Fairness Criterion: Videos & Practice Problems

Here's what students ask on this topic:

What is the majority criterion in voting systems and why is it important for fairness?

The majority criterion in voting systems states that if a candidate receives a majority (more than 50%) of first-rank votes, that candidate should win the election. This criterion is important for fairness because it ensures that the choice preferred by the majority of voters is respected and ultimately selected. Without this criterion, a candidate who is less preferred by most voters could win, which would undermine the democratic principle of majority rule. The majority criterion helps evaluate whether a voting method fairly represents the will of the majority, making it a key standard in comparing different election methods.

Which common voting methods satisfy the majority criterion and how do they ensure a majority winner?

Voting methods that satisfy the majority criterion include the plurality method, plurality with elimination, and pairwise comparison. In the plurality method, the candidate with the most first-rank votes wins, so if a candidate has a majority, they automatically win. Plurality with elimination (also known as instant runoff voting) eliminates the candidate with the fewest votes in rounds until a candidate has a majority, ensuring a majority winner. Pairwise comparison ranks candidates based on head-to-head matchups; a candidate with a majority of first-rank votes will win all these matchups, thus earning the most points and winning the election. These methods guarantee that a majority-supported candidate cannot lose.

Why can the Borda count violate the majority criterion in elections?

The Borda count can violate the majority criterion because it assigns points based on candidates' rankings rather than just first-place votes. In this system, a candidate who is the first choice of a majority might not accumulate the highest total points if many voters rank other candidates highly in their preferences. This means a candidate without majority first-rank support could win if they consistently receive high rankings across ballots. Therefore, the Borda count does not guarantee that a candidate with majority first-rank votes will always win, making it less aligned with the majority criterion and potentially less fair in representing majority preference.

How does the concept of fairness criterion help in comparing different voting systems?

The fairness criterion, particularly the majority criterion, provides a clear standard to evaluate and compare voting systems. It helps determine whether a voting method respects the principle that a candidate preferred by the majority should win. By applying this criterion, we can identify which methods are more democratic and fair in reflecting voters' preferences. For example, methods like plurality and pairwise comparison satisfy the criterion, while others like the Borda count may not. Understanding these differences allows students and policymakers to choose or design voting systems that better represent the will of the majority, enhancing the legitimacy and fairness of elections.

What is the difference between plurality method and plurality with elimination in terms of majority criterion?

The plurality method simply awards victory to the candidate with the most first-rank votes, so if a candidate has a majority, they win immediately. However, if no candidate has a majority, the candidate with the most votes still wins, which may not reflect majority preference. Plurality with elimination (instant runoff voting) addresses this by eliminating the candidate with the fewest votes in successive rounds and redistributing their votes based on preferences until a candidate achieves a majority. This ensures that the winner has majority support, making plurality with elimination more aligned with the majority criterion than the simple plurality method.