MATH AND POLITICS
A LOOK AT HOW MATH AFFECTS ELECTIONS
Jana Behm
Math 320
July 7, 2010
OVERVIEW
 Voting
Systems and how they can
effect outcomes
*Majority Rule
*Plurality Voting
*Electoral College
MAJORITY RULE
*Straight forward
*Excellent for choosing between 2 candidates
*Most votes wins
*No single vote counts more than any other
*Potential problem: TIES (usually broken in some
pre-arranged way)
*Another potential problem: difficult in a multiparty system
PLURALITY VOTING
*More than 2 alternatives in an election
*Simply count the number of 1st place votes
*Possible that no candidate has the majority of
the votes cast
THE MATH OF MAJORITY AND PLURALITY VOTING
*Majority voting: simple majority
>Votes cast: 100 with 2 candidates– winner
needs a simple majority which is (100/2) +1 or 51
votes to win the election.
*Plurality voting: simple math
>Votes cast: 100 with 3 candidates – winner
simply needs the most votes, not necessarily a
majority of the votes cast.
THE MATH OF MAJORITY AND PLURALITY VOTING
Example: 1992 US Presidential Election
 Total Votes
Clinton
Bush

104,425,014
44,909,326
43.01%
39,103,882
37.45%
Perot
19,741,657
18.91%
Therefore Clinton was the winner, but did not receive the
majority of the votes cast
Source:
http://iun.edu/~mathiho/mathpol/fall00/chapter11.htm
U.S. ELECTORAL COLLEGE
*Each state is given an electoral numbers which
equals the number of US representatives + the
2 senators that they have
*How are the representatives divided?
*Is this fair?
*2009 estimates US population to be
307,006,550 people
U.S. ELECTORAL COLLEGE CONTINUED
State
MT
IA
IL
FL
NY
TX
CA
Population
974989
3007856
12910409
18537659
19541453
24782302
36961664
% of US pop
0.32%
0.98%
4.21%
6.04%
6.37%
8.07%
12.04%
US Population = 307,006,550
Electoral votes
3
7
21
27
31
34
55
% of electoral votes
0.56%
1.30%
3.90%
5.02%
5.76%
6.32%
10.22%
Electoral votes possible: 538
Source for population numbers:
http://quickfacts.census.gov/qfd/states/17000.html
WINNING AN ELECTION BUT LOSING THE POPULAR VOTE
2000 Presidential Election
Candidate
Popular Vote
George W. Bush
50,460,110
Albert Gore Jr.
51,003,926
%
47.87%
48.38%
Electoral Vote
271
266
%
50.4%
49.4%
Neither candidate had a simple majority as there were 6 candidates on the ballot.
Plurality voting is not in effect in the United States
President Bush won 2 large electoral states, but MANY of the smaller states that
added up for the electoral win
Mr. Gore won largely populated states, but not enough of them for electoral victory.
Source: http://www.uselectionatlas.org/RESULTS/national.php?f=0&year=2000
2000 ELECTORAL MAP
ELECTORAL MATH
There are 538 electoral votes possible
 Candidates must get a simple majority
 538/2 +1 = 270 votes
 Therefore, they can have a simple majority of
electoral votes without having a majority of
votes cast in an election or even the most votes
cast.

LET’S PLAY WITH THE MATH

http://www.archives.gov/federalregister/electoral-college/calculator.html

http://www.realclearpolitics.com/epolls/maps/
obama_vs_mccain/?map=1
CONCLUSION
Does math effect election outcomes?
 Can one state change the entire course of an
election with as little as 3 electoral votes?
 How many configurations of states will give you
the 270 needed to win? Are the big states
mandatory, or do they just make it easier?
