1. Math 210G Mathematics Appreciation Su Voto es Su Voz

3. [The president is elected by ]
[Popular vote]
[Electoral college]
[Who has the most money]
[Who has the most popular running mate]

4. SNL on Clinton - Trump debate 2

5. Electoral college
Each state is allocated as many electors as it has Representatives and Senators in the United States Congress.

6. Predicting outcomes
538
Vegas oddsmaker's view

7. 2004: Kerry v Bush

8. 2008: Obama v McCain

11. [Who ran against G.W. Bush in 2000]
[Clinton]
[Hart]
[Quail]
[Gore]

12. Close U.S. Presidential elections

13. Close U.S. Presidential elections
Close presidential races are nothing new
Electoral college history: idea based on lack of mass media
Three times elected president lost popular vote (Hayes, Harrison, G.W. Bush)
Changing the system not perceived to be in the best interest of the states.

14. 270 to Win 2000: Gore V Bush

15. The infamous butterfly ballot

16. Florida election tallies (2000)
George W. Bush (W)
2,912,790
(50,456,002)
48.850
Republican
Al Gore
2,912,253
(50,999,897)
48.841
Democratic
Ralph Nader
97,421
(2,882,955)
1.633
Green

18. The electoral college

19. (Penrose)-Banzhaf-(Coleman) power index
Banzhaf, John F. (1965), "Weighted voting doesn't work: A mathematical analysis", Rutgers Law Review 19(2):
Example (Game Theory and Strategy P. D. Straffin):
[6; A:4, B:3, C:2, D:1]
6 votes to pass, possible majorities:
AB, AC, ABC, ABD, ACD, BCD, ABCD
12 total swing votes.
A = 5/12 B = 3/12 C = 3/12 D = 1/12

20. The Banzhaf Power Index: a mathematical representation of how likely a single state would be able to swing the vote
Larger states have more power
Is the electoral college fair?
Does it reflect popular opinion?

21. The Banzhaf Power Index (Bachrach et al 08)
Pivotal (critical) agent in a winning coalition is an agent that causes the coalition to lose when removed from it
The Banzhaf Power Index of an agent is the portion of all coalitions where the agent is pivotal (critical)

22. The Shapley-Shubik Index
The portion of all permutations where the agent is pivotal
Direct application of the Shapley value for simple coalitional games
Applies in situations in which one vote might precede another.

23. Banzhaf calculator for electoral college
General Banzhaf calculator

24. Swing Vote 2008 Link

25. Daily electoral map “Conditional expectation”
How does the power index change when we fix the weights for all states not considered battleground states?
Can New Mexico determine the outcome of the election?

26. Battleground states 2016

27. Banzhaf calculation Can NM swing the vote?
[14; AZ (11) UT (5) FL (29) IA (6) NV (6) NH (4) NC (15) OH (18), GA (16), WI (10), NM(5)]
Other states: 256 to 157. Hilary needs 14 from swing + NM

28. NV+UT+NM forms a winning coalition for Clinton [14; AZ (11) UT (5) FL (29) IA (6) NV (6) NH (4) NC (15) OH (18), GA (16), WI (10), NM(5)]
True
False

29. FL forms a winning coalition for Hillary
[14; AZ (11) UT (5) FL (29) IA (6) NV (6) NH (4) NC (15) OH (18), GA (16), WI (10), NM(5)]
True
False

30. [If you were to vote today, who would you choose for president]
Hillary Clinton
Donald Trump
Jill Stein
Gary Johnson
Other (Castle, De La Fuente, McMullen, La Riva…)
Undecided

31. [Females only: If you were to vote today, who would you choose for president]
Hillary Clinton
Donald Trump
Jill Stein
Gary Johnson
Other (Castle, De La Fuente, McMullen, La Riva…)
Undecided

32. [Males only: If you were to vote today, who would you choose for president]
Hillary Clinton
Donald Trump
Jill Stein
Gary Johnson
Other (Castle, De La Fuente, McMullen, La Riva…)
Undecided

33. [Does your vote matter?]
Yes No

34. Swing votes

35. Is election fraud possible in America?