The Math of Voting – Arrow’s Impossibility Theorem

Kenneth Arrow proved in 1951 that no voting system can satisfy three seemingly fair criteria: no dictator, unanimity (if everyone prefers A over B, A wins), and independence of irrelevant alternatives (adding a losing candidate doesn’t change the winner). Any ranked voting system fails at least one. This applies to elections, committee decisions, and even search engine ranking algorithms. Arrow won the Nobel Prize in Economics for this result. It shows that democracy, mathematically defined, has unavoidable trade‑offs.