Interesting slew of comments here.
When scientists are very united on a particular issue (like many of the issues Ethan described), we average citizens should not get a vote on the matter. Follow the scientists' advice.
When the scientists are not united, then we through our democratic process, should take the path we feel best. Whatever path we take will help the scientists gain more data.
And we have to realize that even 90% of scientists in unity can be wrong. But they are less likely to wrong than average citizens doing their own research. We, as a society, will be making more mistakes with average citizens amassing popular opinion.
In Chapter 8 of my book, I discuss a new government institution called "The Consultancy". This institution will name great minds from the various scientific fields. When the government needs some advice, it refers to the appropriate branch of the consultancy. If the branch is fairly united, their opinion becomes government opinion. If not, the government should probably do some risk/reward assessment to chart the better path of two or more alternatives.