Spring 2008 meeting of the Indiana section of the Mathematical Association of America
Friday - Saturday, March 28-29, 2008
St. Mary's College
Hagelgans (MAA) and
Tommy Ratliff (Wheaton College)
Invited Talks :
Voters Vote and Candidates Win:
What's so hard about that?
The 2000 Presidential election taught many people that the winner of the popular vote may differ from the winner in the Electoral College. However, this is only a small example of the inconsistencies that are possible: If there are more than two candidates, then the voting procedure can have as much impact on the outcome as the preferences of the voters.
The fundamental flaw is that many voting methods only use a portion of the voters' preferences in determining the winner. We will see that several of the most popular proposals for election reform in the United States provide some benefit but do little to address the underlying structural defects of our current system.
A Little Geometry, a Little Linear Algebra,
and a Lot of Insight into Voting
We usually think of voting in the context of political elections, but the same framework used to understand elections can give insights into any group decision process, from deciding where to go to dinner to selecting a committee at your college or university. We will see that a little geometry and linear algebra can go a long way toward explaining many voting paradoxes and how to avoid them.
A planar linkage is constructed in the plane from rigid links or rods that are connected with movable joints. Robot arms and carpenters' rulers are examples of planar linkages in which the links are connected to form a chain. We will examine the reachability regions of robot arms, which are chains with one fixed end. Then we will go on to solve the minimal folding problem of carpenters' rulers with links of different lengths. Finally, we will address some planar linkages that can be used to convert one type of motion to another type of motion.
- Registration (before March 21,2008)
- Before March 21, 2008 - $10 for non-students
- Graduate and Undergraduate Students - free
- After March 21 - $20 for non-students
(order by March 21)
- Friday night Dinner - $16
- Saturday Lunch - $7
Tommy Ratliff is Associate Professor of Mathematics at Wheaton College in Norton, Massachusetts. His formal training was as an algebraic topologist. But for the last eight years he has been doing research in Voting Theory, including geometric interpretations, and issues involved in electing committees. He is also interested in using writing in mathematics classes and was one of the co-authors of "Crushed Clowns, Cars and Coffee to Go", a book of writing projects in mathematics classes published by the MAA. Tommy is also involved in the Northeastern Section of the MAA, and served as Chair of the Northeastern Section of the MAA from 2005 to 2007.
Nancy Hagelgans is Professor Emerita of Mathematics and Computer Science at Ursinus College, where she taught a great variety of mathematics and computer science courses for 26 years and served two terms as department chairperson. She earned a Ph.D. in algebraic topology at Johns Hopkins University and later an M.S. in computer science at Villanova University. Her A. B. in mathematics was awarded by Goucher College, which she entered on a Ford Foundation Early Admissions Scholarship and where she was elected to Phi Beta Kappa. Her interests include discrete mathematics, computer solutions to mathematics problems, and student learning. She was a co-author of the MAA book "A Practical Guide to Cooperative Learning in Collegiate Mathematics". Currently she is a member of the MAA Executive Committee, Chair of the MAA Committee on Sections, Chair of the MAA Strategic Planning Working Group on Sections, and an adjunct faculty member in graduate computer science at Villanova University. She plays the violin in a symphony orchestra and various chamber music groups.
Contributed Talks: Talks can be submitted here.