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.”