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Questions and Answers
The ______ criterion states that if a candidate is preferred over another in head-to-head comparisons, they should win the overall election.
The ______ criterion states that if a candidate is preferred over another in head-to-head comparisons, they should win the overall election.
Condorcet
In voting, ______ methods involve voters ranking candidates in order of preference.
In voting, ______ methods involve voters ranking candidates in order of preference.
Ranking
The ______ comparison method evaluates candidates based on their performance against each other in one-on-one matchups.
The ______ comparison method evaluates candidates based on their performance against each other in one-on-one matchups.
Pairwise
The ______ criterion states that if a candidate is preferred over others, receiving additional support should not harm their chances of winning.
The ______ criterion states that if a candidate is preferred over others, receiving additional support should not harm their chances of winning.
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Fairness in elections means that the methods used should ______ all voters equally, giving everyone an equal chance to influence the outcome.
Fairness in elections means that the methods used should ______ all voters equally, giving everyone an equal chance to influence the outcome.
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The candidate that is preferred in every one-to-one comparison is called the Condorcet ______.
The candidate that is preferred in every one-to-one comparison is called the Condorcet ______.
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In a scenario with four candidates, each candidate will have ______ comparisons.
In a scenario with four candidates, each candidate will have ______ comparisons.
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To be identified as the Condorcet Candidate, a candidate needs to win all ______ comparisons.
To be identified as the Condorcet Candidate, a candidate needs to win all ______ comparisons.
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The Condorcet Candidate earns the maximum of ______ points in the Pairwise Comparison method.
The Condorcet Candidate earns the maximum of ______ points in the Pairwise Comparison method.
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The Fairness Criterion suggests that the Condorcet Candidate should ______ the election.
The Fairness Criterion suggests that the Condorcet Candidate should ______ the election.
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The Monotonicity Criterion states that increasing preference for a candidate should not ______ that candidate's chances of winning.
The Monotonicity Criterion states that increasing preference for a candidate should not ______ that candidate's chances of winning.
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The plurality method can sometimes lead to the Condorcet Candidate not winning, which seems ______.
The plurality method can sometimes lead to the Condorcet Candidate not winning, which seems ______.
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In comparing candidates, the Pairwise Comparison method focuses on ______ comparisons.
In comparing candidates, the Pairwise Comparison method focuses on ______ comparisons.
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The ______ Criterion ensures that if a candidate would win against every other candidate in a head-to-head match, they should be the overall winner.
The ______ Criterion ensures that if a candidate would win against every other candidate in a head-to-head match, they should be the overall winner.
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In ranking methods, voters list their preferences in order. This process can be influenced by the ______ method, where candidates are eliminated based on their lowest votes.
In ranking methods, voters list their preferences in order. This process can be influenced by the ______ method, where candidates are eliminated based on their lowest votes.
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The ______ Comparison Method evaluates candidates based on direct matchups against each other to determine the winner.
The ______ Comparison Method evaluates candidates based on direct matchups against each other to determine the winner.
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The ______ Criterion states that if a winning candidate receives more support after preferences are altered, they should still win.
The ______ Criterion states that if a winning candidate receives more support after preferences are altered, they should still win.
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Fairness in elections is critical to ensure that all voters' preferences are accurately ______ in the final outcome.
Fairness in elections is critical to ensure that all voters' preferences are accurately ______ in the final outcome.
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If a candidate who already has a majority of votes loses after a recount, this violates the ______ Criterion.
If a candidate who already has a majority of votes loses after a recount, this violates the ______ Criterion.
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Using the ______ method, the elimination process continues until one candidate achieves the majority of votes.
Using the ______ method, the elimination process continues until one candidate achieves the majority of votes.
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In elections, ensuring all voters can express their preferences leads to a ______ outcome where each individual's voice is heard.
In elections, ensuring all voters can express their preferences leads to a ______ outcome where each individual's voice is heard.
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Study Notes
Voting Theory Introduction
- Voting theory is the mathematics of determining fair election winners.
- Various methods exist to count votes, and no single method is perfect.
Preference Schedule Voting
- Traditional ballots allow choosing one candidate.
- Majority winner: More than 50% of votes.
- Plurality winner: Candidate with the most votes (ties possible).
- Preference ballots (ranked choice voting): Voters rank candidates in order of preference.
- Preference schedules combine individual ballots to show rankings.
- Plurality winner: Determined by counting 1st choice votes only.
- Majority winner: Determined by whether a candidate has more than 50% of the votes.
Instant Runoff Voting (IRV)/Plurality with Elimination
- Method counts votes and eliminates candidates with the fewest 1st choice votes.
- Process repeats until a majority winner is found.
- If no majority winner, the candidate with the least votes is eliminated.
- This process continues until a majority winner emerges.
- Example: Candidates votes are counted. The candidate with the fewest votes is eliminated. The process repeats and the candidate with a majority of votes wins the election.
Borda Count Method
- Weighs votes based on ranking.
- Lower ranks receive fewer points, highest ranks receive more points.
- Sum of points determines the winner.
- Example: Each 1st choice vote gets 4 points, 2nd- 3 points, 3rd - 2 points, and 4th choice - 1 point. The winner is the candidate with the most points.
Pairwise Comparison/Copeland's Method
- Compares each candidate pair to determine preferences.
- Points awarded to the winner of each pair.
- Candidate with most points wins.
- Example: A and B are compared, and B is the preferred candidate. B is awarded 1 point.
- Candidate with the most points is the winner.
Condorcet Criterion
- Fairness criteria: The winning candidate should be preferred over every other candidate in one-on-one comparisons.
- Inconsistent with other methods.
Monotonicity Criterion
- A candidate's chances shouldn't be harmed if voters increase their preference for them. (e.g.: their voter preference is adjusted in favor of another candidate)
- Inconsistent with some methods.
Majority Criterion
- Fairness criteria: If a candidate receives a majority of first-place votes, that candidate should win.
- Some methods don't satisfy this.
Independence of Irrelevant Alternatives (IIA)
- Fairness criterion: Removing or adding a non-winning candidate should not change the election's outcome.
- Some methods don't satisfy this.
- Example: A candidate who is last in all preference schedules or receives the least votes is removed from all preference schedules and the outcome of the voting changes.
Arrow's Impossibility Theorem
- No voting method satisfies every desired fairness criterion (inconsistent) at the same time.
Approval Voting
- Voters "approve" (or "disapprove") of candidates.
- Highest approval count wins.
- A fast way to tally votes.
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Description
Explore the fundamentals of voting theory, focusing on the various methods of counting votes and determining fair election winners. Learn about traditional ballots, preference schedules, and the instant runoff voting system. Understand how different voting methods impact the outcome of elections.
