Psephos: Rules of the Vote

Three friends rank three restaurants. You count the first choices and the answer is clear. Then someone counts it a different way — just as reasonable, just as ordinary — and a different restaurant wins. That is not a bug in the counting. It is a fact about voting, and Psephos is built around it. FIVE RULES, RUN AT ONCE Plurality, two rounds, instant runoff, Borda count and Condorcet. The same ballots go through all five, and the app’s first sentence is not a name but a verdict: the rules agree, or the winner depends on which rule you chose. Arrow’s theorem proved in 1951 that no ranked rule satisfies every reasonable fairness condition at once. Psephos does not pick one for you and does not call one correct. SOMETIMES THERE IS NO WINNER A majority can prefer A to B, B to C, and C to A — a genuine cycle, first described by Condorcet in 1785. When it appears, there is no winner to name,…