University of California, Irvine
3295 Social Sciences Plaza B
Irvine, CA 92697-3875
For the last half century, a standard approach toward understanding data, voting procedures, decision methods, etc. has been to impose conditions on the procedures. But rather than leading to consensus, debates had arisen about which conditions are better than others, and even impossibilities assertions such as Arrow's Theorem. On the other hand, by emphasizing the underlying symmetry and other structures of data, Arrows' theorem is replaced with a possibility assertion and positive assertions are obtained. The ideas are supported by examples from voting, social choice, engineering, etc.