CHAPTER 1 – M

ATH

ANALYSIS

WH AT D

O I K N O W

SO F

A R ? ? ? MA G N E T

R E V I EW

OLDEST partner describe how the sequential run-off

method works….

Sequential MethodIn a Sequential Runoff system, only the

candidate with the fewest first-place votes is eliminated immediately, and the votes are recalculated. This process is repeated until there are only two candidates remaining, at which point the remaining candidate with the most first-place votes is the winner.

RE DRAW YOUR PREFERENCE SCHEDULES!!

Partner with MORE siblingsExplainHow to

Determine if There

IsA

MAJORITYWINNER

MAJORITY WINNER 

Sometimes people mistakenly refer to a plurality system as “majority rules”, but there is an important distinction: to be a majority winner, a candidate has to be ranked first on over half of the ballots (whereas a plurality winner could have far fewer than half of the votes, as long as they have more than any other candidate).

 

PARTNER with

LIGHTER EYESExplain how

the Borda Method works

In a Borda system, points are awarded to the first, second, third, fourth, (etc) choice on

each ballot. The total points earned by each candidate are compared to determine a final

ranking. The most common point assignment is to award

ONE points for a last-place vote, 2 points for a next-to-last place, and so on (in

a race with n candidates, a first-place vote would award n points).

PARTNER with

MORE PETSExplain how the

RUN – OFF METHOD works

In a Runoff system, all but the two candidates with the most first-place

votes are eliminated immediately, and votes for those candidates are

“inherited” by the highest-ranking candidate on each ballot who is still in the race. Using these updated results, the candidate with the most first-place

votes is the winner.

MAGNET REVIEW DIRECTIONS

1) Choose an alias…think Rock Stars, cartoon characters, actors, famous historians, politician, teacher, Disney characters, talk show hosts… and write that name on the top of each of your four slips. DO NOT CHOOSE INAPPROPRIATE NAMES!

2) Solve the question on your piece of notebook paper and transfer only your answers to the slip. Remember, you are competing against the person sitting next to you so don’t let them see what you are writing down!

3) When Ms. Gagliano gives the OKAY, walk to the board and magnet your answer on your teams side.

4) Sit back and wait and see if you got it right!

QUESTION #1

If there are 35 students running in the election for social chair and Hinsdale Central decides to use a

Run- Off election to determine a winner, how many candidates will be eliminated in the first

round?

ANSWER TO QUESTION #1

33

QUESTION #2 Refer to the preference schedule below to answer

this question..

If a winner is to be determined by the SEQUENTIAL RUN-OFF

Method , tell me which candidate is eliminated in the THIRD round?

ANSWER TO QUESTION #2

C

QUESTION #3Determine if there is a majority winner in the election below

and support your answer with a numerical statement.

ANSWER TO QUESTION 3There is NO majority winner

because C has the most first place votes with 16, but there are a total of 32 votes and to be the majority

winner you must have MORE THAN HALF OF FIRST PLACE

VOTES!16 > 16

QUESTION #4Using the Borda method, determine

how many points A would earn.

ANSWER TO QUESTION #4

A=5(3) + 10(1) + 1(2) + 5(3) + 11(2)

= 64

QUESTION #5:

Determine the CONDORCET

WINNER,If one exists…

ANSWER TO QUESTION #5