September 1, 1998
Media Contact: Mario Aguilera, (619) 534-7572, mcaguilera@ucsd.edu
CHAOS AT THE POLLS: MATHEMATICIANS PROVE THAT
GROUP DECISIONS CAN BE IMPOSSIBLE TO PREDICT
For several years, some political scientists and others
have argued that group decisions such as elections are impossible to
anticipate-even if the preferences of the voters are well established
and the decision-making rules are set.
Now there's a mathematical proof to back that
proposition.
David Meyer of the University of California, San Diego
and Thad Brown of the University of Missouri studied the well
established phenomenon that says that whenever a group tries to choose
among three or more options, its decision will cycle endlessly from one
choice to another.
Mathematician Meyer and political scientist Brown looked
at the phenomenon from a new angle. What if you knew how the voters
would cast their ballots and the voting rules (majority rules, for
example) were established, but the order in which the choices were
presented changed? Meyer and Brown proved through a mathematical model
that if the group's options are presented in different orders-even when
their preferences are fixed-the result will become unpredictable, even
"chaotic." Even if the order of choices is only slightly altered, their
proof showed, the results will be completely unpredictable several
elections down the line.
"If each member of a committee, for example, has his or
her own preference for allocating a budget among two programs, the
outcome will depend crucially on the order in which the alternative
allocations are proposed," said Meyer, a member of UCSD's Project in
Geometry and Physics and the independent Center for Social Computation
and Institute for Physical Sciences. "Thus the person who sets the
agenda-the chairman-can determine the outcome by changing the order of
the alternatives."
"While some political scientists have suggested that
there was a connection between the presence of these voting cycles and
chaotic behavior, that was just a
semantic observation, there was no precise statement of what
that meant, nor a precise
proof that that was the case. What we've done is make a precise
statement and a precise
proof."
While Meyer says this chaotic behavior is less evident
in the United States because there are several mechanisms in place to
dampen its effect, it is more relevant in countries that experience
frequent changes in government.
"In this kind of cyclic, chaotic behavior, if one
little thing changes," Meyer said, "then who knows what government is
going to be in its place?"
Meyer and Brown's study, "Statistical Mechanics of
Voting," appears in a recent edition of Physical Review Letters.
While much more work lies ahead to develop models that
directly apply these studies to human politics, there is a more
immediate application in the fields of computer science and simulation
for developing "computerized agents," software-based mechanisms that can
scan the Internet for information or simulate the outcome of a
real-world scenario to aid in decision making. Such agents have been
used, for example, to establish price ratios by simulating buying and
selling commodities.
"If you're talking about people, there can be a huge
debate about whether people are rational or not," said Meyer, "but if
you're talking about software agents, they're just little bits of code
that are programmed and they have exact sets of preferences, so if
you're using them to search the web or gather information or simulate
some social process, then there's no question that these results apply."
To help guide their research, Meyer and Brown looked at
the behavior of a string of atoms in magnetic materials. By comparing
the logic of the decision making process to the behavior of the string
of atoms, Meyer and Brown demonstrated that the decision process is
often unpredictable.
"We used the string as more than an analogy, it was a
precise one-to-one correspondence," said Meyer. "It told us which
questions to ask."
In addition to voting behavior, the field of chaos has
taken hold in science because of its applications to communication
engineering, chemistry, cardiology and psychiatry. Scientists have
sought the answers that lie within chaotic situations, found in areas as
diverse as chemical reactions inside power plants, weather patterns in
the atmosphere and the ocean and even how dolphins are able to slice
through the seas by vibrating their skin.
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