A Mathematical Survey of Justice (UMAP)

A systematic mathematical survey of various approaches to justice. The module discusses various requirements that a justice function should have and proves that different sets of requirements lead uniquely to different well specified justice functions. The module makes use of simple algebra, diagrams and verbal descriptions and provides examples of how the mathematical theory might be applied to real life justice issues. Students learn how to think logically and precisely about issues in justice and to apply existence and uniqueness proofs, diagrams, and logic to justice issues.

Table of Contents:

1. INTRODUCTION

2. JUSTICE INDIFFERENCE CURVES
2.1 The Utility Tradeoff Froniter and the Feasible Set
2.2 The Utilitarian of Sum of Utilities Approach
2.3 The Maximin and Leximin Concepts of Justice
2.4 The Product of Additional Utilities Approach

3. DESIRABLE CHARACTERISTICS
3.1 Pareto Optimality
3.2 Symmetry About the 45 Degree Axis
3.3 Independence from Irrelevant Alternatives

4. EXISTENCE AND UNIQUENESS THEOREMS
4.1 Independence fron the Origin
4.2 Ordinal Interpersonal Comparisons of Utility
4.3 Invariance with Respect to Linear Utility Transformation

5. MEASUREMENT

6. CONCLUSION

7. FOOTNOTES

8. REFERENCES

9. ANSWERS TO EXERCISES