Math 210G Mathematics Appreciation Dr. Robert Smits by KYSdIX0L

VIEWS: 1 PAGES: 35

									           Math 210G
    Mathematics Appreciation
         Dr. Joe Lakey
Lecture 9: Su Voto es Su Voz
 [The president is elected by ]
A.   [Popular vote]
B.   [Electoral college]
C.   [Who has the most money]
D.   [Who has the most popular running
     mate]
• SNL on Romney – Obama
• youtube version
• youtube second version
Sarah Palin = Tina Fey?
          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]
A.   [Clinton]
B.   [Hart]
C.   [Quail]
D.   [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.     2,912,790      48.850   Republican
Bush (W)      (50,456,002)



Al Gore       2,912,253      48.841   Democratic
              (50,999,897)



Ralph Nader   97,421         1.633    Green
              (2,882,955)
The electoral college
      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.
 (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 2012
• RCP Poll Average Electoral Votes States Obama
  Romney                        Obama Romney
• Colo. 47.6% 47.8%                    09
• Fla. 47.0% 48.7%                    0 29
• Iowa 48.8% 46.8%                    60
• Nev. 49.5% 46.8%                    60
• N.H. 48.2% 47.4%                    40
• 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
        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
 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)]

A. True
B. False
 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)]
A. True
B. False
 [If you were to vote today, who
 would you choose for president]
A.   Gary Johnson/Jim Gray
B.   Romney/Ryan
C.   Obama/Biden
D.   Other
E.   Undecided
[Females only: If you were to vote
 today, who would you choose for
            president]
A.   Gary Johnson/Jim Gray
B.   Romney/Ryan
C.   Obama/Biden
D.   Other
E.   Undecided
  [Males only: If you were to vote
 today, who would you choose for
            president]
A.   Gary Johnson/Jim Gray
B.   Romney/Ryan
C.   Obama/Biden
D.   Other
E.   Undecided
   [Does your vote matter?]
A. Yes
B. No
Swing votes
   Is election fraud possible in
             America?
• http://www.scoop.co.nz/stories/HL0310/S0
  0211.htm

								
To top