Math of Voting
Based on the results above, from a survey of basketball fans about the best player of all time, who did more fans vote for? (Note: Assume the number of voters under 30 was the same as the number of voters 30 or over.)
Three states are being allocated 62 seats in a legislative body. State A has 17% of the population, State B has 37%, and State C has 46%.
Applying these percentages to the 62 seats and rounding to the nearest integer means State A gets 11 seats, State B gets 23 seats, and State C gets 29 seats.
What’s wrong with this approach?
For example, if the voting regions were drawn like this, they would win 1:
A political score \(P\) is a number between 0 and 100 where \(P=0\) represents the extreme left-wing and \(P=100\) represents the extreme right-wing. A candidate's positions are also assigned a score, and each voter will vote for whichever candidate has positions with a score closest to their own.
In a two-candidate race where each candidate wants to get as many votes as possible, what position(s) will they take?
Note: In the case where two candidates are equidistant from a voter, assume the voter decides randomly.
There are four candidates in the beginning of an election: 1, 2, 3, and 4. Given the preferences of the four voters below, the only head-to-head race that will not end in a tie is between candidates numbered \(A\) and \(B.\) What is \(A \times B?\)
\[\begin{align}
\text{Alexa:} \ 1 &> 2 > 3 > 4 \\
\text{Benny:} \ 2 &> 1> 4> 3 \\
\text{Celina:} \ 3 &> 4 > 2 > 1 \\
\text{Dakota:} \ 4&>1>3>2 \\
\end{align}
\]