Preference Ballots and the Plurality Method: 동영상 및 연습문제

The plurality method is a voting system used to determine the winner of an election by counting only the first-place votes each candidate receives. Under this method, the candidate with the greatest number of first-place votes wins the election, regardless of whether they have a majority. This means that the full ranking of preferences from voters is not necessary; only the top choice counts. For example, if Candidate A receives 40% of first-place votes, Candidate B 35%, and Candidate C 25%, Candidate A wins by plurality because they have the highest number of first-place votes, even though they do not have more than 50% of the votes. This method is simple and commonly used but can result in a winner who does not have majority support.

Winning by plurality means a candidate has more first-place votes than any other candidate but does not necessarily have more than half of all votes. Winning with a majority means the candidate has received more than 50% of the total votes. For example, if there are 100 votes, a majority winner must have at least 51 votes. A plurality winner could have fewer than 51 votes but still more than any other candidate. This distinction is important because a plurality winner may not represent the preference of the majority of voters, which can affect the perceived legitimacy of the election outcome.

In the plurality method, only the first-place votes are counted to determine the winner. Because the winner is the candidate with the most first-place votes, the full preference table showing voters' rankings beyond their top choice is not required. This simplifies the counting process and reduces complexity. For instance, if you already know the number of first-place votes each candidate received, you can identify the winner without analyzing the entire preference order. However, this simplicity comes at the cost of ignoring voters' secondary preferences, which might be important in other voting methods.

The plurality method has several limitations. First, it only considers first-place votes, ignoring voters' preferences for other candidates. This can lead to a winner who does not have broad support. Second, it can result in a candidate winning without a majority, meaning more than half of voters preferred someone else. Third, in elections with multiple candidates, the vote can be split, allowing a candidate to win with a relatively small percentage of total votes. These limitations can cause dissatisfaction among voters and may not always reflect the true preference of the electorate.

To determine if a candidate has a majority, you compare the number of first-place votes they received to half of the total votes. Let $V$ be the total number of votes and $v$ be the number of first-place votes for the candidate. The candidate has a majority if:

$v>\frac{1}{2}V$

This means the candidate must have more than half of all votes to claim a majority.