Don Saari's Home Page

 

 
Donald G. Saari

UCI Distinguished Professor: Mathematics and Economics

Professor (courtesy): Logic and Philosophy of Science

Director:

Institute for Mathematical Behavioral Sciences

2123 SSPA
Administrative Manager: Joanna Kerner jkerner@uci.edu
Phone: (949) 824-8651
FAX: (949) 824-3733

Department of Mathematics

and

Department of Economics
University of California
Irvine, California 92697-5100

dsaari@uci.edu

PERSONAL INFORMATION

Personal information , such as an abbreviated CV and a description of some of my background is available here. 

 

 

Institute for Mathematical Behavioral Sciences


Without question, this is one of the more exciting periods in history to be a mathematician! Just think about all of the advances that have been made, the number of major problems solved within the last couple of decades, the new directions being pioneered. In addition, in recent years other academic areas have become mathematically more sophisticated; as such, expect them to introduce new, unusual, and unexpected mathematical structures and questions. This has been the case with the physical sciences, and it now is happening in the behavioral and social sciences.

One of the goals of the Institute for Mathematical Behavioral Sciences is to enhance these mathematical connections and extract the new mathematical structures while helping to advance these behavioral and social sciences. If you wish to learn more about the active conference, colloquia and seminar series we are planning in these directions, please contact us IMBS. Even better, how about joining in with us?


Fourth Grade Experience

A popular item on my old webpage when I was at Northwestern University was a description of an experience I had when teaching a class of fourth graders!  For those that are interested, the link to this article is given here.  

 

-------------------------------------------------------------------------------------------------

 
2008 MATH AWARENESS MONTH

Here are two non-technical quicktime movies that I made for the 2008 Math Awareness Month, which has the theme of Mathematics of Voting.

The first one is an introductory lecture indicating how mathematics plays a central role in understanding whether the "will of the voters" is, indeed, respected with our voting systems. Beware: after watching this lecture, be prepared to worry whether the "correct person won" in the last election of importance to you, whether it was for a chair of your group or the vote in a primary.

-- Mathematics of Voting

We all have seen voting paradoxes, but where do they come from? This lecture shows how to create a wide selection of them. After this lecture, you should be able to create some surprising results using nothing that is mathematically difficult.

--Creating Voting Paradoxes


This third lecture,  "What Causes  Voting Paradoxes,"  is based on a talk I gave at a 2/9/08 Institute for Mathematical Behavioral Science conference on mathematics and voting.  The purpose is to explain what causes voting paradoxes as well as  Arrow's famed theorem; e.g., I show why Arrow's Theorem does not mean what we have thought it meant for the last half-century.  By the way, listening to the lecture, I discovered a couple of mistakes; they are not serious and I am sure you will catch them.  The lecture runs about 45 minutes.


--What Causes  Voting Paradoxes 

Current research interests

 

 

Recent books

Chaotic Elections! A mathematician looks at voting, American Mathematical Society, 2001.  We know that voting leads to all sorts of paradoxes, but what are they?  This book, intended for a layperson with, say, a first year of calculus, explains many of these mysteries. 

 

 

 

 

 




Decisions and Elections; Explaining the Unexpected, Cambridge University Press, 2001.  A problem with voting theory is that it is full of “impossibility theorems.”  This book shows that they do not mean what we have generally thought they meant.  For instance, it is shown how Arrow’s Theorem has a benign interpretation.   

 

 

 

 

 

The Way it Was, AMS. 2004, This book describes the early years of the AMS as described by early articles in the Bulletin.   Some of these reprinted articles are by Poincare, Hilbert, etc.   

 

 

 



Collisions, Rings, and other Newtonian N-body Problems AMS, 2005.  This book is a written version of my CBMS lectures of 2002.  While it provides an introduction to aspects of the N-body problem and describes several unsolved problems, many of the results are new and will be of interest to experts.

 

 

 

 

 

 

My 2008, Cambridge University book "Disposing Dictators, Demystifying Voting Paradoxes" has the two main themes.  The first is to show and explain  why many of the "dictatorial conclusions" that have dominated in social choice do not mean what we have thought they meant for the last half century.  The second is to explain why all of those voting paradoxes, which have amazed all of us, occur.  The explanation for  both themes is that information we expect to be used by the voting rules is not considered at all.

 

 

 


 

 

 

------------------------------------------------------------------------------------------------------------------------------------------------

Some recent preprints

My research interests concern Dynamical Systems and its applications to the physical and social sciences. A selection of my recent preprints, given below, are divided according to subject area. The general topics are