Which voting system is the best? - Alex Gendler

Key Concepts

• Plurality Voting (First Past the Post): The candidate with the most votes wins, regardless of whether they have a majority.
• Instant Runoff Voting (Ranked-Choice Voting): Voters rank candidates, and the candidate with the fewest first-place votes is eliminated. Their votes are then redistributed to the voters' next choice, and the process repeats until one candidate has a majority.
• Tactical Voting: Voting strategically to prevent a less-preferred candidate from winning, even if it means not voting for one's true favorite.
• Condorcet Method: Voters express a preference in every possible head-to-head matchup between candidates. The candidate who wins the most matchups is the Condorcet winner.
• Condorcet Paradox: A situation where, with three or more candidates, the collective preferences of voters can be cyclical (e.g., A > B > C > A), making it impossible to select a Condorcet winner.
• Fairness Criteria: Theoretically desirable properties of a voting system, such as equal influence for voters and consideration of minority preferences.
• Arrow's Impossibility Theorem: A mathematical theorem stating that no voting system with three or more candidates can satisfy all fairness criteria simultaneously.

Martian Space Port Voting Scenario

The video uses a hypothetical scenario of building a space port at one of four Martian bases (West, North, South, and East) to illustrate different voting methods and their potential flaws. The population distribution across the bases is:

• West Base: 42 colonists
• North Base: 26 colonists
• South Base: 15 colonists
• East Base: 17 colonists

The colonists are assumed to prefer the space port to be as close to their base as possible.

Plurality Voting (First Past the Post)

• Description: Each voter casts a single ballot for their preferred location. The location with the most votes wins.
• Outcome: West Base wins with 42 votes.
• Critique: The video argues that this outcome is undesirable because West Base is the most remote location for the majority of colonists. It highlights the potential for plurality voting to elect a candidate that is disliked by most voters.

Instant Runoff Voting (Ranked-Choice Voting)

• Description: Voters rank the locations in order of preference. The location with the fewest first-place votes is eliminated, and their votes are redistributed to the voters' next choice. This process continues until one location has a majority.
• Process:
  1. Initial ranking: South Base receives the fewest first-place votes (15) and is eliminated.
  2. South's votes are allocated to East Base, giving East a total of 32 votes.
  3. North Base is eliminated.
  4. North's votes are allocated to East Base, giving East a total of 58 votes.
  5. East Base wins.
• Outcome: East Base wins.
• Critique: The video points out that East Base started in second-to-last place and was ranked among the two least preferred options by a majority of voters. This raises questions about the fairness of instant runoff voting in this scenario.

Tactical Voting and Runoff Voting

• Description: Voting occurs in multiple rounds, with the top two winners from the first round proceeding to a separate runoff election.
• Tactical Voting Example: Residents of East Base strategically vote for South Base in the first round to prevent North Base from advancing to the runoff.
• Outcome: South Base wins the second round due to the tactical voting of East Base residents.
• Critique: The video questions whether a system that incentivizes lying about one's preferences can be considered fair. It highlights how tactical voting can lead to outcomes that do not reflect the true preferences of the electorate.

Condorcet Method

• Description: Voters express a preference in every possible head-to-head matchup between locations. The location that wins the most matchups is the Condorcet winner.
• Process:
  1. West vs. North: North wins (58 votes to 42).
  2. All other matchups are conducted similarly.
• Outcome: North Base wins three matchups, and South Base wins two.
• Rationale: North and South are the two most central locations, and North has the advantage of not being anyone's least preferred choice.
• Critique: The video acknowledges that the Condorcet method is not always ideal, as it can fail to select a winner in cases of cyclical preferences (Condorcet Paradox).

Arrow's Impossibility Theorem and the Nature of Fairness

• Key Argument: Mathematical proofs have shown that for any election with more than two options, it is impossible to design a voting system that satisfies all theoretically desirable fairness criteria.
• Explanation: Our intuitive concept of fairness contains a number of assumptions that may contradict each other.
• Examples of Conflicting Criteria:
  • Equal influence for all voters vs. consideration of minority preferences.
  • Preventing voters from gaming the system.
• Conclusion: Democracy is not just about counting votes but also about considering who benefits from the different ways of counting them. The choice of voting system can have a significant impact on the outcome of an election and the representation of different groups' preferences.