1
Announcement
Math 113 section 21-26 Instructor: M.Xiao
Help sessions
Monday 3:30-4:45p.m. at Parkinson 107
Tuesday 5-6:15p.m. at Life Science II 450
Wednesday 6:30-7:45p.m. at Life Science II 450
Wednesday 5-6:15p.m. at Lawson 121
•The Third Hour Exam:
Nov. 6, Friday in class.
Oct. 12, 2009
Chapter 10/12: Electing the
President
Social choice theory
attempts to address the
problem of finding good
procedures that will turn
individual preferences
for different candidates
into a single choice by
the whole group.
Voting Systems
Purpose of Voting: Method by which a democratic society makes
decisions.
Uses: •Congress passes a bill.
•Stockholders decide on a course of action.
•A presidential candidate is nominated
•Community elects school board members.
Arrow’s Impossibility Theorem, there can never be a perfect voting
system. No single method works.
Voting method chosen & strategies used greatly influence results
of elections.
Majority Rule Method
-elections with only two alternatives.
Only first place votes are considered, and the candidate
receiving over half of the total 1st place votes is
declared the winner.
Methods of Voting
May’s theorem:
If the number of voters is odd, and we are interested only in voting
systems that never result in a tie, then the majority rule is the only
voting system for two alternatives that satisfies the three conditions
listed next:
Majority Rule Method
Majority rule has at least three desirable properties:
1. All voters are treated equally.
2. Both candidates are treated equally.
3. If a new election were held and a single voter were to change
his or her ballot from being a vote for the loser of the previous
election to being a vote for the winner of the previous election,
and everyone else voted exactly as before, then the outcome of
the new election would be the same as the outcome of the
previous election.
Old Exam Question
A ballot consisting of such a rank ordering
of candidates is called a preference list, or
more precisely, an individual preference
list.
