Determine whether the specified paradox occurs.
-A town has 13 police officers to be apportioned among 3 precincts based on the population of each Precinct. The populations for the years 1998 and 1999 are given in the following table. $$\begin{array} { l l l l }
\hline \text { Precinct } & \mathbf { 1 } & \mathbf { 2 } & \mathbf { 3 } \
\hline \text { 1998 Population } & 930 & 738 & 415 \
\text { 1999 Population } & 975 & 750 & 421 \
\hline
\end{array}$$
Does the population paradox occur using Hamiltonʹs method of apportionment?
A) Yes
B) No

Question

Determine whether the specified paradox occurs.
-A town has 13 police officers to be apportioned among 3 precincts based on the population of each Precinct. The populations for the years 1998 and 1999 are given in the following table. $$\begin{array} { l l l l } 
\hline \text { Precinct } & \mathbf { 1 } & \mathbf { 2 } & \mathbf { 3 } \
\hline \text { 1998 Population } & 930 & 738 & 415 \
\text { 1999 Population } & 975 & 750 & 421 \
\hline
\end{array}$$
Does the population paradox occur using Hamiltonʹs method of apportionment?
A) Yes
B) No

Quizplus · Accepted Answer

The population paradox occurs when a precinct with a higher growth rate receives fewer representatives than a precinct with a lower growth rate after apportionment, despite both precincts increasing in population. Using Hamilton's method for both years:- Total population in 1998: 930 + 738 + 415 = 2083- Total population in 1999: 975 + 750 + 421 = 2146Standard divisor for 1998: 2083 / 13 = 160.23Standard divisor for 1999: 2146 / 13 = 165.08Standard quota for precincts in 1998:- Precinct 1: 930 / 160.23 ≈ 5.80- Precinct 2: 738 / 160.23 ≈ 4.61- Precinct 3: 415 / 160.23 ≈ 2.59Standard quota for precincts in 1999:- Precinct 1: 975 / 165.08 ≈ 5.91- Precinct 2: 750 / 165.08 ≈ 4.54- Precinct 3: 421 / 165.08 ≈ 2.55After rounding the quotas to allocate the exact number of officers, it's possible that despite Precinct 1 and Precinct 2 both increasing in population, the rounding process could result in Precinct 1 gaining an officer at the expense of Precinct 2, which also increased in population but at a slower rate. This demonstrates the population paradox, where the precinct with a higher growth rate (Precinct 1) could potentially receive more representatives than before, while a precinct with a lower growth rate (Precinct 2) could receive fewer, despite both precincts growing.

Determine Whether the Specified Paradox Occurs Does the Population Paradox Occur Using Hamiltonʹs Method of Apportionment