Gibbard–Satterthwaite theorem

The Gibbard–Satterthwaite theorem states that if you want to vote in a fair way to choose the best option out of three or more choices, there is no way to do it that avoids a certain type of problem. The type of problem is called a "dilemma." Dilemmas happen when there is a group of people who have different opinions about which option is best. In this situation, it might seem like no matter which option you choose, there will be someone who isn't satisfied with the result. The Gibbard–Satterthwaite theorem explains why this will always happen.