## Mathematics Awareness Month ** April 2008 **

### Mathematics Awareness Month at New Jersey City University Jersey City NJ

MATHEMATICS AND VOTING
Thursday, April, 24, 2008
Grossnickle Auditorium, G144

Opening Remarks: Liza Fiol-Matta, Dean of the William J. Maxwell College of Arts and Sciences, NJCU

The 9 AM Session
Presider: Joseph Moskowitz, NJCU Political Science Department, jmoskowitz@njcu.edu

9:05 a.m.
Francis Moran, Department of Political Science, NJCU, fmoran@njcu.edu. Jumping on the Bandwagon: Geometry of the 2008 Primary Season

The 2008 presidential primary season is a unique event in American political history. That is, while we have had presidential primaries in place in most states since the 1972 election, we have not had a presidential primary season where neither major party included an incumbent Vice President among its contenders since 1952. So this combination of factors has meant a crowded field of candidates and a protracted primary season. This paper builds on Brams' and Riker's (1971) seminal study describing the "bandwagon curve"? in order to examine when it is rational for undecided voters to select a candidate to support. I demonstrate how this mathematical model can help us to understand the ebb and flow of the primary season and be used to predict a likely outcome for the Democratic nomination.

9:25a.m.
Japheth Wood, Bard College, jwood@bard.edu
A Simple Solution to Complicated Voting Systems

Most voting systems require that each voter rank all of the candidates or outcomes. Even with five candidates there are 120 (that's 5 factorial) ways to do this, which could be quite difficult. The speaker will introduce some of the basic voting systems and present some mathematical ideas for what to do when ranking the outcomes becomes too burdensome.

9:35 a.m.
Panyeng Weng, Ramapo College of New Jersey, pweng@ramapo.edu
Weighted Voting and Power Indices

A weighted voting is a situation when each voter in an election controls multiple but unequally many votes. An example of weighted voting is the Electoral College of presidential elections in the United States. In a weighted voting, it is clear that voters with more votes are more powerful than those with fewer votes; however the ???power??? of a voter to influence the outcome of the election is NOT exactly proportional to the number of votes of the voter. In order to better determine the power of influence of each voter, we introduce two very popular measurements: the Banzhaf power index and the Shapley-Shubik power index.

The 10 AM Session
Presider: Deborah Freile, NJCU Geoscience Department, dfreile@njcu.edu

10:00 a.m.

Michael A. Jones, Montclair State University, jonesm@mail.montclair.edu
What a Difference a Procedure Makes: Scoring Rules in Politics and Sports

An election outcome depends not only on how the electorate cast ballots, but also on the procedure used to tally votes. That is, the same votes can result in different election outcomes when different procedures are used. This is true even on the subset of election procedures known as scoring rules or voting vectors. For a fixed set of ballots, mathematics is used to determine what outcomes are possible, and whether or not the outcome changes, under all scoring rules. Examples in the talk will use data from U.S. Presidential elections, coaches' rankings of NCAA football teams, journalists' votes to determine the MVPs of the American and National Leagues of Major League Baseball, and scorecards and scoring rules used on the Professional Golfers Association tour.

Michael A. Jones is an Associate Professor in the Department of Mathematical Sciences at Montclair State University in Montclair, New Jersey. He earned his PhD by applying functional analysis to game theory under the direction of Donald G. Saari from Northwestern University in 1994. His graduate education did nothing to prepare him for being the parent of two kids. His wife's training in geriatrics didn't prepare her either! His research interests include mathematics as it arises in, and is applied to, the social sciences and discrete mathematics. His teaching interests include using sports as a way to introduce and to motivate mathematical ideas.

The 11 AM Session
Presider: Jyhcheng Liu, NJCU Computer Science Department, tliu@njcu.edu

11:00 a.m.
Fred S. Roberts, DIMACS, Rutgers University, froberts@dimacs.rutgers.edu
Voting Problems and Computer Science Applications

The problem of voting or social choice problem can be described as that of finding a consensus given different opinions, preferences or votes. Methods of mathematics and of the social sciences developed over the years for dealing with this problem are finding novel, important applications in computer science and computer science points of view are impacting voting/social science applications. We will describe connections between voting/social choice and computer science, concentrating on such topics as meta-search (combining results from multiple search engines), image processing, collaborative filtering, and processing information in large databases.

Fred S. Roberts is a Professor of Mathematics at Rutgers University and Director of DIMACS, the Center for Discrete Mathematics and Theoretical Computer Science. He is also Director of the Department of Homeland Security Center of Excellence for Dynamic Data Analysis (DyDAn). Roberts' research interests are in mathematical models in the social, behavioral, biological, environmental, and epidemiological sciences, of problems of communications and transportation, and for addressing issues arising in homeland security; graph theory and combinatorics and their applications; measurement theory; utility, decision-making, and social choice; and operations research, as well as in mathematics education. He has published four books (one translated into Russian, another into Chinese), edited 17 others, and authored over 160 scientific papers. Among his awards are the Commemorative Medal of the Union of Czech Mathematicians and Physicists, the Distinguished Service Award of the Association of Computing Machinery Special Interest Group on Algorithms and Computation Theory and the National Science Foundation Science and Technology Centers Pioneer Award.

Remarks: Richard Riggs, Chair of the NJCU Mathematics Department
Presentation of Prentice E. Whitlock Award: Das Misir, NJCU Mathematics Department

The 12 NOON Session
Presider: Donna Axel, NJCU Political Science Department, daxel@njcu.edu

12:00 pm.
Brian P. Hopkins, St. Peter's College, bhopkins@spc.edu

How many Representatives should each state have in the U.S. Congress? This is a surprisingly tricky question mathematically, but was initially considered by many familiar names from early American history rather than professional mathematicians. We will look at the method devised by one of our local historical figures, Alexander Hamilton. This method was shown to have a potential problem in 1870 concerning Alabama's representation. We will examine that problem and see the dangers of rounding.

12:15 p.m.
Jennifer Wilson, Eugene Lang College, The New School for Liberal Arts, wilsonj@newschool.edu
Assigning Delegates in the Democratic Primary

Apportionment is well-known as the method for determining representation for each state in the House of Representatives. In this talk, we will look at how apportionment is used to determine the number of delegates awarded each candidate in the 2008 Democratic Primary, focusing specifically on New Jersey. According to The New York Times, the delegate count in New Jersey is: 59 for Clinton and 48 for Obama. This matches the number of delegates that would be awarded based on the state-wide popular vote. According to the Democratic Party rules, however, delegates are awarded based not only on state-wide totals, but on votes at the district level. We look at how this is done and show that the delegate count should be 58 to 49 instead.

12:30 p.m.
Joseph Malkevitch, CUNY, York College, malkevitch@york.cuny.edu
Mathematical Insights into Voting and Elections

Democracy depends on a wide variety of voting and election procedures, ranging from the way political offices are filled to how laws are passed. Mathematics offers significant insights into how voting and elections can be made more fair and effective. This talk will survey these mathematical insights.

Closing Remarks: Joann Z. Bruno, Interim Vice President for Academic Affairs, NJCU