We now consider an important example of manipulation of sequential pairwise voting. Suppose three voters on City Council have to decide whether to add a new sales tax. Initially

• A prefers the tax

• B prefers the tax

• C prefers no tax

so a tax will be introduced.

However, let’s assume A hates income taxes and will never vote for one. On the other hand, B prefers income tax to sales tax. Suppose C moves an amendment to change the tax to an income tax.

We now have:

Original motion: that a city sales tax of 5% be introduced.

Amendment (moved by C): change “sales tax of 5%” to “income tax of 2%.”  (We’ll assume the 2% income tax will provide the same total as the 5% sales tax.)