Mathematics

### Paper 1, due Monday, March 1

There are three possibilities for this paper. Pick one.

#### 1. Apportionment

You are on the staff of the Judiciary Committee of the United States of Representatives. You have been assigned to write a 3-to-5 page paper on the question: Should the method of apportioning the United States House of Representatives be changed, and if so, to what?

The current method is Huntington-Hill. You may recommend that its use continue, or you may recommend that it be replaced by another method, such as Hamilton, Webster, or one we have not discussed such as Dean's method.

You should clearly explain:

1. What criteria should, in your opinion, be used to select a good apportionment method, and why these criteria are important.
2. Why other criteria that have been proposed are not, in your opinion, appropriate, and should not be used.
3. Why, given the criteria you have decided to use, the method you recommend is the best.

Try for:

1. Clarity and precision. The reader should not have to wonder what you mean.
2. Accuracy. If you explain standard criteria, or describe problems with these criteria, do so accurately.
3. Logic. Pay attention to the relationship between the points that you make.
4. Depth. Superficial cleverness is not useful to the House Judiciary Committee. You should try to imagine objections to your recommendation and deal with them seriously and respectfully.

In human affairs, there are usually reasonable arguments on several sides of an issue. Nevertheless, we must try to sort things out as best we can and make a choice.

#### 2. Voting methods

You are on the staff of the General Assembly of North Carolina. You have been assigned to write a 3-to-5 page paper on the question: Should the method of electing the governor and other statewide officials be changed, and if so, to what?

Currently the governor and other statewide officials are elected by plurality vote: There may be more than two candidates on the ballot, but whoever gets the most votes wins, even if that is not a majority. You may recommend that we continue to use the plurality method, or you may recommend that it be replaced by another method, such as Hare, Borda count, or one we have not discussed, such as instant runoff among the top two vote-getters, or approval voting.

You should clearly explain:

1. What criteria should, in your opinion, be used to select a good voting method, and why these criteria are important.
2. Why other criteria that have been proposed are not, in your opinion, appropriate, and should not be used.
3. Why, given the criteria you have decided to use, the method you recommend is the best.

Try for:

1. Clarity and precision. The reader should not have to wonder what you mean.
2. Accuracy. If you explain standard criteria, or describe problems with these criteria, do so accurately.
3. Logic. Pay attention to the relationship between the points that you make.
4. Depth. Superficial cleverness is not useful to the General Assembly of North Carolina. You should try to imagine objections to your recommendation and deal with them seriously and respectfully.

In human affairs, there are usually reasonable arguments on several sides of an issue. Nevertheless, we must try to sort things out as best we can and make a choice.

#### 3. Other

A topic of your choice approved in advance by the instructor.