Arrow's impossiblity theorem is wrong as stated, here's proof

Arrow's famous theorem says you can't have a "perfect" voting system—there's always something that goes wrong when you try to combine everyone's preferences fairly. But this paper shows that Arrow's impossibility isn't actually absolute; it depends on using classical logic, where every question has a definite yes-or-no answer.

The key insight is that Arrow's proof relies on being able to definitively say "this group of voters is decisive" or "that group is decisive" everywhere, all at once. But in non-classical mathematical worlds (called non-Boolean topoi), you can have situations where different voters are decisive in different contexts, without anyone being a global dictator. It's like having different people in charge for different issues or at different times, without any single person controlling everything.

The paper constructs an explicit example of a voting system that satisfies all of Arrow's fairness conditions simultaneously—something that's impossible in ordinary mathematics. The trick is that "who's decisive" varies across contexts in a way that classical logic can't capture. When you force everything back into classical yes-or-no logic, the impossibility returns, confirming that Arrow was right within his framework—but the framework itself isn't the only option.