Why Democracy Is Mathematically Impossible

The Nugget

Democracy is mathematically impossible because no ranked voting system can satisfy all fair voting criteria simultaneously, a result known as Arrow's Impossibility Theorem.
Alternative voting methods like approval voting may provide better approximations but require further real-world testing.

Make it stick

💡 First past the post results in majority power often not reflecting the majority vote.
🔄 Condorcet Paradox: Preference loops where no clear winner emerges (e.g., A > B > C > A).
🏴‍☠️ Arrow's Impossibility Theorem: It’s impossible to design a ranked voting system satisfying all fairness criteria with three or more candidates.
👍 Approval voting: Voters approve of multiple candidates, potentially reducing negative campaigning and the spoiler effect.

Majority doesn’t rule: Often, parties with minority votes control the government.
Spoiler Effect: Minor candidates can skew results, leading to less-preferred outcomes.
Strategic voting: Encourages voting for more popular candidates instead of personal preference.

Ordinal voting systems: Including instant runoff and preferential voting, which still have inherent flaws like the non-monotonicity problem.
Condorcet method: Each candidate faces all others in head-to-head matchups, but can result in paradoxes.

Conditions: Unanimity, no dictator, unrestricted domain, transitivity, and independence of irrelevant alternatives.
Conclusion: No ranked-choice voting system can meet all these criteria simultaneously.

Simplicity: Voters simply approve all candidates they find acceptable.
Advantages: Increases voter turnout, reduces negative campaigning, and prevents the spoiler effect.
Historical and current use: Historically used by the Vatican and currently by the United Nations.

"Arrow’s impossibility theorem seems to say so**: If there are three or more candidates to choose from, there is no ranked Choice method to rationally aggregate voter preferences."
"The pivotal voter determines society’s preferences, essentially making them a dictator."
"Approval voting is not new. It was used by priests in the Vatican to elect the pope between 1294 and 1621."
"Just because things aren’t perfect doesn’t mean we shouldn’t try. Being politically engaged is important; it might be one of the few ways we can make a real difference in the world."
"Democracy is the worst form of government, except for all the other forms that have been tried." - Winston Churchill

This summary contains AI-generated information and may have important inaccuracies or omissions.