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The Mathematics of Voting: The...
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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," , defined the way it is?

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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

Candidate 1 2 3 4 5

A 1st 1st 1st 3rd 3rd

B 2nd 2nd 2nd 4th 4th

C 3rd 3rd 3rd 1st 1st

D 4th 4th 4th 2nd 2nd

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?

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

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4 . How many voters' ballots matter under each method?

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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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