American Institute of Physics
SEARCH AIP
home contact us sitemap
Physics News Update
Number 385 (Story #1), August 3, 1998 by Phillip F. Schewe and Ben Stein

GROUP DECISIONS CAN BE MATHEMATICALLY UNPREDICTABLE even with total knowledge of everyone's individual choices and the use of completely explicit decision making rules, a new study shows. As it turns out, the order in which the choices are presented to a group can make the course of the decision process impossible to anticipate. Not only does this new result address the murky human process of amending Congressional bills, but it also confirms the idea that groups of computerized "intelligent agents" each with its own rules for buying and selling commodities can cause prices to fluctuate in a mathematically chaotic fashion. Whenever a group tries to choose among three or more options by weighing two at a time, its decision can often cycle endlessly from one choice to another, especially when there is a large diversity of preferences. To address the consequences of such cycles, David Meyer (UC-San Diego, 619-534-5524) and Thad Brown (Univ. Missouri) model each possible sequence of choices as a minimum-energy configuration of a one-dimensional system, such as the string of atoms with up and down spins used in studying magnetic materials. For those sequences that cycle endlessly through different options, the system has a greater-than- zero entropy--meaning that there is an uncertainty in what the group's next choice will be. In this case the dynamics are chaotic---the next choice in the cycle is unpredictable since it depends sensitively on the order in which options are presented to the group. (Meyer and Brown, Physical Review Letters, 24 August 1998.) See figure at Physics News Graphics