Why Democracy Is Mathematically Impossible

Voting Systems

• First Past the Post voting involves voters selecting their favorite candidate on a ballot, with the candidate receiving the most votes declared the winner. (46s)
• Instant Runoff Voting, also known as Ranked Choice Voting, requires voters to rank candidates from most to least favored. If no candidate secures a majority, the candidate with the fewest votes is eliminated, and their votes are redistributed based on the voters' subsequent preferences. This process continues until a candidate achieves a majority. (5m19s)
• Approval voting, where voters select all candidates they approve of, has been shown to increase voter turnout, decrease negative campaigning, and prevent the spoiler effect. (20m11s)

Condorcet's Method and its Challenges

• Mathematician Marquis de Condorcet, considered a pioneer in applying mathematical principles to voting systems, is recognized as one of the founders of social choice theory. (8m9s)
• In 1785, Marquis de Condorcet proposed a voting system where the winner must beat every other candidate in a head-to-head election based on voters ranking their preferences. (9m19s)
• Condorcet's method can lead to a situation known as Condorcet's Paradox, where there is no clear winner due to a cyclical preference loop. (11m9s)

Limitations of Ranked Voting Systems

• Kenneth Arrow's Impossibility Theorem, published in 1951, proved that it is impossible to design a ranked voting system with three or more candidates that satisfies five seemingly reasonable conditions (unanimity, non-dictatorship, unrestricted domain, transitivity, and independence of irrelevant alternatives). (14m4s)
• If a ranked choice voting system is used with three or more candidates, a pivotal voter, or dictator, will always exist. (18m33s)

The Median Voter Theorem

• Duncan Black argued that if voters and candidates exist on a single political spectrum, the median voter's preference will align with the majority, avoiding inconsistencies. (19m21s)