Is Democracy Mathematically Possible?

TL;DR

Democracy is possible, but no ranked voting system can perfectly translate collective preferences into a rational result when there are three or more candidates, according to Arrow's Impossibility Theorem. First past the post can misrepresent majorities, encourage strategic voting, and create spoiler effects, while ranked-choice and approval voting offer improvements with their own tradeoffs. Read on to compare how these systems work and where each one fails.

Transcript

• Democracy might be mathematically impossible. (serious music) This isn't a value judgment, a comment about human nature, nor a statement about how rare and unstable democratic societies have been in the history of civilization. Our current attempt at democracy, the methods we're using to elect our leaders, are fundamentally irrational. And this i... Read More

Key Insights

• Arrow's Impossibility Theorem proves no ranked voting system can meet all rational criteria with three or more candidates.
• First past the post voting often fails to reflect the majority's preference, leading to potential misrepresentation.
• Ranked-choice voting can mitigate some issues but introduces paradoxes like the spoiler effect.
• Approval voting allows voters to express approval for multiple candidates, potentially increasing voter satisfaction.
• Condorcet's paradox shows that collective preferences can be cyclic, complicating fair decision-making.
• Duncan Black's theorem suggests that the median voter can often determine election outcomes, aligning with majority preference.
• Rated voting systems, unlike ranked ones, can satisfy more rational criteria and reduce negative campaigning.
• Democracy's flaws do not negate its value as the best governance system tried so far.

Questions & Answers

Q: Is democracy mathematically possible?

Democracy is possible, but its voting methods cannot perfectly represent every group's preferences. Arrow's Impossibility Theorem shows that no ranked voting system can satisfy all rational criteria when there are three or more candidates, so every such system requires compromises.

Q: What does Arrow's Impossibility Theorem say about voting systems?

Arrow's Impossibility Theorem says that no ranked voting system can simultaneously meet all rational criteria with three or more candidates. Consequently, no method of combining individual rankings can always produce a perfectly rational collective preference.

Q: How does first past the post voting work?

Each voter marks one candidate as their favorite, and the candidate receiving the most votes wins. The winner does not need an actual majority or a particular threshold, despite the system's name.

Q: Why can first past the post misrepresent the majority?

A party can win a majority of parliamentary seats even when most voters did not vote for it. The transcript notes that this happened repeatedly in the British Parliament, allowing a party supported by a minority of voters to hold government power.

Q: What is the spoiler effect in an election?

The spoiler effect occurs when similar candidates divide their shared pool of support and change which opponent wins. In the presidential election discussed, Ralph Nader received almost a hundred thousand Florida votes, while George W. Bush led Al Gore there by fewer than 600 votes; many Nader voters preferred Gore to Bush but could not express that preference.

Q: Why does first past the post encourage strategic voting and two-party systems?

Voters may avoid their genuine favorite when they believe that candidate is too small to win, choosing a larger party instead. This winner-takes-all pressure concentrates power among larger parties and can eventually produce a two-party system, an effect called Duverger's Law.

Q: How does ranked-choice voting work?

Voters rank candidates from favorite to least favorite. If nobody initially has at least 50% plus one of the vote, the candidate with the fewest votes is eliminated and those ballots move to the voters' next preferences until someone has a majority.

Q: How can ranked-choice voting affect candidate behavior?

Candidates have an incentive to seek second and third choices instead of only attacking rivals. In the Minneapolis mayoral race described, 35 candidates remained notably cordial and even sang “Kumbaya” together after the final debate.

Summary & Key Takeaways

• Arrow's Impossibility Theorem demonstrates the inherent flaw in ranked voting systems, where no method can perfectly reflect collective preferences with three or more candidates. This mathematical insight challenges the rationality of current democratic voting systems.

• First past the post voting, commonly used worldwide, fails to accurately represent the majority's preference, often leading to misrepresentation and strategic voting. Ranked-choice voting offers some improvements but introduces its own set of paradoxes.

• Approval voting emerges as a promising alternative, allowing voters to express approval for multiple candidates, potentially increasing voter satisfaction and reducing negative campaigning. Despite democracy's imperfections, it remains the best governance system available.