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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
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