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Math 210G Mathematics Appreciation Dr. Joe Lakey Lecture 9: Su Voto es Su Voz

Math 210G Mathematics Appreciation Dr. Joe Lakey Lecture 9: Su Voto es Su Voz. [The president is elected by ]. [Popular vote] [Electoral college] [Who has the most money] [Who has the most popular running mate]. SNL on Romney – Obama youtube version youtube second version.

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Math 210G Mathematics Appreciation Dr. Joe Lakey Lecture 9: Su Voto es Su Voz

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  1. Math 210G Mathematics AppreciationDr. Joe LakeyLecture 9: Su Voto es Su Voz

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

  3. SNL on Romney – Obama • youtube version • youtube second version

  4. Sarah Palin = Tina Fey?

  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

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

  10. Close U.S. Presidential elections

  11. 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.

  12. 270 to Win2000: Gore V Bush

  13. The infamous butterfly ballot

  14. Florida election tallies (2000)

  15. The electoral college

  16. Historical observation… • GOP almost always wins “toss-ups” • Counting these puts Romney at 257 and Obama at 281. • If Romney were to win Ohio, this would put Romney at 257+18=275 and Obama at 281-18=263. • Obama strategy should be… (1) Ohio, Ohio Ohio and try to nail down (2) try to swing Virginia, Colorado (3) nail down Nevada, Iowa Wisconsin (4) don’t forget CA.

  17. (Penrose)-Banzhaf-(Coleman) power index • Banzhaf, John F. (1965), "Weighted voting doesn't work: A mathematical analysis", Rutgers Law Review 19(2): 317-343 • 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

  18. 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?

  19. 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)

  20. 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.

  21. Banzhaf calculator for electoral college • General Banzhaf calculator

  22. Swing Vote 2008 Link

  23. 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?

  24. Battleground states 2012 • RCP Poll Average Electoral Votes States Obama Romney Obama Romney • Colo. 47.6% 47.8% 0 9 • Fla. 47.0% 48.7% 0 29 • Iowa 48.8% 46.8% 6 0 • Nev. 49.5% 46.8% 6 0 • N.H. 48.2% 47.4% 4 0 • N.C. 44.7% 50.3% 0 15 • Ohio 47.9% 45.8% 18 0 • Va. 48.0% 48.0% 0 13 • Wis. 49.5% 46.8% 10 0 • Swing-State Votes 44 66 • Leaning/Likely State Votes 237 191 • Total Overall Votes 281 257

  25. Banzhaf calculation • Can NM swing the vote? • [37; CO(9) FL (29) IA (6) NV (6) NH (4) NC (15) H (18) VA (13), WI (10), NM(5)] • Other states: 233 to 191. Obama needs 37 from swing + NM

  26. VA+OH+NM forms a winning coalition for Obama[37; CO(9) FL (29) IA (6) NV (6) NH (4) NC (15) H (18) VA (13), WI (10), NM(5)] • True • False

  27. All but FL and NC and VA forms a winning coalition for Obama[37; CO(9) FL (29) IA (6) NV (6) NH (4) NC (15) H (18) VA (13), WI (10), NM(5)] • True • False

  28. [If you were to vote today, who would you choose for president] • Gary Johnson/Jim Gray • Romney/Ryan • Obama/Biden • Other • Undecided

  29. [Females only: If you were to vote today, who would you choose for president] • Gary Johnson/Jim Gray • Romney/Ryan • Obama/Biden • Other • Undecided

  30. [Males only: If you were to vote today, who would you choose for president] • Gary Johnson/Jim Gray • Romney/Ryan • Obama/Biden • Other • Undecided

  31. [Does your vote matter?] • Yes • No

  32. Swing votes

  33. Is election fraud possible in America? • http://www.scoop.co.nz/stories/HL0310/S00211.htm

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