Overview
This lecture explored different voting systems, focusing on their mathematical properties and real-world implications, particularly how they affect election outcomes and fairness when multiple candidates are present.
Problems with Plurality Voting
- In elections with more than two candidates, a winner can be chosen without majority support.
- Candidates can win with a small percentage (e.g., 20%), leaving most voters unrepresented.
- "Spoiler effect" occurs when third-party candidates change the outcome between major contenders.
- Plurality voting can lead to insincere voting, where people don't vote for their true preference.
Alternative Voting Methods
- Jungle Primary: All candidates, regardless of party, compete in a single primary, and the top two advance to the general election.
- Instant Runoff Voting (IRV)/Ranked Choice Voting (RCV): Voters rank candidates by preference; lowest-ranked candidates are eliminated in rounds, reallocating votes to next preferences until a winner emerges.
- IRV is used in Australia, Ireland, India, Oakland (CA), Maine, Papua New Guinea, and for some awards.
Mathematical Critiques of Voting Systems
- IRV can result in "exhausted votes" when all ranked choices are eliminated.
- Condorcet Winner: A candidate who would beat every other candidate in head-to-head competition; a desirable but not guaranteed outcome in many systems.
- Different systems (Plurality, IRV, Condorcet, Borda Count) can yield different winners from the same voter preferences.
Arrow’s Impossibility Theorem
- Shows no voting system is perfectly fair when more than two candidates are involved.
- All systems have inherent limitations and can produce unfair outcomes for some voters.
Real-World Examples
- US elections (e.g., Bush vs. Gore 2000, Michigan 2016) demonstrate how voting methods impact winners.
- Third parties can have significant effects even with low percentages of votes.
Key Terms & Definitions
- Plurality Voting — Candidate with most votes wins, regardless of majority.
- Jungle Primary — All candidates in one primary, top two advance.
- Instant Runoff Voting (IRV)/Ranked Choice Voting (RCV) — Voters rank candidates; lowest ranked eliminated in rounds.
- Condorcet Winner — Candidate who defeats all others in head-to-head comparisons.
- Spoiler Effect — Third-party candidate alters the outcome between major candidates.
- Exhausted Votes — Ballots that cannot be counted in a round because all ranked choices are eliminated.
- Arrow’s Impossibility Theorem — No voting method perfectly satisfies all fairness criteria with three or more candidates.
Action Items / Next Steps
- Understand and review definitions and examples of voting systems.
- Reflect on the strengths and weaknesses of different voting methods.
- Investigate Arrow's Impossibility Theorem for further study.