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September 1, 1998


Media Contact: Mario Aguilera, (619) 534-7572, mcaguilera@ucsd.edu




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



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



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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