A Fair Division Question

Prepared by:

Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451



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Four people (Alice, Bob, Charles, and David) have summer homes that are used intensively during the summer and visited throughout the year along a single road that branches off from a (paved) highway. The road their homes lie along is unpaved and not in good condition. The four home owners agree that it would benefit them all if the road were paved. They solicited bids for the work and received the firm estimate of $72,000 for the whole job.

Starting from the highway, where the unpaved road begins:

Alice lives at the 1 mile mark.

Bob lives at the 2 mile mark.

Charles lives at the 4 mile mark.

David lives at the 8 mile mark.

1. In your judgment what would be the best/fairest way to assign a share of the costs for carrying out this project to Alice, Bob, Charles, and David? Your solution should be based only on the information given.

2. What are other ways to divide the costs that you or someone else might have considered but rejected in favor of the approach you chose?

3. What additional information, which had it been available to you, might have lead to a different/better approach to allocating the $72,000 cost?

4. Describe the "algorithm" behind your method so that someone could apply the method you developed to any number of individuals who had to share a cost for paving a single road, given information about the distance they are from the start of the road.

5. Describe other "situations" where your method seems like a reasonable one for sharing costs.

6. Suppose the houses that were along unpaved roads which connect to a paved highway at a single location were not along a single road but had a more complex "geometry." How might you proceed?