Mathematical Modeling in the Social and Life Sciences

CHAPTER 6

Social Choice and Voting Procedures

The general will is always right and tends to the public advantage; but it does not follow that the deliberations of the people are always equally correct. Our will is always for our own good, but we do not always see what that is; the people is never corrupted, but it is often deceived.

—Jean-Jacques Rousseau

I. Three Voting Situations

This chapter illustrates the use of axiomatic models by investigating some of the procedures groups of voters use to determine collective judgments from individual preferences. These procedures characteristically have certain injustices associated with them. An axiomatic approach reveals that attempts to redesign the procedures or invent new ones to avoid these inequities are doomed to frustration.

An illustrative real-world example is the U.S. Senate and its attempts to reach agreement on certain types of important issues. The model we develop concerns certain kinds of collective judgments, which are exemplified by the following three illustrations.

Example 1

The president nominates a South Carolina lawyer for a position on the U.S. Supreme Court. The Senate must decide whether to confirm the nomination or not.

Example 2

Three proposals for dealing with the dependents' deduction feature of the federal income tax have been offered. Proposal A calls for a substantial increase in the amount of the deduction so that it will more accurately reflect the costs of rearing children in today's economy. Proposal ...