Math 210G Mathematics Appreciation 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 Clinton - Trump debate 2

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

Predicting outcomes 538 Vegas oddsmaker's view

2004: Kerry v Bush

2008: Obama v McCain

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

Close U.S. Presidential elections

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.

270 to Win 2000: Gore V Bush

The infamous butterfly ballot

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

The electoral college

(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

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?

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)

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.

Banzhaf calculator for electoral college General Banzhaf calculator

Swing Vote 2008 Link

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?

Battleground states 2016

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

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

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

[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

[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

[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

[Does your vote matter?] Yes No

Swing votes

Is election fraud possible in America?