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Math and politics A look at how math affects elections

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Voting Systems and how they can effect outcomes

- *Majority Rule
- *Plurality Voting
- *Electoral College

*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 multi-party system

Majority Rule*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

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 votingExample: 1992 US Presidential Election

Total Votes Clinton Bush Perot

104,425,014 44,909,326 39,103,882 19,741,657

43.01% 37.45% 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

The math of Majority and plurality voting*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 collegeState Population % of US pop Electoral votes % of electoral votes

MT 974989 0.32% 3 0.56%

IA 3007856 0.98% 7 1.30%

IL 12910409 4.21% 21 3.90%

FL 18537659 6.04% 27 5.02%

NY 19541453 6.37% 31 5.76%

TX 24782302 8.07% 34 6.32%

CA 36961664 12.04% 55 10.22%

US Population = 307,006,550 Electoral votes possible: 538

Source for population numbers: http://quickfacts.census.gov/qfd/states/17000.html

U.S. electoral college continued2000 Presidential Election

Candidate Popular Vote % Electoral Vote %

George W. Bush 50,460,110 47.87% 271 50.4%

Albert Gore Jr. 51,003,926 48.38% 266 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

Winning an election but losing the popular voteThere 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.

Electoral Mathhttp://www.archives.gov/federal-register/electoral-college/calculator.html

http://www.realclearpolitics.com/epolls/maps/obama_vs_mccain/?map=1

Let’s play with the mathDoes 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?

conclusion
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