Mathematics and Social Advocacy

Since the Enlightenment, there has been the hope that reason would allow us to create a better society. Mathematics is perhaps the ultimate expression of reason, so mathematics may be of considerable value in designing an ideal society.

Thus far, this hope has not been realized, in large part because those who actually understand mathematics tend to be very, very bad at understanding people. However, all is not lost, and in recent years, mathematics has become increasingly important in assessing a broad range of societal issues. I'm part of an NSF-sponsored grant to identify and elaborate on societal issues can be resolved (or at least analyzed) using mathematical tools. Part of the goal is to design curricular materials. The grant sponsored the Mid-Hudson Conference on Mathematics and Social Advocacy, and the project has produced the following handouts.

• • Mathematics and Politics

  • Gerrymandering: Is a districting plan fair?

  • The Art of the Dummymander

  • How Important is Your Vote?

  • Should you vote for President?

  • Seats-Votes Curves: How much influence does a political party have?

  • Seats-Votes Curves, Part Two: How can we assess a proposed redistricting?

  • Finding the Banzhaf Index Using Generating Functions

  • Finding the Shapley-Shubik Index Using Generating Functions

  • Approximating the Banzhaf Index

  • One Man, 3.312 Votes

    • Designing a Weighted Voting System

  • Should a regime act against peaceful protesters?

  • Does martyrdom work?

  • Is it war: When does violence cross over into civil disorder?

  • Mathematics and Criminology

  • Death in WIsconsin

  • An introduction to Social Network Analysis

  • Who's important in an organization?

  • How Large Can Conspiracies Be?

  • Who should be targeted in a criminal investigation?

  • How can you find hidden networks (and spouses)?

  • How do terrorists (and universities) grow?

  • How well do centrality measures work?

  • Mathematics and Juries

  • Jury Size and Quota

  • Does discrimination exist in a jury?

  • Jury Discrimination and the Small Sample Problem

  • Peremptory Challenge Basics

  • Peremptory Challenges: More is More?

  • Fisher's Test and Peremptory Challenges

  • How can we assess the accuracy of a jury?

  • Ten Six Guilty Set Free to One Innocent Imprisoned?

  • SAM and Biased Jurors

  • A Jury of One Peer

  • Are we expecting too much from a jury?

  • Utility Theory and Juries

  • Mathematics and Discrimination

  • Employment Discrimination Basics

  • Employment Discrimination and Hypergeometric Probability

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