CS 6100 Homework 3 This assignment can be done in groups of one, two or three. Summary: CS 6100 Homework 3 This assignment can be done in groups of one, two or three. Chapter 12 1. Arrow's impossibility theorem states that it is impossible to have a voting system which achieves all six desirable properties shown below. One idea is to eliminate one of the requirements. How would eliminating rule (a) help? Explain. a) A social preference ordering >* should exist for all possible inputs (Note, I am using >* to mean "is preferred to.) b) >* should be defined for every pair (o, o')O c) >* should be asymmetric and transitive over O d) The outcomes should be Pareto efficient: i. if i A, o >i o' then o >* o` (not misorder if all agree) e) The scheme should be independent of irrelevant alternatives (if all agree on relative ranking of two, should retain ranking in social choice): f) No agent should be a dictator in the sense that >i o' implies o >* o' for all preferences of the other agents 2 For this majority graph (in which an arc ab means that a wins in a pairwise competition between the two), pick three different (reasonable) orderings for Collections: Computer Technologies and Information Sciences