A sensible way to fund public projects
There are lots of worth while projects such as SETI or 'Folding at Home' that use the idle computer cycles of participants.
I'd think that if perhaps half the cycles were used for mining and the rest for the main effort, people would be just as willing to participate.
Maybe pay out 10% of any winnings to the lucky participant whose computer struck paydirt, use the balance to fund the overhead.