Modern Math Quiz - Voting Methods part 1

How many people voted as represented by the preference schedule shown?

Answer explanation

A preference ballot is a ballot in which the voter ranks the choices in order of preference.

These individual ballots are typically combined into one preference schedule, which shows the number of voters in the top row that voted for each option.

Based on the preference schedule shown, how many votes would a food need to have for a majority vote?

​

Answer explanation

A majority is over 50%; it is possible for a winner to have a plurality without having a majority.

Based on the preference schedule shown, is there any food that has a majority vote?

​ ​ ​ (a)  

• Yes, Chicken
• No, there is not a majority
• Yes, Hot Dogs
• Yes, Burgers
• Yes, Tacos
• Yes, Salad
• Yes, Pizza

Answer explanation

A majority is over 50%; it is possible for a winner to have a plurality without having a majority.

Based on the preference schedule shown, which food is the winner of the election using the Plurality Method?

​ (a)  

• Tacos
• Hot Dogs
• Burgers
• Salad
• Pizza
• Chicken

Answer explanation

Plurality Method: the choice with the most first-preference votes is declared the winner. Ties are possible, and would have to be settled through some sort of run-off vote.

Based on the preference schedule shown, which food wins the election by calculating the Condorcet winner?

​ ​ ​ ​ (a)  

• Hot Dogs
• Burgers
• Tacos
• Chicken
• Salad
• Pizza

Answer explanation

If there is a choice that is preferred in every one-to-one comparison with the other choices, that choice should be the winner.

We call this winner the Condorcet Winner, or Condorcet Candidate.

Based on the preference schedule shown, which food is the winner of the election using Instant Runoff Voting (IRV)?

​ (a)  

• Pizza
• Hot Dogs
• Burgers
• Tacos
• Chicken
• Salad

Answer explanation

Instant Runoff Voting (IRV):

In IRV, voting is done with preference ballots, and a preference schedule is generated.

The choice with the least first-place votes is then eliminated from the election, and any votes for that candidate are redistributed to the voters’ next choice.

This continues until a choice has a majority (over 50%).