The Electoral College

(1)

The Electoral

College

Excursions in Mathematics

,

Chapter 2 Thinking Mathematically,

Chapter 14

(2)



Play video found at:

(3)

Article II of the United States Constitution

Section 1. The executive Power shall be vested in a President of the United States of America. He

shall hold his Office during the Term of four Years, and, together with the Vice President, chosen for the same Term, be elected, as follows:

Each State shall appoint, in such Manner as the Legislature thereof may direct, a Number of

Electors, equal to the whole Number of Senators and Representatives to which the State may be entitled in the Congress: but no Senator or

(4)

Amendment 12 - Choosing the President, Vice-President.

The Electors shall meet in their respective states, and vote by ballot for President and Vice-President, …they shall make distinct lists of all persons voted …which lists they shall sign …and transmit sealed to …the President of the Senate; The President of the Senate shall, in the presence of the Senate and House of Representatives, open all the certificates and the votes shall then be counted; The person having the greatest Number of votes …shall be the President, if such number be a majority of the

whole number of Electors appointed; and if no

person have such majority, then from the persons having the highest numbers not exceeding three … the House of Representatives shall choose

immediately, by ballot, the President. …the votes shall be taken by states, the representation from each state having one vote; a quorum for this

(5)

Amendment 23 - Presidential Vote for District of Columbia.

1. The District constituting the seat of Government of the United States shall appoint in such manner as the Congress may direct: A number of electors of President and Vice President equal to the whole

number of Senators and Representatives in

Congress to which the District would be entitled if it were a State, but in no event more than the least populous State; they shall be in addition to those appointed by the States, but they shall be

considered, for the purposes of the election of President and Vice President, to be electors

appointed by a State; and they shall meet in the

District and perform such duties as provided by the twelfth article of amendment.

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538 electors for each election

since 1964

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Why are there 538 electors?

435 House

100 Senate

3 D.C.

538 TOTAL

+

The number is set by law, to be divided among states according to the ten-year

U.S. census. According to the

constitution, there are 2 senators for each of the 50

states.

A constitutional amendment gives D.C. a number of electors equal to 2 senators

+ a number of

representatives at least equal to those of the

smallest state.

RECALL

Electors per state =

Representatives +

Senators

OR

Congressional Districts +

Senators

OR

(8)

g Increase 1

elector

g Increase 2+

electors

g Decrease 1

elector

g Decrease 2

electors

g No change

US Electoral College

Changes for 2012

(9)

How do the electors

vote?



Most states are “winner takes all.”

 _{In 48 states and D.C., the plurality winner of the}

popular vote in each state gets all the electoral votes for that state.

 _{In Maine and Nebraska, one electoral vote}

corresponds to the popular vote in each

congressional district and the remaining two electoral votes go to the overall state popular vote winner.



Most electors pledge their vote in advance.

 _{Electors are usually chosen by political parties as a}

reward for service to that party. They pledge to vote for the party’s official candidate.

 _{In 26 states and D.C., state laws}_require_{electors to}

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g Law for

pledge

g ~Law for pledge

g No Law

States with Laws

(11)

Has an elector ever voted

differently than pledged?

 In 57 elections for president, some electors voted

differently than pledged in 19 (33%) elections!

 From 1 to 63 electors voted differently than

pledged in elections, for a total of 158 electors.

 The reasons include:

 _{2 by accident}

 _{2 for same party}  _{3 for another party}  _{3 for non-candidate}  _{4 in protest}

 _{6 for VP as president}  _{63 since candidate}

died

 _{75 only changed VP}

 _{7 for another party}  _{8 since candidate}

died

 _{23 in protest}  _{37 for}

non-candidate These faithless

electors have never changed an

election’s final outcome!

Discounting changing a pledged vote when the candidate died, there have

only been

87 faithless voters in 17 elections.

This amounts to 30% of the 57 elections but only 0.4% of the approximately 23,027

(12)

How often do popular vote results

and electoral vote results differ?



There have been 57 presidential elections.



In 53 of these (about 93%), the winner of

the electoral college vote is also the

winner of the national popular vote.

(13)

How often do popular vote results

and electoral vote results differ?



These are the exceptions:



_{1824, John Q. Adams vs. Andrew Jackson}

Here’s the story…

Jackson had a plurality of popular votes and electoral votes, but not majority. The House of

Representatives, whose Speaker was now-eliminated candidate Henry Clay, voted for Adams. After being elected, Adams appointed Clay Secretary of State.

The decision went to the House in 1800 also. Then the 1st place

candidate was president and 2nd_place

was VP. Thomas Jefferson and Aaron Burr ran for president and VP; they got equal votes. Soon after, the 12th

(14)

How often do popular vote results

and electoral vote results differ?



These are the exceptions:



_{1824, John Q. Adams vs. Andrew Jackson}



_{1876, Rutherford B. Hayes vs. Samuel J.}

Tilden

(15)

How often do popular vote results

and electoral vote results differ?



These are the exceptions:



_{1824, John Q. Adams vs. Andrew Jackson}



_{1876, Rutherford B. Hayes vs. Samuel J.}

Tilden



_{1888, Benjamin Harrison vs. Grover}

Cleveland

(16)

How often do popular vote results

and electoral vote results differ?



These are the exceptions:



_{1824, John Q. Adams vs. Andrew Jackson}



_{1876, Rutherford B. Hayes vs. Samuel J.}

Tilden



_{1888, Benjamin Harrison vs. Grover}

Cleveland



_{2000, George W. Bush vs. Al Gore}

After the election, media reported Bush had 246

electoral votes, Gore had 255, and 270 were needed to win. Three states were too close to call: New

Mexico (5), Oregon (7), and Florida (25). Gore had a plurality of the popular vote (48.4%) over Bush

(17)

Could we have used

a different system?

Congress could choose the president.

 _{Might upset the balance of power}

State legislatures could select the president.

 _{Might make president prefer one state to another}

People could elect the president by popular vote.

 _{Might vote only for “favorite son” with no information about the} other candidates

 _{Might only have presidents from large, populous states}

A “Committee of Eleven” proposed an indirect election of the president through a College of

(18)

Should we still use the

Electoral College system?

PROS

 It allows small states to

have a say in the election.

 It creates political stability

by encouraging a 2-party system.

 With the winner-takes-all

allocation of votes, the victory seems conclusive.

 It avoids the possibility of a

national recount; recounts in close elections would be confined to a few states.

CONS

 Some votes are “worth” more

than others; votes in small states are disproportionate to those in larger states.

 It discourages 3rd parties.

 A person can win without

having a majority of the popular vote.

 There is a risk of selecting

faithless electors.

 Voter turnout may be lower

(19)

(20)

How are Representatives, and

therefore Electors, apportioned?



Hamilton’s Method



Jefferson’s Method



Adams’s Method



Webster’s Method

Hamilton’s Method

Alexander Hamilton

• _{Founding father of United}

States

• ₁st Secretary of State under Washington

Hamilton’s Method

• _{Congress passed method in}

1791

• _{Pres. Washington vetoed (1}st ever veto)

• _{Adopted in 1852 and used until}

(21)

standard divisor = total population

number of allocated items =

1890

30 =63

The Republic of Collier

Has 4 states with 30 total representatives.

State A B C D TOTA

L

Population 275 383 465 767

Hamilton’s Method

L

Population 275 383 465 767 1890

number of allocated items standard divisor = total population

number of allocated items =

1890 30

standard quota = group population standard divisor

L

Population 275 383 465 767 1890 Standard

Quota

L

Quota 4.37

L

Quota 4.37 6.08

L

Quota 4.37 6.08 7.38

L

Quota 4.37 6.08 7.38 12.17

L

Quota 4.37 6.08 7.38 12.17 30

L

Quota 4.37 6.08 7.38 12.17 30 Final

Apportionmen t

L

Quota 4.37 6.08 7.38 12.17 30 Final

Apportionmen

t 4

L

Quota 4.37 6.08 7.38 12.17 30 Final

Apportionmen

t 4 6

L

Quota 4.37 6.08 7.38 12.17 30 Final

Apportionmen

t 4 6 7

L

Quota 4.37 6.08 7.38 12.17 30 Final

Apportionmen

t 4 6 7 12

L

Quota 4.37 6.08 7.38 12.17 30 Final

Apportionmen

t 4 6 7 12 29

Which state gets the

extra representati

(22)

The Republic of Collier

Has 4 states with 30 total representatives.

Hamilton’s Method

L

Quota 4.37 6.08 7.38 12.17 30 Final

Apportionmen

t 4 6 7 12 29

HAMILTON’S METHOD

1. Calculate each group’s standard quota.

2. Round down to the nearest whole number (lower quota).

3. Give any extra items, one at a time, to the group with the largest decimal part before the rounding.

(23)

Hamilton’s Method

There were many problems with Hamilton’s Method.

 The Alabama Paradox: An increase in the total

number of representatives being apportioned forces a state to lose one of its representatives.

 The Population Paradox: A positive population

growth rate in one state forces it to lose one or more of its representatives to a state with a small or even zero population growth rate.

 The New-States Paradox: The addition of a

new state with its fair share of seats can affect the apportionment of other states.

(24)

How are Representatives, and

therefore Electors, apportioned?



Hamilton’s Method



Jefferson’s Method



Adams’s Method



Webster’s Method

Jefferson’s Method

Thomas Jefferson

• _{Wrote the Declaration of}

Independence

• ₃rd President of the United States

Jefferson’s Method

• ₁st apportionment used by U.S. Congress

• _{Used from 1791 until 1842} • _{Gave no “preferential}

(25)

The Republic of Collier

Has 4 states with 30 total representatives.

Jefferson’s Method

L

Quota 4.37 6.08 7.38 12.17 30 1st Try

Apportionmen

t 4 6 7 12 29

number of allocated items

Find a modified divisor. Then when the quota is calculated and rounded down, the total number of representatives is correct.

= 1890

30 =63

Need this number bigger, so try smaller

divisor!

(26)

The Republic of Collier

Has 4 states with 30 total representatives.

Jefferson’s Method

L

Population 275 383 465 767 1890 Modified

Quota 30

Final Apportionmen

t

= 1890

30 =6360

L

Quota 4.58 6.38 7.75 12.78 30 Final

Apportionmen t

L

Quota 4.58 6.38 7.75 12.78 30 2nd Try

Apportionmen

t 4 6 7 12 29

(27)

The Republic of Collier

Has 4 states with 30 total representatives.

Jefferson’s Method

L

Quota 30

Final Apportionmen

t

= 1890

30 =6360 55

L

Quota 5.00 6.96 8.45 13.95 30 Final

Apportionmen t

L

Quota 5.00 6.96 8.45 13.95 30 3rd Try

Apportionmen

t 5 6 8 13 32

(28)

The Republic of Collier

Has 4 states with 30 total representatives.

Jefferson’s Method

L

Quota 30

Final Apportionmen

t

= 1890

30 =6360 55 59

L

Quota 4.66 6.49 7.88 13.00 30 Final

Apportionmen t

L

Quota 4.66 6.49 7.88 13.00 30 Final

Apportionmen

t 4 6 7 13 30

SUCCES S! Notice that State D increased, rather than

(29)

The Republic of Collier

Has 4 states with 30 total representatives.

Jefferson’s Method

JEFFERSON’S METHOD

2. Round down to the nearest whole number (lower quota).

3. If the total does not match the number of

representatives, adjust to a modified divisor (by trial-and-error) and repeat.

L

Quota 4.66 6.49 7.88 13.00 30 Final

Apportionmen

t 4 6 7 13 30

Standard divisor =

63

Modified divisor =

(30)

Jefferson’s Method

There were problems with Jefferson’s Method as

well:



There is no formula to find the modified divisor.



It violates the

Quota Rule

which states that a

group’s apportionment should either be the

lower quota (the standard quota rounded

down) or the upper quota (the standard quota

rounded up).

In trying to be fair, Jefferson’s Method

(31)

How are Representatives, and

therefore Electors, apportioned?



Hamilton’s Method



Jefferson’s Method



Adams’s Method



Webster’s Method

Adams’s Method

John Quincy Adams

• ₆th President of the United States

• _{Served in House of}

Representatives 18 yrs

Adams’s Method

• _{Was a “mirror image” of}

Jefferson’s Method, using modified upper quotas

• _{Was never actually used by}

(32)

The Republic of Collier

Has 4 states with 30 total representatives.

L

Quota 4.37 6.08 7.38 12.17 30 Final

Apportionmen t

Find a modified divisor. Then when the quota is calculated and rounded up,

the total number of representatives is correct.

= 1890

30 =63 Try ₆₅

Adams’s Method

Round UP!

L

Quota 4.37 6.08 7.38 12.17 30 Final

Apportionmen

t 5 7 8 13

L

Quota 4.37 6.08 7.38 12.17 30 1st Try

Apportionmen

t 5 7 8 13 33

Need this number smaller, so

(33)

The Republic of Collier

Has 4 states with 30 total representatives.

L

Quota 30

Final Apportionmen

t

= 1890

30 =63

Adams’s Method

Round UP!

65

L

Quota 4.23 5.89 7.15 11.80 30 Final

Apportionmen t

L

Quota 4.23 5.89 7.15 11.80 30 Final

Apportionmen

t 5 6 8 12

L

Quota 4.23 5.89 7.15 11.80 30 2nd Try

Apportionmen

t 5 6 8 12 31

(34)

The Republic of Collier

Has 4 states with 30 total representatives.

L

Quota 30

Final Apportionmen

t

= 1890

30 =63

Adams’s Method

Round UP!

65 67

L

Quota 4.10 5.72 6.94 11.45 30 Final

Apportionmen t

L

Quota 4.10 5.72 6.94 11.45 30 Final

Apportionmen

t 5 6 7 12

L

Quota 4.10 5.72 6.94 11.45 30 Final

Apportionmen

t 5 6 7 12 30

(35)

The Republic of Collier

Has 4 states with 30 total representatives.

ADAMS’S METHOD

2. Round up to the nearest whole number (upper quota).

3. If the total does not match the number of

Standard divisor =

63

Modified divisor =

67

Adams’s Method

L

Quota 4.10 5.72 6.94 11.45 30 Final

Apportionmen

(36)

Of course, there were problems with Adams’s

Method:



There is no formula to find the modified divisor.



It also violates the

Quota Rule

which states

that a group’s apportionment should either be

the lower quota (the standard quota rounded

down) or the upper quota (the standard quota

rounded up).

In trying solve the problem of upper quota

violations caused by Jefferson’s Method,

Adams’s Method created a lower-quota

violation.

(37)

How are Representatives, and

therefore Electors, apportioned?



Hamilton’s Method



Jefferson’s Method



Adams’s Method



Webster’s Method

Daniel Webster

• _{Served in House of}

Representatives 8 yrs, the Senate 19 yrs, Secretary of State 4 yrs

Webster’s Method

• _{Used modified quotas but}

conventional rounding

• _{Used 1842 – 1852 and again}

(38)

The Republic of Collier

Has 4 states with 30 total representatives.

L

Quota 4.37 6.08 7.38 12.17 30 Final

Apportionmen t

Find a modified divisor. When the quota is

calculated and rounded as usual, the total number of representatives is correct.

= 1890

30 =63 Try ₆₅

Webster’s Method

Regular Rounding: up for 5 or larger, else down.

L

Quota 4.37 6.08 7.38 12.17 30 Final

Apportionmen

t 4 6 7 12

L

Quota 4.37 6.08 7.38 12.17 30 1st Try

Apportionmen

t 4 6 7 12 29

(39)

The Republic of Collier

Has 4 states with 30 total representatives.

L

Quota 30

Final Apportionmen

t

= 1890

30 =63

Webster’s Method

65

L

Quota 4.23 5.89 7.15 11.8 30 Final

Apportionmen t

L

Quota 4.23 5.89 7.15 11.8 30 Final

Apportionmen

t 4 6 7 12

L

Quota 4.23 5.89 7.15 11.8 30 2nd Try

Apportionmen

t 4 6 7 12 29

Still not right…

(40)

The Republic of Collier

Has 4 states with 30 total representatives.

L

Quota 30

Final Apportionmen

t

= 1890

30 =63

Webster’s Method

65 62

L

Quota 4.44 6.18 7.50 12.37 30 Final

Apportionmen t

L

Quota 4.44 6.18 7.50 12.37 30 Final

Apportionmen

t 4 6 8 12

L

Quota 4.44 6.18 7.50 12.37 30 Final

Apportionmen

t 4 6 8 12 30

Lots of guessing

(41)

The Republic of Collier

Has 4 states with 30 total representatives.

WEBSTER’S METHOD

2. Round normally to the nearest whole number. 3. If the total does not match the number of

Standard divisor =

63

Modified divisor =

62

Webster’s Method

L

Quota 4.44 6.18 7.50 12.37 30 Final

Apportionmen

(42)

Webster’s Method is a little better choice, but:



There is no formula to find the modified divisor.



It does not favor large or small states.



It may violate the

Quota Rule

but violations

are rare. (Note: If Webster’s Method had been

used for all apportionments from 1790 until

2000, no violation of the quota rule would have

occurred.)

Many believe that Webster’s Method is the

best overall apportionment method and

that we might return to it …but it is not

what the U.S. is currently using.

(43)

So what does the U.S.

currently use for apportionment?

• _{Speaker of House requests mathematical}

formula

• _{Joseph Hill, Chief Statistician of the Bureau}

of the Census

• _{Edward Huntington, Professor of Mechanics}

and Mathematics at Harvard University

• _{Aka Method of Equal Proportions}

• _{FDR signed 1941 Apportionment Act which}

made it the permanent, self-executing method for 435 House seats

• _{Rounding is done by comparing the}

fractional part of the quota to the geometric mean of the upper and lower quotas and