Gibbard-Satterthwaite Theorem

The Gibbard-Satterthwaite Theorem states that in any voting system where voters choose from three or more options, it’s impossible to design a method that always accurately reflects true preferences without someone having an incentive to manipulate their vote. In other words, every voting method can be exploited or strategically influenced, making it impossible to ensure perfectly fair and truthful outcomes in complex elections. This theorem highlights inherent challenges in creating completely honest voting systems when multiple choices are involved.