Mathematics and the Law

Course design and development supported by NSF DUE Award #0942670.

Course Description: Mathematical, statistical, and probabilistic arguments have become an increasingly important part of the legal process. We will examine the underlying mathematical principles of some of these arguments, and use various documents, including court records and legislative acts, to see how these principles have been incorporated into the legal system.

Required Prerequistes: None

Recommended Prerequistes: A basic algebra course like College Algebra

Rationale: Over the past hundred years, mathematics has played an increasingly prominent role in the modern legal system. This course will examine the use of mathematics by the courts in a broad range of situations.

The course description has been kept purposefully brief to allow faculty with different interests to bring their unique perspective into the course.

Audience: Students in any major are eligible to take thos course as the only prerequistes are high school mathematics, but students in the social and political sciences will get the most use out of it,

Learning Objectives:

  • Students will understand the basic concepts of probability and statistics.
  • Students will be able to apply methods of probability and statistics to reach legally admissible conclusions.
  • Students will be able to distinguish between valid and invalid probabilistic and statistical arguments.


Week 1: Introduction. Graphical representation of data, introduction to courtroom procedures.

  • “Statistical Reasoning in the Legal Setting”, Joseph L. Gastwirth.
  • “The statistics of genocide,” Mary Gray and Sharon Marek.
  • “New issues in human rights statistics,” David Banks and Yasmin H. Said.
  • “Florida 2000: A Legal and Statistical Analysis of the Election Deadlock and the Ensuing Litigation,” Richard A. Posner.

Week 2: Measures of central tendency, measures of dispersion

Week 3: Correlation and Regression

  • Teamsters v. United States, CT v. Teal
  • Pay discrimination (Wilkins v. University of Houston, Craik v. University of Minnesota)
  • “Can Statistics Tell Us What We Do Not Want to Hear? The Case of Complex Salary Structures,” Mary W. Gray.
  • “Reverse Regression, Fairness, and Employment Discrimination,” Conway and Roberts.

Week 5: Gathering Data, Design of Experiments

  • “Statistical thinking and data analysis enhancing human rights work,” Jorge Luis Romeu
  • “The demography of conflict-related mortality in Timor-Leste (1974-1999): Reflections on empirical quantitative measurement of civilian killings, disappearances, and famine-related deaths,” Romesh Silva and Patrick Ball.
  • “Afghan refugee camp surveys: Pakistan 2002, James Bell, David Nolle, Ruth Citrin and Fritz
  • Scheuren.- Metagora: a set of experiments in measurement of democratic governance,” Jan-
  • Robert Suisser and Raul Suarez
  • “Obtaining evidence for the international criminal court using data and quantitative analysis,” Spirer and Seltzer.

Week 6: Probability

  • People v. Risley, NM v. Sneed, People v. Collins “Interpretation of Statistical Evidence in Criminal Trials: The Prosecutor's Fallacy and the Defense Attorney's Fallacy”, Thompson.

Week 7: Probability (continued)

  • “Mathematical Probability in Election Challenges”, Finkelstein and Robbins.
  • State v. Pankow, Branion v. Gramley

Week 8: Random Variables

  • Brinks v. City of New York
  • “Why Estimate Direct and Indirect Casualties from War? The Rule of Proportionality and Casualty Estimates,” Asher (Chapter 3, p. 51-63).

Week 9: Sampling Distribution andConfidence Intervals

  • Ippolito v. Power, Castenada v. Partida, Hillery v. Vasquez, Hazelwood v. US
Week 10: Tests of Significance
  • EEOC v. Federal Reserve Bank of Richmond)
  • “Civil Liberties in the Era of Mass Terrorism,” Hardin.
  • “What Happened in Hazelwood: Statistics, Employment Discrimination, and the 80% Rule,” Meier, Sacks, and Zabell.

Week 11: t-tests

  • Isabel v. Memphis, NAACP v. Mansfield

Week 12: Two sample Tests

  • Grant v. Nashville

  1. Asher, Jana, David Banks, Fritz J. Scheuren, eds. Statistical Methods for Human Rights. Springer-Verlag 2008.
  2. Banzhaf, John F. III. “Multi-Member Electoral Districts. Do They Violate the "One Man, One Vote Principle.” The Yale Law Journal, Vol. 75, No. 8 (Jul., 1966), pp. 1309-1338.
  3. Conway, Delores A., Harry V. Roberts, "Reverse Regression, Fairness, and Employment Discrimination." Journal of Business & Economic Statistics, Vol. 1, No. 1 (Jan., 1983), pp. 75-85
  4. Degroot, Morris H., Stephen E. Fienberg, Joseph B. Kadane, Statistics and the Law. John Wiley, 1986.
  5. Carpenti, Walter L. “Legislative Apportionment: Multimember Districts and Fair Representation.” University of Pennsylvania Law Review, Vol. 120, No. 4 (Apr., 1972), pp. 666-700.
  6. Finkelstein, Michael O., William B. Fairley. “A Bayesian Approach to Identification Evidence.” Harvard Law Review, Vol. 83, No. 3 (Jan., 1970), pp. 489-517.
  7. Finkelstein, Michael O. Basic Concepts of Probability and Statistics in the Law. Springer-Verlag, 2009.
  8. Finkelstein, Michael O., Herbert E. Robbins. “Mathematical Probability in Election Challenges.” Columbia Law Review, Vol. 73, No. 2 (Feb., 1973), pp. 241-248
  9. Finkelstein, Michael O., Bruce Levin. Statistics for Lawyers, 2nd edition. Spring-Verlag, 2001.
  10. Gray, Mary W. “Can Statistics Tell Us What We Do Not Want to Hear? The Case of Complex Salary Structures.” Statistical Science, Vol. 8, No. 2 (May, 1993), pp. 144-158
  11. Gastwirth, Joseph L. “Statistical Reasoning in the Legal Setting.” The American Statistician, Vol. 46, No. 1 (Feb., 1992), pp. 55-69.
  12. Grofman, Bernard. “Fair Apportionment and the Banzhaf Index.” The American Mathematical Monthly, Vol. 88, No. 1 (Jan., 1981), pp. 1-5.
  13. Grofman, Bernard, Howard Scarrow. “Weighted Voting in New York.” Legislative Studies Quarterly, Vol. 6, No. 2 (May, 1981), pp. 287-304.
  14. Hardin, Russell. “Civil Liberties in the Era of Mass Terrorism.” The Journal of Ethics, Vol. 8, No. 1, Terrorism (2004), pp. 77-95.
  15. Huntington, Edward V. “Methods of Apportionment in Congress.” The American Political Science Review, Vol. 25, No. 4 (Nov., 1931), pp. 961-965.
  16. Huntington, Edward V. “The Role of Mathematics in Congressional Apportionment.” Sociometry, Vol. 4, No. 3 (Aug., 1941), pp. 278-282
  17. Meier, Paul, Jerome Sacks, Sandy L. Zabell. “What Happened in Hazelwood: Statistics, Employment Discrimination, and the 80% Rule.” American Bar Foundation Research Journal, Vol. 9, No. 1 (Winter, 1984), pp. 139-186.
  18. Owens, F. W. “On the Apportionment of Representatives.” Quarterly Publications of the American Statistical Association, Vol. 17, No. 136 (Dec. 1921), pp. 958-968
  19. Posner, Richard A. “Florida 2000: A Legal and Statistical Analysis of the Election Deadlock and the Ensuing Litigation.” The Supreme Court Review, Vol. 2000 (2000), pp. 1-60.
  20. Taylor, Alan D., Allison Pacelli, Mathematics and Politics. Springer-Verlag, 2008.
  21. Thompson, William C., Edward L. Schumann. “Interpretation of Statistical Evidence in Criminal Trials: The Prosecutor's Fallacy and the Defense Attorney's Fallacy.” Law and Human Behavior, Vol. 11, No. 3 (Sep., 1987), pp. 167-187.