Use the following information to answer the Questions
A group of 22 young people must decide whether to go to the beach (B), the mountain (M), or the zoo (Z) on a field trip. Their preference rankings are summarized in the table below, and the decision will be made using a Borda count. $ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$\text { Number of voters }$
$\begin{array} { l c c c }
& 10 & 8 & 4 \
\text { First choice } & \mathrm { B } & \mathrm { M } & \mathrm { Z } \
\text { Second choice } & \mathrm { M } & \mathrm { B } & \mathrm { M } \
\text { Third choice } & Z & Z & \mathrm {~B}
\end{array}$
-Can the 10 voters in the first column change the results of the vote to their favor by changing their preference rankings?

Question

Use the following information to answer the Questions 
A group of 22 young people must decide whether to go to the beach (B), the mountain (M), or the zoo (Z) on a field trip. Their preference rankings are summarized in the table below, and the decision will be made using a Borda count. $ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$\text { Number of voters }$
$\begin{array} { l c c c } 
& 10 & 8 & 4 \
\text { First choice } & \mathrm { B } & \mathrm { M } & \mathrm { Z } \
\text { Second choice } & \mathrm { M } & \mathrm { B } & \mathrm { M } \
\text { Third choice } & Z & Z & \mathrm {~B}
\end{array}$
-Can the 10 voters in the first column change the results of the vote to their favor by changing their preference rankings?

Quizplus · Accepted Answer

In a Borda count, voters rank options in order of preference, and points are assigned based on position in each voter's ranking (e.g., 2 points for a first choice, 1 point for a second choice, and 0 points for a third choice in this scenario). The original rankings give the beach (B) 20 points (10 voters * 2 points), the mountain (M) 26 points (8 voters * 2 points + 4 voters * 1 point + 10 voters * 1 point), and the zoo (Z) 8 points (4 voters * 2 points). Changing the preference rankings of the 10 voters for B will not increase the total points for B beyond those for M, as the maximum additional points B can gain is from those 10 voters placing M as their third choice instead of their second, which does not affect the total points for B directly. The outcome is determined by the total points each option receives, and the preferences of the 10 voters for B primarily influence the points for B and M indirectly through their second and third choices.

Use the Following Information to Answer the Questions a \quad

Use the Following Information to Answer the Questions
a $\quad$