In the early 1950s, Kenneth Arrow published his PhD thesis where he demonstrated that it does not exist a method of converting individual preferences into a single group preference that is not limited by a 'voting paradox' at some point. Here is a great video explaining in layman's terms how Arrow's impossibility theorem works.
Needless to say how important this idea is for social choice theory and that it gave Arrow a Nobel Prize in economics. Curious fact. Five of Arrow's former students have won the Nobel Prize.