The Arrow's Impossibility Theorem

Arrow's Impossibility Theorem states that no voting system can perfectly convert individual preferences into a collective decision while meeting certain fairness criteria. Specifically, if we want a system where outcomes reflect individual choices, respect everyone's preferences, and avoid dictatorial power, it's impossible to achieve all these at once. In essence, the theorem highlights the challenges in designing fair democratic processes, showing that any method will encounter certain contradictions, such as situations where collective preferences may not align with individual ones, making perfect group decision-making inherently elusive.