**Problems 1-10**

These problems are designed to help you understand the material of this section. Read each criteria and then paraphrase it into your own words as requested in each of these problems.

**Problems 11-14**

These problems are based on the majority criterion, as shown in Example 1.

**Problems 15-16**

These problems are based on the fairness criteria, as shown in Examples 5 and 6.

**Problems 17-18**

These problems are based on the Condorcet criterion, as shown in Example 2.

**Problem 19**

This problems are based on the irrelevant alternatives criterion, as shown in Example 4.

**Problems 20-24**

These sets of problems are based on the Condorcet, as shown in Example 2.

**Problems 25-29**

These sets of problems are based on the Condorcet, as shown in Example 2.

**Problems 30-35**

These problems are based on the irrelevant alternatives criterion, as shown in Example 4.

**Problems 36-37**

These problems are based on the monotonicity criterion, as shown in Example 3.

**Problems 38-39**

These pairs of problems are based on the fairness criteria, as shown in Examples 5 and 6.

**>Problems 40-41**

These pairs of problems are based on the fairness criteria, as shown in Examples 5 and 6.

**Problems 42-45**

These problems are based on the Condorcet criterion, as shown in Example 2.

**Problems 46-50**

These problems are based on the fairness criteria, as shown in Examples 5 and 6.

**Problems 51-56**

These problems are based on Arrow’s impossibility theorem and insincere voting, as shown in Example 7.

### Note: Homework Hints are given only for the Level 1 and Level 2 problems.

However, as you go through the book be sure you look at all the examples in the text. If you need hints for the Level 3 problems, check some sources for help on the internet (see the LINKS for that particular section. As a last resort, you can call the author at (707) 829-0606.

On the other hand, the problems designated “Problem Solving” generally require techniques that do not have textbook examples.

There are many sources for homework help on the internet.

Algebra.help

Here is a site where technology meets mathematics. You can search a particular topic or choose lessons, calculators, worksheets for extra practice or other resources.

http://www.algebrahelp.com/

Quick Math

This site provides online graphing calculators. This is especially useful if you do not have your own calculator.

http://www.quickmath.com/

The Math Forum @ Drexel

This site provides an internet mathematics library that can help if you need extra help. For additional homework help at this site, click one of the links in the right-hand column.

http://mathforum.org/