Number of possible electoral college ties

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Discussion Overview

The discussion revolves around the theoretical calculation of the number of possible electoral college ties, specifically focusing on achieving a 269 to 269 outcome. Participants explore mathematical methods, historical context, and the implications of including the District of Columbia in these calculations.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant suggests that coding may be necessary to calculate the number of possible ties.
  • Another participant mentions that there are at least 33 mathematical formulas that can lead to a 269-269 tie, referencing a source for further information.
  • A participant claims to have found a specific number of ways to achieve a tie (17,057,441,245,652) using a generating polynomial and discusses the probability of such an event occurring.
  • Concerns are raised about the accuracy of the calculations presented in the referenced source, with one participant noting a mistake in the method while agreeing on the basic approach.
  • There is a discussion about whether the District of Columbia should be included in the calculations, with conflicting views on its electoral representation.
  • Some participants argue that the District of Columbia is heavily Democratic and should not be considered a toss-up state in the context of the calculations.

Areas of Agreement / Disagreement

Participants express differing views on the inclusion of the District of Columbia in the calculations, and there is no consensus on the accuracy of the initial claims regarding the number of possible ties or the probability calculations. Multiple competing views remain regarding the mathematical methods and assumptions involved.

Contextual Notes

Participants note limitations in the calculations, including the need to account for the District of Columbia's electoral votes and the assumptions made about which states are considered toss-ups. There are unresolved mathematical steps related to the probability calculations.

Loren Booda
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Considering all 50 states and their current distribution of electoral votes, how many possible ties (totaling 269 to 269) can theoretically be generated?
 
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This is something you'll have to write a little code for.
 
Then crunch it with a Cray. Are there any approximate methods?
 
Strange you should ask, I just got this from MSNBC: There are no fewer than 33 mathematical formulas by which the Electoral College winds up in a 269-269 tie. See:http://www.msnbc.msn.com/id/6385561/ Is this any help? Or were you hoping to see the math? (They have only considered the battleground states.)

By gosh! I found the answer: 17,057,441,245,652 ways, and the method is to use a generating pollynominal and check the 269th coefficient. This also allows us to compute the probability, if every state is a toss up, which is about one election out of 66. See: http://www.izzycat.org/math/index.php?p=28

Historical note: In the election of 1800, Thomas Jefferson and Aaron Burr each got 73 electoral votes.
 
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There's at least one (relevant) mistake in that site. The basic method seems sound, and the coeffecient is correctly calculated, but:

In any case, when we do that expansion, the coefficient of x269 in g(x) is 17057441245652, which is the number of ways we can choose some states out of the 50 to have
269 electoral votes. Dividing by 250 (the number of ways in total to pick states) gives 0.01515, or about 1 in 66.

One must divide by 2^51, since the DC casts electoral votes and is included in the equation. This gives a probability of 17057441245652 / 2 ^51 ~ 0.758% ~ 1/132.
 
robert,

I did indeed get my idea from NBC, whose calculation included only those states they saw as relevant.

CR,

Are you sure that DC gets an electoral vote? They have no representation in the House of Representatives (or the Senate), which has been a sore spot for them as of late.


Thanks for the "results," guys!
 
Loren Booda said:
CR,

Are you sure that DC gets an electoral vote? They have no representation in the House of Representatives (or the Senate), which has been a sore spot for them as of late.

The District of Columbia has no representation in Congress, but casts 3 electoral votes (almost always for the Democratic candidate) per the 23rd Amendment, ratified in 1961:

Amendment XXIII.

Section 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.

Section 2.
The Congress shall have power to enforce this article by appropriate legislation.
 
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It would appear that NBC got it wrong (see robert's link).
 
Loren Booda said:
It would appear that NBC got it wrong (see robert's link).

The nine toss-up "states" would not include DC, which is heavily Democratic, but it should have been considered for the probability problem as CR Greathouse notes.
 
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  • #10
robert Ihnot said:
The nine toss-up "states" would not include DC

Most certainly not. DC, currently polling at about 76% for Kerrry, is the most liberal 'state'.
 
  • #11
Gokul43201 said:
Most certainly not. DC, currently polling at about 76% for Kerrry, is the most liberal 'state'.

That is certainly true -- the DC has never cast an electoral vote for a Republican. (They did abstain from one of their electoral votes in 2000, so they haven't always voted Democratic.)
 
  • #12
Gokul43201 said:
Most certainly not. DC, currently polling at about 76% for Kerrry, is the most liberal 'state'.

Are you sure the figure isn't 90% for Kerry? That's how it looks election night.
 

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