June 2, 2000: Volume 49, Number 10

Math Could Solve Navajo-Hopi Dispute: Manygoats

Jaime Manygoats '00 is no stranger to the long-running Navajo-Hopi land dispute.

As a Navajo raised on native lands near the "Four Corners" of the Southwest, the dispute was part of her culture, so well known in her communities – Window Rock, Ariz., and Two Grey Hills, N.M., where she moved at age 12 – there was no need to teach it in schools.

But it wasn't until last spring when the mathematics major first met with her thesis advisor, Prof. Alan Taylor, that she realized that a mathematical technique could resolve a dispute that in the last century has caused more forced relocation than the interment of Japanese Americans during World War II.

This spring, the senior presented her thesis – "Fair Division: A Proposed Mathematical Resolution of the Navajo-Hopi Land Dispute" – to both Navajo and Hopi leaders.

Her proposal uses a procedure called Adjusted Winner (developed by Taylor and Steven Brams of New York University, authors of The Win-Win Solution: Guaranteeing Fair Shares for Everybody), which gives an equitable, envy-free and efficient solution. The procedure calls for each player to assign a value to each "good" or "issue" in dispute, up to a total of 100 points. The player who assigns the highest value to a particular item "wins" that good or issue.

After studying the A.W. technique, Manygoats thoroughly researched the Navajo-Hopi land conflict, says Taylor. She then identified 16 controversial issues – ranging from land to sacred sites to grazing rights – proposed what winning and losing on each would entail, and made an educated guess as to how each side would quantify its preferences, he said.

Ironically for Manygoats, U.S. President Chester A. Arthur (Union Class of 1848) was partly responsible for the start of the dispute. Arthur's 1882 executive order established a rectangular 2.4 million-acre reservation for the Hopi and "such other Indians as the Secretary of the Interior may see fit to settle thereon." Though the order was intended to protect the Hopi, the reference to "such other Indians" also included the Navajo. When the reservation was created – with no inquiry by the government about actual land usage, according to Manygoats – there were over 900 sacred sites (mostly Navajo) on the Hopi reservation.

"This was an excellent thesis, and a model for how mathematics can and should be applied," said Taylor. "The hope is that the adjusted winner resolution will at least shed some light in this struggle."

Manygoats concedes that her proposal "does not provide both parties with all that they would like. However, like many important settlements, it represents a compromise for each of the parties, not a perfect solution for anyone."

As for the likelihood that tribal leaders will adopt her proposal, she says she is realistic but optimistic. "I was skeptical at first until I studied it," she recalled. "But now that I know there are procedures out there like Adjusted Winner, I find myself conditioned to use it for any dispute I see."

Manygoats received the Eugene W. Hellmich Mathematics Prize, to a student preparing for a career in teaching mathematics, and she was selected to be a class marshal at Commencement.

The daughter of teachers Paul and Thelma Manygoats, she will begin study this fall at the Teachers College of Columbia University toward a master's degree in mathematics education.

Ultimately, she plans to teach on the Navajo nation, where there is a shortage of Navajo teachers. "I grew up there and I saw the trend of many youths not being encouraged to go to college," she said. "I think it is important that they have a role model they can relate to."

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