**Fairness, Equity, Elections, and Games: Important Resources**

Prepared by:

Joseph Malkevitch

Department of Mathematics

York College (CUNY)

Jamaica, New York 11451

email:

__malkevitch@york.cuny.edu__

web page:

__http://york.cuny.edu/~malk__

Balinski, M. and R. Laraki, Majority Judgment: Measuring, Ranking, and Electing, MIT Press, Cambridge, 2010.

Balinksi, B. and H.P. Young, Fair Representation: Meeting the Ideal of One Man, One Vote, Second Edition, Brookings Institution Press, Washington, 2001.

Börgers, C., The Mathematics of Social Choice, SIAM, Philadelphia, 2010.

Brams, S. and A. Taylor, Fair Division: From Cake-Cutting to Dispute Resolution, Cambridge U. Press, New York, 1996.

Brams, S. and A. Taylor, The Win-Win Solution, Norton, NY, 1999.

Gura, E-Y and M. Maschler, Insights into Game Theory, Cambridge U. Press, New York, 2008.

Luce, R. D. and Raiffa, H., Games and Decisions: Introduction and Critical Survey. Wiley, New York. Paperback reprint, Dover, New York.

Moulin, H., Axioms of Cooperative Decision Making, Cambridge U. Press, New York, 1988.

Roth, A. and M. Sotomayor, Two-Side Mathcing: A Study in Game-Theoretic Modeling and Analysis, Cambridge U. Press, New York, 1990.

Saari, D., Decision and Elections: Explaining the Unexpected, Cambridge U. Press, New York, 2001.

Straffin, P., Game Theory and Strategy, Mathematical Association of America, Washington, 1993.

Taylor, A., Social Choice and the Mathematics of Manipulation, Cambridge U. Press, New York, 2005.

Young, H.P., Equity: In Theory and Practice, Princeton U. Press, Princeton, 1994.

**Fundamental Axioms for General Fair Division Questions**

1. Proportionality

If there are n claimants, each claimant should get at least 1/n of the proceeds ("estate") from that claimant's point of view.

2. Envy-Freeness

No claimant would give up what was given to him/her so as to get what was given to someone else.

3. Pareto Optimality (Efficiency)

There is no other solution (way of distributing the "pot") which will make at least one claimant better off and all the other claimants no worse off.

4. Equitability

The number of "utiles" each claimant gets from that claimant's point of view is numerically the same as the number of utilities each other claimant gets (from the point of view of that other claimant).