I had to go through the book shelf to find this one because I've talked about it before and wanted to share.
Arthur C. Clarke - The Songs of Distant Earth (audiobook)
The wiki unfortunately doesn't go into details enough. Basically the plot takes place on a distant planet after the Earth has been destroyed by a supernova and the society was created by a seed ship. The officials are elected by a lottery and there's a form of direct democracy if my memory serves me right in a passage. I wish I could expand on it more but the book is just amazing and I don't want to spoil it to much for those who are interested. If you have the time I linked the audio book and it's based off a former short story of his with the same title.