$\begin{array} { l | c c c c c }
\text { State } & \mathrm { a } & \mathrm { b } & \mathrm { c } & \mathrm { d } & \mathrm { e } \
\hline \text { Population } & 131 & 140 & 304 & 178 & 197
\end{array}$
-If the Hamilton Method is used to apportion legislative seats to three original states and a new state with the populations given in the table, then one of the states loses a seat to another if the original Number of seats being apportioned is 60. $$\begin{array} { l | c c c c }
\text { State } & \text { Original State a } & \text { Original State b } & \text { Original State c } & \text { New State d } \
\hline \text { Population } & 62,700 & 230,700 & 606,600 & 78,000
\end{array}$$ Which state loses a seat to which state, and does the New States paradox occur?
A)c loses a seat to b, yes
B)c loses a seat to a, yes
C)b loses a seat to a, yes
D)a loses a seat to b, yes

Question

$\begin{array} { l | c c c c c } 
\text { State } & \mathrm { a } & \mathrm { b } & \mathrm { c } & \mathrm { d } & \mathrm { e } \
\hline \text { Population } & 131 & 140 & 304 & 178 & 197
\end{array}$
-If the Hamilton Method is used to apportion legislative seats to three original states and a new state with the populations given in the table, then one of the states loses a seat to another if the original Number of seats being apportioned is 60. $$\begin{array} { l | c c c c } 
\text { State } & \text { Original State a } & \text { Original State b } & \text { Original State c } & \text { New State d } \
\hline \text { Population } & 62,700 & 230,700 & 606,600 & 78,000
\end{array}$$ Which state loses a seat to which state, and does the New States paradox occur?
A)c loses a seat to b, yes
B)c loses a seat to a, yes
C)b loses a seat to a, yes
D)a loses a seat to b, yes

Quizplus · Accepted Answer

State c loses a seat to state b, and the New States paradox occurs. This is because when a new state is added and the total number of seats is redistributed, the relative proportions of the original states' populations can cause one of the original states to lose a seat to another, despite the overall number of seats increasing. This paradox highlights the counterintuitive outcome where adding a new state (and more seats) can lead to an original state losing a seat to another due to the way the Hamilton method of apportionment redistributes seats based on updated population proportions.

-If the Hamilton Method Is Used to Apportion Legislative Seats