Project I: There is one critical fact about the criminal justice system that nobody knows--the rate of false positives. Of people convicted, how many are innocent? Opinions about issues such as the death penalty, plea bargaining, admissable evidence, and much else depend on that fact. So far as I know, there is no serious research that would let us estimate the rate--only anecdotal evidence.
I have a solution to that problem. Find a jurisdiction friendly to research. Identify all convictions in that jurisdiction from before DNA testing for which tissue evidence survives, such that testing it should provide strong evidence for or against guilt. Test all of it--or if that exceeds your budget, a random sample. See how many of those convicted turn out to be innocent.
It isn't a perfect test, of course, since suitable cases are not a random sample of all cases. But it would give us at least a first approximation of an answer. If the rate turned out to be one in a thousand, the case for the death penalty (and many other things) would be a lot stronger than if it turned out to be one in three.
Of course, a good deal of such testing has been done by innocence projects around the country. But it focusses not on a random sample but on prisoners whom there is good reason to suspect are innocent.
Project II: Low volume toilets are supposed to save water. They also, at least in my experience, tend to get stopped up more than ordinary toilets. Someone should do a statistical study relating the fraction of low volume toilets in an area to both water usage and expenditures on plumbers. Assuming water is saved--the process of getting a toilet unstopped can require multiple flushes--it might turn out to be very expensive water.
And yes, this was written after yet another session applying a plumber's snake to a low flow toilet.