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Chapter 13: Problem 39

How are modified quotas rounded using Webster's method?

Short Answer

Expert verified
Webster's method applies standard rounding to the calculated quotas. Fractions under 0.5 are rounded down, and those 0.5 or above are rounded up for a fairer and more proportional allocation.

Step by step solution

01

Understanding the basics

Webster's method modifies quotas by using standard rounding practices. Each quota gets rounded to the nearest whole number. This means any quota with a fractional part less than 0.5 gets rounded down, and any with a fractional part of 0.5 or more gets rounded up.
02

Handling specific scenarios

For fractional quotas exactly halfway between two whole numbers (i.e., ending in .5), traditional rounding rules dictate rounding to the nearest even whole number. However, in Webster's method, such amounts are always rounded up to the next whole number, broadening the chance for the overrepresented parties.
03

Ensuring a fair allocation

The rounded quotas are then summed up. If they add up to the exact total that was needed, the process ends. If not, adjustments may be needed, usually involving revisions to the standard divisor and subsequent recalculation of standard quotas. This process is repeated as many times as necessary to reach the required total. It's worth noting that these revisions aim to keep the distribution of quotas as proportional and fair as possible.

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Most popular questions from this chapter

a. A country has three states, state \(A\), with a population of 99,000 , state \(B\), with a population of 214,000 , and state \(C\), with a population of 487,000 . The congress has 50 seats, divided among the three states according to their respective populations. Use Hamilton's method to apportion the congressional seats to the states. b. Suppose that a fourth state,state D, with a population of 116,000 , is added to the country. The country adds seven new congressional seats for state D. Use Hamilton's method to show that the new-states paradox occurs when the congressional seats are reapportioned.

MTV's Real World is considering three cities for its new season: Amsterdam (A), Rio de Janeiro (R), or Vancouver (V). Programming executives and the show's production team vote to decide where the new season will be taped. The winning city is to be determined by the plurality method. The preference table for the election is shown at the top of the next column. $$ \begin{array}{|l|c|c|c|c|} \hline \text { Number of Votes } & \mathbf{1 2} & \mathbf{9} & \mathbf{4} & \mathbf{4} \\ \hline \text { First Choice } & \text { A } & \text { V } & \text { V } & \text { R } \\ \hline \text { Second Choice } & \text { R } & \text { R } & \text { A } & \text { A } \\ \hline \text { Third Choice } & \text { V } & \text { A } & \text { R } & \text { V } \\ \hline \end{array} $$ a. Which city is favored over all others using a head-tohead comparison? b. Which city wins the vote using the plurality method? c. Is the head-to-head criterion satisfied? Explain your answer.

Describe the apportionment problem.

A town has five districts in which mail is distributed and 50 mail trucks. The trucks are to be apportioned according to each district鈥檚 population. The table shows these populations before and after the town鈥檚 population increase. Use Hamilton鈥檚 method to show that the population paradox occurs. $$ \begin{array}{|l|c|c|c|c|c|c|} \hline \text { District } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { Total } \\ \hline \begin{array}{l} \text { Original } \\ \text { Population } \end{array} & 780 & 1500 & 1730 & 2040 & 2950 & 9000 \\ \hline \text { New Population } & 780 & 1500 & 1810 & 2040 & 2960 & 9090 \\ \hline \end{array} $$

The winner by the plurality method violates the irrelevant alternatives criterion.
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