Some passing thoughts...
By statisticians of course. Statistical science is a highly developed area -they can calculate how many samples you need to acquire a given degree of accuracy. This means that you can achieve an arbitrary degree of accuracy. I would settle for 99.9% accuracy, but if you wanted 99.999% or better, the statisticians will tell you exactly how large your jury should be. Now I feel that I should point out that when I use the term jury, I don't mean it must be a restricted size like a courtroom jury -'jury' just means a group of people gathered to make a decision. To achieve an extremely high degree of accuracy might require a large auditorium (or maybe even a stadium) full of people. Of course, because of modern technology, there is nothing that necessitates these people all be gathered in the same room.
Statisticians you say? You seem to have greater faith in statistics than I do. I side with the guy (or girl) who said: "There are three types of lies - lies, damn lies, and statistics."
Statistics are one of the easiest things to manipulate while still maintaining the facade of "science". Just ask
Darrell Huff. Statisticians are not objective and uninvolved superhumans, they are just as vulnerable to bias as anyone else. And nothing would be more obviously open to the abuses of bias than their choices of what sort of population would be "statistically significant" for the whole country. You could spend 4 years arguing jury selection!
Hey, here's an idea - to achieve an even more extremely high degree of accuracy, why don't we expand beyond the stadium and just allow everyone in the country to vote? Then we wouldn't have any arguments about statistics lasting into forever.
Who decides what the relevant issues are now? You'd be hard pressed to make a system that is worse than the one we use now at delivering important information to people during election time. I really don't care how many times Mr.X kissed a baby, but if our media was a reliable indicator, that's all that the voters care about. Delivering info on relevant issues is a strong point of election by jury, not a weak point. The specifics would have to be worked out, but almost any formulation would outdo our current system. Consider the following. Each party has a candidate speaker deliver a presentation. Following this is a debate of arbitrary length with questions asked by the jury members themselves. We have debates of party leaders now, but here are some advantages the system I propose holds. The debate is not filtered through a news channel. The debate is delivered to effectively 100% of the voter population. The topic of discussion is generated entirely by the voter population, and any issue that is relevant enough to be statistically significant is addressed.
Who decides what the relevant issues are now? Everyone does for themselves. People make-up their minds in regards to what they care about, and they find out more if they wish. It's called personal freedom. People are free to be idiots, unfortunately, but free nonetheless.
The advantages of debating in a jury election I will grant you. But I wonder - if you need a stadium to represent the whole population, then will everyone in that stadium get a chance to ask their question?
Honestly David, are you really going to tell me that this is less controversial, and more difficult to manipulate, than a general election?