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Chapter 13: Problem 17

According to Balinski and Young's Impossibility Theorem, can the democratic ideal of "one person, one vote" ever be perfectly achieved? Explain your answer.

Short Answer

Expert verified
According to Balinski and Young's Impossibility Theorem, the democratic ideal of 'one person, one vote' cannot be perfectly achieved. This is because no apportionment method in a representative democracy can meet all the criteria for fairness outlined in the theorem, which implies that there will always be some imbalance in the value of individual votes.

Step by step solution

01

Understand 'One person, one vote' principle

'One person, one vote' is a democratic principle that emphasizes that each citizen's vote should hold the same weight in an electoral process. In essence, every person gets one vote, and all votes are equal.
02

Understand Balinski and Young's Impossibility Theorem

Balinski and Young's Impossibility Theorem addresses the issue of fair apportionment in the context of choosing proportional representation for states in the US Congress or seats in parliament. Essentially, the theorem states that no apportionment method can meet all of four fairness criteria: non-decreasing quota, population proportionality, house monotonicity, and quota.
03

Apply Balinski and Young's Impossibility Theorem to the 'One person, one vote' principle

Applying the theorem to the 'one person, one vote' principle, it implies that a perfectly fair representation where every person's vote has equal influence is impossible in a representative democracy. This is due to the fact that apportionment methods will always fail in at least one of the fairness criteria outlined by Balinski and Young.

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Most popular questions from this chapter

In your own words, describe Hamilton's method of apportionment.

A town has 40 mail trucks and four districts in which mail is distributed. 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 $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { District } & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\ \hline \text { Original Population } & 1188 & 1424 & 2538 & 3730 & 8880 \\ \hline \text { New Population } & 1188 & 1420 & 2544 & 3848 & 9000 \\ \hline \end{array} $$

Describe the plurality method. Why is ranking not necessary when using this method?

Throughout this Exercise Set, in computing standard divisors, standard quotas, and modified quotas, round to the nearest hundredth when necessary. A small country is comprised of four states, \(A, B, C\), and \(D\). The population of each state, in thousands, is given in the following table. Use this information to solve Exercises $1-4 . $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { State } & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\ \hline \begin{array}{l} \text { Population } \\ \text { (in thousands) } \end{array} & 138 & 266 & 534 & 662 & 1600 \\ \hline \end{array} $$ According to the country's constitution, the congress will have 80 seats, divided among the four states according to their respective populations. a. Find the standard divisor, in thousands. How many people are there for each seat in congress? b. Find each state's standard quota. c. Find each state's lower quota and upper quota.

$$ \begin{array}{|l|c|c|c|c|c|} \hline \text { Number of Votes } & \mathbf{1 6} & \mathbf{1 4} & \mathbf{1 2} & \mathbf{4} & \mathbf{2} \\ \hline \text { First Choice } & \text { A } & \text { D } & \text { D } & \text { C } & \text { E } \\ \hline \text { Second Choice } & \text { B } & \text { B } & \text { B } & \text { A } & \text { A } \\ \hline \text { Third Choice } & \text { C } & \text { A } & \text { E } & \text { B } & \text { D } \\ \hline \text { Fourth Choice } & \text { D } & \text { C } & \text { C } & \text { D } & \text { B } \\ \hline \text { Fifth Choice } & \text { E } & \text { E } & \text { A } & \text { E } & \text { C } \\ \hline \end{array} $$ a. Using the Borda count method, who is the winner? b. Is the majority criterion satisfied? Explain your answer. c. Is the head-to-head criterion satisfied? Explain your answer.
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