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, and naming one would hide it. Psephos draws the cycle and marks its weakest link: the number of votes that would break it. HOW MUCH WOULD HAVE TO CHANGE Beside every result is the number of ballots that would overturn it. Under plurality that number is exact. Under Condorcet and instant runoff it is a lower bound, and it is written as one — “at least 10”. A number without that distinction claims a certainty nobody measured. TIES ARE NOT BROKEN Where a rule stops at a tie, Psephos stops with it and says so. Real chambers break ties by lot; a coin toss dressed up as a calculation would produce a winner the ballots did not. UNRANKED MEANS UNRANKED Rank two of five and the other three are not treated as last. That ballot expresses no preference between them, and counting one would put words in a voter’s mouth. SEATS, THREE WAYS Give it a chamber size and the same first preferences are divided by D’Hondt, Sainte-Laguë and the largest-remainder method. D’Hondt favours the largest party; Sainte-Laguë tracks proportion more closely; largest remainder is exactly proportional and can take a seat away from a party when the chamber grows — the Alabama paradox, from a real dispute in the 1880s United States census. Where the last seat is a genuine draw, it says so instead of resolving it. ON YOUR WRIST One line: the verdict, and the winner’s name only when the rules agree. The watch performs no count of its own — the same ballots counted twice on two devices could show two answers, and that would end trust in both. NOTHING IS COLLECTED A secret ballot is only secret if nobody gathers it. There is no account, no room, no invite link, no server. There is no field that ties a ballot to a person, and there cannot be. No network code of any kind, no permissions requested, no analytics, no ads. Each of those lines is a gate that fails the build if it stops being true, not a promise made in a paragraph like this one. Free. No in-app purchases, no subscription. Everything runs on your device, so there is nothing to bill you for. For a board election, a hiring shortlist, a book club, a study of a real ballot, or a classroom. iPhone, iPad and Apple Watch. Six languages. A psephos was the pebble an Athenian dropped in a jar. The pebble is the easy part. What you do with the jar is the whole argument.