Arrow's Theorem: What Does It Really Mean and How Does It Affect All Academic Disciplines?
Institute for Mathematical Behavioral Sciences
University of California - Irvine
"Arrow's Theorem" is a beautiful mathematical result; it is among the mathematical theorems that have had the greatest impact over the last half century. Yet, most mathematicians have, at best, only a passing acquaintance with it. After introducing the theorem in this expository lecture, I will then explain why the result does not mean what almost everyone has accepted for 50 years. After a reinterpretation and extension, it will then be shown how this result has serious implications for all disciplines—in particular, engineering, astronomy, decision analysis, and so forth.