So far we have discussed various methods of collecting sample data.
We then learned to summarize the sample data using frequency
distribution; we also visualized the data using histogram and other
In the next two lectures, we will ta
Undergraduate Senior Thesis
University of Washington
Voting Theory and Banzhaf
Professor Sara Billey
This paper gives a general description of voting theory and looks specifically at
problems relating to
Math 017 Lecture Notes
Preference Ballots and Schedules
Set of choices/candidates to choose from
Voters whom make these choices
Ballots lets voters designate their choices
(vote on something): ski/snowboard/other (both ways)
Snapsho t s o f m o d e r n m athematics
from Ob e r wo l f a c h
How to choose a winner : the
mathematics of social choice
Victor ia Powers
Suppose a group of individuals wish to choose among
several options, for example electing one of several
M ATH 1340: Mathematics and Politics
Homework 4 solutions
ASSIGNMENT: exercises 2, 3, 4, 8, and 17 in Chapter 2, (pp. 6568).
Solution to Exercise 2.
A coalition that has exactly 12 votes is winning because it meets the quota. This coalition
Math13 HW 6 Chapter 10
1. If a voting system has three or more alternatives, satisfies the Pareto condition, always produces a
unique winner, and is not a dictatorship, what conclusion follows from the GS theorem?
2. Are there voting methods that are neve
4] VOTING SYSTEMS (Part Three):
SOME SHORTCOMINGS OF k-ALTERNATIVE SYSTEMS; k>2
4.1) Name at least five desirable properties that k-Alternative Voting
Systems, k > 2, should satisfy.
4.2) State the Condorcet Winner Criterion (CWC). (Page 292)
In many actual voting situations, the principal one person one vote
is not justified. For example,
At a company shareholders meeting, the number of votes a
person has corresponds to the number of shares owned.
In a law firm, a senior partner usually has m
WHICH METHODS SATISFY OR VIOLATE WHICH CRITERIA?
Recall that the four fairness criteria are majority, Condorcet, monotonicity, and independence of irrelevant alternatives. Also recall that for a method to satisfy a fairness criterion,
every possible elect
Collection of methods for
Organizing, summarizing and presenting data
Analyzing the data
Interpreting the data
Drawing conclusions from the data
Suppose you want to buy optional audio equipmen
Section 4.4 Multiplication rule
In this section, the event A and B will mean:
( A occurs in the first trial ) and ( B occurs in the second trial ).
Suppose there are two questions in an exam:
1. (true or false) Abraham Lincoln was the president during Civ
Section 4.3 Addition Rule:
Consider the events A and B
We can combine the events with OR to create a new event.
Therefore A or B is a also an event
We will always consider the inclusive OR.
By the event A or B, we mean
In a single trial (i.e., when the
Chapter 4 (Section 4.2)
In this chapter, we will talk about `probability of an `event, which is an `outcome
of a `procedure (a `random phenomenon or an `experiment).
Procedure (random phenomenon or experiment): It has outcomes, but the
outcomes are uncer
Measures of Relative Standing:
Consider the following scenario:
In Sec. 1 of a statistic course, Jack scored 86 out of 100 in Exam 1, where
the mean and the standard deviation of the class were = 80 and s = 4.
In Sec. 2 of the same course, Jill scored 1
In this lecture, we will discuss how to describe the variation in the data.
Consider two samples of size
30, 40, 50, 60, 70, 80, 90
57, 58, 59, 60, 61, 62, 63
Both the sample data have the same mean.
However, the values in the second data set ar
MATH 392 Topics in Mathematical Economics
Topic 4 Voting methods with more than 2 alternatives
4.1 Social choice procedures
4.2 Analysis of voting methods
4.3 Arrows Impossibility Theorem
4.4 Comparison voting methods
Social Choice Procedures