Chapter 13, Problem 1RE

The 12 preference ballots for four candidates (A, B, C, and D) are shown. Construct a preference table to illustrate the results of the election.

ABCD BDCA CBDA ABCD CBDA ABCD

BDCA BDCA CBAD CBAD ABCD CBDA

To determine

A preference table to show the results of the election from the data given below –

The $12$ preference ballots for the four candidates, namely A, B, C, and D, are as shown below:

ABCD, BDCA, CBDA, ABCD, CBDA, ABCD, BDCA, BDCA, CBAD, CBAD, ABCD, CBDA

Answer to Problem 1RE

Solution:

The preference table is shown below:

Number of candidates voted	$4$	$3$	$3$	$2$
First choice	A	C	B	C
Second choice	B	B	D	B
Third choice	C	D	C	A
Fourth choice	D	A	A	D

Explanation of Solution

Given:

The $12$ preference ballots for the four candidates, namely A, B, C, and D, are as shown below:

ABCD, BDCA, CBDA, ABCD, CBDA, ABCD, BDCA, BDCA, CBAD, CBAD, ABCD, CBDA

Construct the table for the given poll.

First, write the same order preferences once as shown below:

ABCD occurs four times.

CBDA occurs three times.

BDCA occurs three times.

CBAD occurs two times.

Now, construct a preference table with five columns and five rows:

Number of candidates voted	$4$	$3$	$3$	$2$
First choice	A	C	B	C
Second choice	B	B	D	B
Third choice	C	D	C	A
Fourth choice	D	A	A	D