I look at it in a similar way to Michael. To me, it's what is the cost or burden to the individual and what is the benefit that the individual or his or her family derives. The burden may be a bit less, especially if you're bitterly opposed to answering some questions. On the other hand, the benefits drop dramatically under this circumstance. We go from having good, reliable information from which governments, individuals, and voluntary organizations can make good decisions, to that being thrown seriously in doubt.
I'd say the burden is similar or will maybe drop a bit, but the benefits drop dramatically. The balance swings very disproportionately.