Arrow's theorem on social choice

Arrow's theorem states that no voting system can perfectly convert individual preferences into a fair, collective decision while meeting all desirable fairness criteria. Specifically, when ranking options, any system will either be unconstitutional, biased, or inconsistent — like ignoring individual preferences or allowing tactical voting. This means there's no perfect way to aggregate choices that always respects individual wishes, maintains fairness, and avoids paradoxes. The theorem highlights inherent limitations in designing a completely fair and logical method for group decision-making, underscoring the complexity of achieving perfect collective choices in democracy.