The solution to NIMBY's seems simple... "We would like to put a power line through your village. Here are the plans. We will to give every resident £400 to compensate them for the trouble, and it will only happen if at least half the residents vote yes. If the plan goes ahead, all voters will be eligible for the £400, even if you vote no.".
It turns out most people don't really care about a power line, but do like money. You won't have to offer much money to have a majority saying yes.
