Weighted Voting for Madison Count

Madison County, the county where you now live, has a Board of Supervisors, one from each town and four from the city of Oneida. Consequently, they use a weighted voting system. You have been hired by the board as a consultant to devise a weighted voting system for Madison Count, based on the 2010 census.

1. Calculate the percentages of population, to two decimal places, for each town and Oneida district, given the populations below.

Brookfield 2,545

Cazenovia 7,086

DeRuyter 1,589

Eaton 5,255

Fenner 1,726

Georgetown 974

Hamilton 6,690

Lebanon 1,332

Lenox 9,122

Lincoln 2,012

Madison 3,008

Nelson 1,980

Oneida w1-2-3 6,220 (2 representatives on board)

Oneida w 4-5-6 5,173 (2 representatives on board)

Smithfield 1,288

Stockbridge 2,103

Sullivan 15,339

2. Select a starting total number of weighted votes for the county. This is arbitrary. The current total is 1500 votes distributed among the towns. You may choose a higher or lower starting number of votes.

3. Use the program and data file supplied by the instructor to calculate the Banzhaf index when the number of votes for each town matches the percent of the population.

4. Using the program, repeatedly adjust the vote by adding and subtracting votes from different towns, until you develop a weighted vote so that the Banzhaf power index for a majority vote, as a percent, for each town is within +/-2% of the percent of population that town has. For example if a town has 9.8% of the population, then its Banzhaf index, as a percent, should be 9.8 +/- 0.19, or from 9.61 to 9.99. This relative error is given by the program. You must make the adjustments in your votes so that the total remains the same as your starting total, or so that the additions and subtractions add to zero.

5. Repeat step 5 for a vote requiring a 2/3 majority, you may use a threshold of +/-3% for the relative error.

6. Write a report suitable for the Madison County Board of Supervisors describing your recommended assignment of weighted votes for the simple majority and two-thirds majority. If you have two or more possibilities that fall within the threshold, describe all the alternatives that you have come up with. This report should not include the details of your calculation, but should indicate how you developed your recommended vote assignments in a way suitable for a non-expert, e.g. someone who might be on the Board of Supervisors.