Why Democracy Is Mathematically Impossible

Summary

This video delves into the mathematical challenges of democracy, particularly in voting systems. It critiques the 'first past the post' method, highlighting its tendency to produce majority governments that don't reflect the majority's will. The script explores alternatives like instant runoff voting and points out its own paradoxes, such as how a poorly performing candidate can influence election outcomes. It introduces Arrow's Impossibility Theorem, which states that no ranked voting system can satisfy all desired fairness conditions, and contrasts it with Black's Median Voter Theorem, suggesting a more optimistic view of democratic voting. The video concludes by advocating for approval voting as a potentially fairer method and encourages political engagement despite the imperfections of the democratic process.

Takeaways

• 😀 Democracy's current voting methods are fundamentally irrational, leading to potential instability and misrepresentation.
• 🏛️ 'First past the post' voting, used by 44 countries, can result in parties gaining power without majority support, as seen in the UK's parliamentary history.
• 🗳️ The spoiler effect, as in the 2000 US presidential election, can lead to unintended election outcomes due to vote-splitting among similar parties.
• 🔄 'Instant runoff' or ranked-choice voting can mitigate the spoiler effect and encourage more cooperative candidate behavior, as demonstrated in the 2013 Minneapolis mayoral race.
• 🔢 Arrow's Impossibility Theorem states that no ranked voting system can satisfy five reasonable conditions simultaneously, suggesting inherent limitations in democratic voting systems.
• 🤔 Condorcet's method, which involves pairwise comparison of candidates, can result in paradoxes where cyclic preferences prevent a clear winner from emerging.
• 📊 Black's Median Voter Theorem offers a more optimistic view, suggesting that in one-dimensional political spectra, the preference of the median voter can determine the majority decision.
• 👍 Approval voting, an alternative to ranked voting, allows voters to express approval for one or more candidates and can increase voter turnout and reduce negative campaigning.
• 🏆 Approval voting has historical precedents, such as electing the Pope in the Vatican and the Secretary-General of the United Nations.
• 💡 Despite theoretical challenges, democracy remains the best form of government available, and engagement in the political process is crucial for making a difference.
• 🌐 The script concludes with a call to expand knowledge and critical thinking skills to better understand and participate in an ever-changing world.

Q & A

What is the main argument presented in the video about democracy and mathematics?

The video argues that the methods currently used to elect leaders in democratic societies are fundamentally irrational from a mathematical perspective, leading to potential instability and misrepresentation.

What is 'first past the post' voting and why does it have issues?

'First past the post' is a voting system where the candidate with the most votes wins. It has issues because it can lead to situations where the majority of the country did not vote for the party that ends up holding power, and it can cause similar parties to 'steal' votes from each other, leading to a two-party system.

What is the 'spoiler effect' in elections?

The 'spoiler effect' occurs when a candidate with similar views to another takes votes away, potentially causing the less preferred candidate to win. This effect discourages voters from voting for their true preference if it's not a leading contender.

What is the 'instant runoff' voting system and how does it work?

The 'instant runoff' voting system, also known as preferential or ranked-choice voting, allows voters to rank candidates by preference. If no candidate has a majority after the first count, the candidate with the fewest votes is eliminated, and their votes are redistributed according to the voters' second preferences, repeating this process until a candidate has a majority.

How does the 'instant runoff' system affect candidate behavior?

The 'instant runoff' system encourages candidates to be more cordial and polite to each other, as they are vying for second and third preferences from voters who support other candidates.

What is Arrow's Impossibility Theorem and what does it imply for voting systems?

Arrow's Impossibility Theorem states that it is impossible to create a ranked voting system that satisfies five reasonable conditions when there are three or more candidates. This implies that no voting system can perfectly and rationally aggregate voter preferences without some form of compromise.

What are the five conditions outlined by Kenneth Arrow for a fair voting system?

The five conditions are: Unanimity (if everyone prefers one option, the group should too), Non-dictatorship (no single vote should override all others), Unrestricted Domain (all voters can vote freely and the system must produce a conclusion), Transitivity (if the group prefers A over B and B over C, they should prefer A over C), and Independence of Irrelevant Alternatives (adding or removing a candidate should not affect the preference between two existing candidates).

What is Condorcet's method and how does it differ from other voting systems?

Condorcet's method is a voting system where the winner is the candidate who would win in a head-to-head election against every other candidate. It differs from other systems by focusing on pairwise comparisons of candidates rather than aggregating total points or votes.

What is Condorcet's Paradox and how does it challenge the fairness of voting systems?

Condorcet's Paradox occurs when there is a circular preference among three or more options, where each option is preferred to the next and the last is preferred to the first, creating a logical loop with no clear winner. This paradox challenges the idea that a voting system can always produce a fair and consistent outcome.

What alternative voting system is suggested in the video as a potential solution to the issues with ranked voting?

The video suggests rated voting systems, such as approval voting, as a potential solution. In approval voting, voters indicate which candidates they approve of, and the candidate with the highest approval wins, which can increase voter turnout and decrease negative campaigning.