The following questions review the main ideas of this chapter. Write your answers to the...

The following questions review the main ideas of this chapter. Write your answers to the questions and then refer to the pages listed by number to make certain that you have mastered these ideas.

What is the difference between a simple majority and a supermajority? pg. 184 What is the quota and how is a weighted voting system represented? pg. 184

Reference:

WEIGHTED VOTING SYSTEMS

In a weighted voting system, any particular voter might have more than one vote. Because it can be confusing to talk about voters having more than one vote, we speak instead about the weight assigned to each voter. For example, in the electoral college system, a state’s weight is its number of electoral votes (the number of senators plus the number of representatives). In an election held by company stockholders, the voter’s weight is the number of shares of stock owned by that voter. To describe the situation, we can list the voters and their respective weights in the form of a table (Table 3.28).

For mathematical purposes, the voters’ names are unimportant; all we really need to know are the number of voters and their weights. That minimal information is usually recorded as a sequence of numbers in square brackets with the weights listed in decreasing order of size. The crucial mathematical information from Table 3.28 is captured in the following notation: [12, 11, 9, 8].

To denote the voters and their weights, we generally use subscripts. The voter with weight 12 is simply called the “first voter” and is given the name P₁. The weight of this first voter is represented by W₁, so in this case W₁ = 12. The voter with weight 11 is called the “second voter,” is denoted as P₂, and has weight W₂ =11. The remaining voters and their weights are represented in a similar manner.

In this section, we will limit our discussion to voting on simple yes/no questions. Such questions are commonly called motions. We will assume that a final decision of “no” defeats the motion and leaves the status quo (the current situation) unchanged, while a decision of “yes” passes the motion and changes the status quo. Generally speaking, for a motion to pass, voters whose weights total more than half the total weight must vote yes on that motion. In presidential elections, for example, the winning candidate must receive at least 270 electoral votes, which is one more than half the total 538 electoral votes. The requirement that a candidate must receive one more than half of the votes is called a simple majority. Sometimes, however, the threshold for changing the status quo may be set even higher than one more than half the total weight. This requirement is called a supermajority. For example, it is common for legislative bodies to require a two-thirds vote to pass constitutional amendments. In fact, a two-thirds vote is necessary in both the House and Senate chambers to override a presidential veto.