Joseph Smith taught a surprising amount on the principles of government. Unfortunately, very little of his ideas are evident in the governments of areas where the majority of people profess to believe he was a prophet of God.
Over a year ago, a man named Marc Martinez did an excellent job writing a ~200 page summary of these ideas, as well as those of later Latter-day Saint leaders. The ideas in the book are worth thinking about for all people, and the book is well-written and easy to read.
Marc is not a scholar by trade, but a carpenter. I mention this because I know from experience that it is not easy to write books when you have a full-time job to attend to that has little to do with your writing. To me, if someone in such a situation is willing to spend the time involved, and manages to produce something worth reading, it catches my attention more than someone doing it to earn a paycheck. Also, I have a bias towards carpenters who set out to live and teach the gospel.
Marc recently made the book free to download, and there are print copies available on Amazon for the print cost. I highly recommend this book, and I hope those of you who live in predominately LDS areas find it to be something you can pass along to your neighbors and friends.
This part is not from his book, but my own caveat to it: The United States will be utterly destroyed. But when the kingdom of God arises, which will replace it geographically, it will operate according to principles that either resemble or can be best prepared for by living according to the good portions of the government God inspired the Founding Fathers to erect.