Kenneth Arrow proved something devastating in 1951: for three or more choices, NO voting system can satisfy a short list of obviously-fair requirements at once — unless it’s a dictatorship. There is no perfect way to turn individual preferences into a group decision. Here’s one crack you can watch: add a losing candidate and the winner FLIPS. Slide the irrelevant candidate in and out.
Arrow’s Impossibility Theorem: for ≥3 alternatives, no ranked voting rule can jointly satisfy unrestricted domain, unanimity (Pareto), independence of irrelevant alternatives (IIA), and non-dictatorship. Something must give. The instrument shows the IIA failure directly with a Borda count: a set of ballots makes A beat B; add a candidate C that everyone ranks in the middle or last — changing NOTHING about A-vs-B on any ballot — and the Borda winner can flip to B, because C shuffles the points. So the social choice between A and B depended on an IRRELEVANT third option. A fail-loud self-check throws unless the winner can change when only an irrelevant candidate is added. ◆ real social-choice theory, node-verified.
The IIA violation is demonstrated on the Borda rule (every non-dictatorial rule violates one of Arrow’s conditions somewhere); the full theorem is a general impossibility, not a bug in one method — the winner-flips-on-irrelevant-candidate failure is exact.