HSMS 330 Mathematical Topics in the Social Sciences II (UH)
A rigorous mathematical treatment of the following topics:
1. Apportionment of the House of Representatives with focus on the mathematical theory and the paradoxes involved; history and development of apportionment procedures from the early contributions of Alexander Hamilton and Thomas Jefferson to the currently used Hill-Huntington procedure; the impossibility theory of Balinski and Young; different measures of inequity and the alternative approach to the apportionment problem through equity considerations.
2. Social Welfare theory including a thorough treatment of Arrow's impossibility theorem and Arrow's axioms of unrestricted domain, collective rationality, weak Pareto and independent of irrelevant alternatives; dictatorship, oligarchy and the weakening Arrow's axioms.
Prerequisite
University Honors Program