Photo credit: Commonwealth Secretariat, Nigeria Elections 2019 | https://www.flickr.com/photos/comsec/47206819721/in/photostream/ Democracy, in its most familiar form—"one person, one vote"—rests on an intuitive appeal. It feels fair. Yet mathematicians and social choice theorists have spent decades demonstrating that this intuition is mathematically flawed. The claim that "democracy is impossible" is not a political opinion but a formal theorem. The claim that plurality voting—the system used in the United States and many other countries—is among the worst is also grounded in rigorous mathematical analysis. This article surveys the mathematical case against conventional democracy, reviews the empirical evidence on voting system performance, and examines mathematically superior alternatives. Arrow's Impossibility Theorem and Its Implications. The Core Problem. The foundational argument that no voting system can be "perfect" was established by economi...
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