Math Is Fun Forum

baldwine

Member

Registered: 2021-11-06

Posts: 2

Math

Hello I'm having a difficult time with the following questions.
Please Help

1.
A preference table helps to organize data for a variety of situations. Often it is used to help organize the preferred choice of those that are surveyed. The data below references a three-way race for a political office. Use the preference table to answer the following question:

Which candidate would be the winner by plurality?

First Choice

Michael

Jessica

Peter

Jessica

Second Choice

Peter

Peter

Jessica

Michael

Third Choice

Jessica

Michael

Michael

Peter

22

20

17

8

Question 1 options:

Peter

Michael

Jessica

No candidate won by plurality.

2 question

When analyzing a preference schedule, it is noted that there are six candidates. There was a total of 25 votes counted. According to the Borda count method, what is the total number of points awarded to the candidates?

Question 2 options:

625

525

900

25

baldwine

Member

Registered: 2021-11-06

Posts: 2

Re: Math

I'm having a difficult time figuring out this question. please explain the steps.

When analyzing a preference schedule, it is noted that there are six candidates. There was a total of 25 votes counted. According to the Borda count method, what is the total number of points awarded to the candidates?

Question 2 options:

625

525

900

25

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Math

hi baldwine

Welcome to the forum.

I had not met these voting systems before so I used google.

According to http://croninmath.pbworks.com/w/file/fe … ethods.pdf

plurality means "the candidate with the most first-place votes is the winner"

There is a winner with question 1 and it is easy to see who it is.

I found a definition of border count on Wikipedia https://en.wikipedia.org/wiki/Borda_count

If a candidate is placed first by a voter then that candidate scores 5 + 4 + 3 + 2 + 1 for that vote.  There must be 25 candidates (not all different of course) who get that score so the total score must be 25 x (1+2+3+4+5) Unfortunately that doesn't correspond to any of the multi choice answers.  Not sure where to go from here.

Do you have an alternative definition of borda counting?

1+2+3+4+5 must feature so I am now looking at dividing the possible answers by 15.  Only two qualify.  And one of these is correct if there are 35 not 25 voters.  Any help?

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

T897T

Member

Registered: 2021-09-21

Posts: 42

Re: Math

I think with 6 candidates he counts from 6 to 1 in which case 525.
I do think baldwine could have made the questions clearer

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Forced purity isn't pure.
Good and Evil are different for each person.
I chose 8 9 and 7 randomly.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Math

hi T897T

You may be right. I had not met this method of vote counting before and just used the Wiki example.  If the scores as as you say it bumps up everyone's totals but doesn't affect the overall ranking of the vote count, so it would still work the same, and give the same winner.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob