Chapter 1: The Mathematics of Voting: The Paradoxes of Democracy
Internet Excursions


Get Out The Vote!

Many U.S. city councils are elected using the extended (or "at-large") plurality method, in which each voter casts as many votes as there are open seats, and the winning candidates are the top vote-getters. This method is easy for voters to understand. However, once a candidate has enough votes to win, any further votes for that candidate make no difference. And none of the votes for a losing candidate make any difference either. This can lead many voters to feel that they needn't have bothered voting at all.

For this reason, some people favor a system in which more of the ballots really matter. One city using such a system is Cambridge, Massachusetts (home of Harvard University). The type used there is called the single transferable vote method, or STV for short.

1.  

Why is the "quota," GRAPHIC_1, defined the way it is?

2.  

Consider a race among candidates A, B, C, and D for two open seats on a city council, and imagine that there are only five voters: 1, 2, 3, 4, and 5. Suppose the voters' preferences among the candidates are as follows:

Voter
Candidate12345
A1st1st1st3rd3rd
B2nd2nd2nd4th4th
C3rd3rd3rd1st1st
D4th4th4th2nd2nd

Clearly there are two voting blocks: voters 1–3, and voters 4 and 5.

In an extended plurality vote, each voter would cast a vote for each of his or her two favorite candidates. Which candidates would win?

3.  

Use the demo to find the winners under the STV method.

4.  

How many voters' ballots matter under each method?

5.  

STV is often called a type of proportional representation, because it tends to give groups of voters power in proportion to their relative numbers. How does the above scenario illustrate this?


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