Voting Procedures

Voting procedures consist of using a specific method to determine the victor or the winner of the vote.

The winner is the candidate who obtains more than half of the votes, or in other words, the absolute majority.

Secondary 5 students from a school voted for their favourite of four winter activities. The following table shows the results of the vote.

Under majority rule, no activity wins this vote. To win, an activity would have to receive more than |50\%| of the vote (|173| or more votes out of |345|).

The winner is the candidate who wins the greatest number of votes, or in other words, the relative majority.

Secondary 5 students from one school voted for their favourite of four winter activities. The following table shows the results of the vote.

According to plurality voting, alpine skiing wins because it received the most votes.

Each voter ranks the candidates according to their order of preference. If there are |n| candidates, |n| points are awarded to the 1st choice of each voter, |n-1| points to the 2nd choice, and so on, until only a single point is granted to the last choice. The candidate who obtains the highest number of points wins.

The following table shows who should be awarded the title of the kindest teacher in a school according to Secondary 5 students.

Given that the contest is between |3| candidates, if we use the Borda count method, each is awarded |3| points for a 1st choice vote, |2| points for a 2nd choice vote and |1| point for a 3rd choice vote.

The following table shows the number of points received by each candidate.

According to the Borda count, Mr. Gauthier is the nicest teacher in the school, since he received the most points.

Each voter ranks the candidates in order of preference. To win, a candidate must defeat all the other candidates in a one-on-one confrontation.

The candidates are compared by recording the number of votes obtained by head-to-head matchups.

The winner is the person who won all of his matchups against the other candidates.

The following table shows who should be awarded the title of the kindest teacher in a school according to Secondary 5 students.

• |115| students |(73+42)| prefer Ms. Drolet to Mr. Poulin, while |112| prefer Mr. Poulin to Ms. Drolet. Ms. Drolet is therefore the winner of this matchup.

• |115| students |(73+42)| prefer Mr. Gauthier to Mr. Poulin, while |112| prefer Mr. Poulin to Mr. Gauthier. Mr. Gauthier is therefore the winner of this matchup.

• |154| students |(112+42)| prefer Mr. Gauthier to Ms. Drolet, while |73| prefer Ms. Drolet to Mr. Gauthier. Mr. Gauthier is therefore the winner of this matchup.

So, according to the Condorcet method, Mr. Gauthier is the nicest teacher in the school.

To win, the candidate must obtain an absolute majority of votes, which means more than half of the votes. If this does not happen, proceed as follows.

• First, eliminate the candidate with the fewest votes as a 1st choice and distribute these votes to the following candidate.

• In the second step, a new count is made to designate first place. If a candidate then obtains the majority of the votes, they are the winner. Otherwise, the procedure starts again from the first step.

The following table shows who should be awarded the title of the kindest teacher in a school according to Secondary 5 students.

If we use elimination voting, we first observe that no one receives more than half of the votes for the 1st choice.

Mr. Gauthier must be eliminated, since he received the fewest 1st-place votes, that is, |42| votes.

Mr. Gauthier's 1st-choice votes are then attributed to Ms. Drolet, because she is the 2nd most preferred candidate in the list. After redistributing the votes, Mr. Poulin still holds |112| 1st-choice votes, but Ms. Drolet now has |115| |(73+42).|

Therefore, according to elimination voting, Ms. Drolet gets the award for being the kindest teacher in the school.

Each voter votes only once, but for as many candidates as they wish. The candidate who obtains the most votes wins.

Four candidates ran in an election: Julian, Simon, Emilie and Claudine. Each voter can vote for more than one candidate if they wish. Here are the results of the vote.

Julian received |96| votes |(45+28+23),| Simon received |60| votes |(32+28),| Claudine received |60| votes |(32+28)| and Emilie received |77| votes |(45+32).|

According to approval voting, Julian wins the election.

The decision-making weight is distributed among the possible choices in proportion to the number of votes obtained.

A city decides to allocate |10| seats on the city council. Three parties are running for election. Here are the results of the vote.

The number of seats allocated to each party can be calculated as follows.

• Party A: |\dfrac{15\ 235}{41\ 557}\times10\approx3.67|
  So Party A will have at least |3| seats.

• Party B: |\dfrac{23\ 429}{41\ 557}\times10\approx5.64|
  So Party B will have at least |5| seats.

• Party C: |\dfrac{2893}{41\ 557}\times10\approx0.7|
  So Party C will not have any seats from the start.

Therefore, |8| seats are already allocated (|3| to party A and |5| to party B). The other |2| seats are allocated by placing the remainders (the decimals) in ascending order. Party C |(0.7)| will have one seat and Party A |(0.67)| will have the last seat.

So, according to proportional representation, Party A will have |4| seats, Party B will have |5| and Party C will have only one.