating Make Tests Less Informative?

It's immoral to cheat on tests, so they say.  But here's a question: If everyone cheated on tests, would the results be less informative?

Suppose you copy one of your neighbors' answers.  If you copy all of them perfectly, you get the same grade.  That might be hard.  If you copy with mistakes, you probably get a worse grade.  But, that aside, which neighbor do you copy?  What if the neighbor whose answers you copy is dumber than you?  How do you know?  The most effective cheater may be someone who knows the material well enough to recognize a good answer when he sees it.  Maybe he'd get the best grade anyway, but not on every question; and when he sees that his neighbor remembers a certain question better than he does, he knows that's when to copy-- maybe with modifications.

To allow copying neighbors would create incentives to figure out who the smart students were and sit next to them.  But suppose you just know the general consensus of your fellow test-takers.  For example, it's a multiple-choice test, and people take it on computers, and as they do, a projector shows how many people have made each answer to each question.  So you have to think, "20 out of 30 people so far answered 'A' to this one, but I think it's 'B'-- how confident am I?"

Provided the questions are hard enough that the consensus isn't always right, I wonder if this wouldn't allow the best students to distinguish themselves better than the usual, non-cheating exam.  It would mimic real-world cognitive-skills situations better, for one is usually able to observe the decisions of some others before making one's own decisions.