Lecture Notes: Voting Systems and Arrow's Impossibility Theorem

Introduction to Voting Systems

Plurality Voting Flaw
- Effective in a two-way race.
- Introducing more than two options can lead to unexpected outcomes.
- Violates the "Independence of Irrelevant Alternatives" rule.
- Example: Adding a Yellow Party candidate affects Orange Party's standing.

Multiple rules exist that define ideal voting system properties.
Non-Dictatorship Rule
- No single individual's preferences should dictate the outcome.

Mechanism
- Voters rank candidates.
- Candidates with least support are eliminated.
- Votes are reallocated to the next choice until a candidate has >50% votes.
Voting Process
- First choice votes are counted.
- If no majority, eliminate last place candidate.
- Recast votes of eliminated candidate to the next choice.
- Continue until a candidate achieves the majority.
Example with Three Parties
- Initial votes: A = 6, B = 4, C = 3.
- C eliminated, votes reallocated.
- New result: A = 6, B = 7; B wins.

Citizen Sovereignty Violation
- Changes in voter preferences can unexpectedly alter outcomes.
- Example with Purple Voter: Switching preference between B and C allows A to win.
- Encourages strategic voting instead of honest ranking.

Kenneth Arrow's Contribution
- Proved no voting system can satisfy all criteria simultaneously.
- Demonstrates inherent flaws in aggregating preferences.
Impact on Democracy
- Explains the difficulties of achieving a perfect democratic system.
- Reference to Winston Churchill's view on democracy.

Markets Adhering to Criteria
- Markets convert ordinal preferences into cardinal ones through willingness to pay.
- Avoid challenges found in government systems.

Economics as a Tool
- Helps understand and navigate real-world complexities.
- Provides insight into both economic and societal structures.
Encouragement for Students
- Use acquired knowledge to pursue goals and overcome challenges.