# Why Democracy Is Mathematically Impossible

28 Aug 2024 (18 days ago)

## 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.
• 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.
• 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.

## 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.
• 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.
• 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.

## 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).
• If a ranked choice voting system is used with three or more candidates, a pivotal voter, or dictator, will always exist.

## 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.