Wednesday, October 08, 2008

The Magic Number

There is one number which is foremost on the minds of both candidates for President. It is not $700 billion, the amount of the recently-passed bailout of the financial system. Nor is it the budget deficit, the mean time between Biden gaffes, the tax rate, the number of houses John McCain owns, the number of Americans without medical insurance, or the number of months until we leave Iraq.

The number which dominates the thoughts of John McCain and BO is 270.

That is how many electoral votes are required to be elected President. Both campaigns are working the numbers every which way, trying to figure out how to piece together 270 Electoral College votes. 269 is not enough, and 271 is excessive.

"One man, one vote" is a central principle in democracy. You may be wondering how much weight your vote really carries. It seems that John McCain and BO are spending lots of time and advertising dollars in Ohio, Florida, Colorado, Indiana, Virginia, North Carolina, and Missouri, while here in Texas we have never seen either candidate. They have not been to California, New York, Illinois, or Arizona lately either. That is because McCain takes our vote for granted while BO has given up on it. The Electoral College (EC) system forces candidates to concentrate on states where the vote appears to be close. So the candidates are pouring money and time into the swing states, where those resources are most likely to pay off.

But the Electoral College tampers with the "one man, one vote" system in a different way.

Small states (when I refer to the "51 states", that includes DC, which counts as a state in the EC even though it is a district) get proportionally more EC votes per capita than larger states. The District of Columbia gets 3 votes in the electoral college decided by 588,292 citizens (I say "citizens" because that is the total population, not just eligible voters or actual voters). Each EC vote represents 196,097 citizens. California gets 55 EC votes decided by 36,553,215 citizens. Each vote represents 664,603 citizens. A vote in DC carries 3.3 times as much weight in the Electoral College as a vote in California.

In the unlikely event of a tie, when both candidates get 269 votes, the House of Representatives elects the President, but each state delegation gets one vote. So Alaska's 683,478 people have exactly as much clout as California's 36,553,215. This has never happened, but my analysis allows for it.

With the Electoral College, the swing states get the bulk of the attention. Without the Electoral College, the large urban areas where the bulk of the population is concentrated would get the majority of the attention. Small states and rural areas would be forgotten. There is no perfect system, but the Electoral College is certainly better than electing a president by popular vote.

It would be almost impossible to eliminate the Electoral College system, because that would require a Constitutional Amendment, which must be ratified by three fourths of the states, or 38 states. The smaller 25 states would lose influence with a popular vote, so they would surely not ratify such an amendment.

My point is not that the Electoral College is bad. I am just saying that it is important to understand how the EC affects the electoral process, and how your vote weighs differently than the vote of someone in some other state.

To quantify this, I did some analysis in which I used Monte Carlo simulation to determine the probability that each state would affect the outcome of the election. Using a state-or-the-art random number generator I assigned each of the 51 states a status either red or blue. Then I summed the electoral votes. If red had a majority, I looked for all the blue states which had enough electoral votes to flip the outcome to blue. I incremented the running tally for those states. If blue had a majority, I did the same for red states. In the case of a tie, every state, red or blue, could affect the outcome. Using a significant amount of computing horsepower, I repeated the process one hundred million times. This is rocket science applied to a real-world problem with world-history-altering ramifications, that you will not find anywhere but on this blog.

The results quantify the difference is the influence of each vote from one state to another. After normalizing the result, the final outcome indicates that one man in some states gets 0.7 votes and in other states gets 2.2 votes simply because of which state he lives in.



There are 26 states which have 7 or fewer electoral votes, making 7 the median influence in the EC. As expected, the normalized weight of a single vote in states with 7 votes is close to 1.0. Iowa, with 7 electoral votes, has a normalized weight of 0.97 per vote, very close to the average weight of the 51 states. Iowa is the only state in the union where one man gets one vote.

Below is the raw data for you to chew on. Column-by-column, an explanation for the data is:

1. The name of the state

2. How many votes that state gets in the EC

3. The state's population according to the most recent census (generally expect the voter turnout to be roughly one third of the population, because the population includes people not eligible to vote and those who simply don't vote, the 2/3 irresponsible, ignorant, apathetic majority. The 1/6 of the population who are under 18 have an excuse for being in this category. The adults... People who are not willing to be informed ought not to vote. It is well known that ignorant people base their voting decisions on which candidate is taller, which candidate as a more pleasing tone of voice, or which candidate is endorsed by Oprah. Thus, ignorant voters vote Democrat ten to one.)

4. The tally for the number of cases in 100 million in which that state altered the outcome of the EC vote.

5. The probability of that state altering the outcome of the EC vote. California changing from red to blue alters the margin of the EC vote by 110 votes, which changes the outcome in 47.5% of the cases. Alaska's 3 votes change the margin by 6 votes, which affects the outcome in only 2.27% of the cases.

6. The "weight" of each vote, or the "per capita" probability that each ballot alters the outcome of the EC vote. This is the probability that your vote is the one which alters the outcome of the election from John McCain to BO, or the probability that if you had voted the other way the other candidate would have won. These numbers are too small, on the order of one in 100 million, to easily understand their significance, so next we have...

7. The normalized weight of each vote. The normalization forces the average vote across the nation to be weighted as 1 vote. Normalized votes with weight more than one have more influence than the average vote. Those with weight less than one have less influence.




(For some reason you will have to scroll WAY down to reach the table)
















































































































































































































































































































































































































































































































































































































































































































































































































































































































State




EC votes




Population




Tally




P




PerCapita
weight




Normalized
Weight




California




55




36,553,215




47,504,902.00




0.475049




0.0000000129961




0.71289800




Texas




34




23,904,380




26,631,544.00




0.266315




0.0000000111409




0.61113000




New York




31




19,297,729




24,144,337.00




0.241443




0.0000000125115




0.68631500




Florida




27




18,251,243




20,874,019.00




0.20874




0.0000000114370




0.62737700




Illinois




21




12,852,548




16,103,665.00




0.161037




0.0000000125296




0.68730600




Pennsylvania




21




12,432,792




16,103,665.00




0.161037




0.0000000129526




0.71051100




Ohio




20




11,466,917




15,322,452.00




0.153225




0.0000000133623




0.73298700




Michigan




17




10,071,822




12,981,786.00




0.129818




0.0000000128892




0.70703500




Georgia




15




9,544,750




11,431,322.33




0.114313




0.0000000119766




0.65697200




North
Carolina




15




9,061,032




11,431,322.33




0.114313




0.0000000126159




0.69204400




New
Jersey




15




8,685,920




11,431,322.33




0.114313




0.0000000131608




0.72193000




Virginia




13




7,712,091




9,893,928.00




0.098939




0.0000000128291




0.70373800




Washington




11




6,468,424




8,359,528.00




0.083595




0.0000000129236




0.70892100




Massachusetts




12




6,449,755




9,124,030.00




0.09124




0.0000000141463




0.77599400




Indiana




11




6,345,289




8,359,528.00




0.083595




0.0000000131744




0.72267800




Arizona




10




6,337,755




7,595,333.50




0.075953




0.0000000119843




0.65739400




Tennessee




11




6,156,719




8,359,528.00




0.083595




0.0000000135779




0.74481300




Missouri




11




5,878,415




8,359,528.00




0.083595




0.0000000142207




0.78007500




Maryland




10




5,618,344




7,595,333.50




0.075953




0.0000000135188




0.74157200




Wisconsin




10




5,601,640




7,595,333.50




0.075953




0.0000000135591




0.74378300




Minnesota




10




5,197,621




7,595,333.50




0.075953




0.0000000146131




0.80159800




Colorado




9




4,861,515




6,831,295.33




0.068313




0.0000000140518




0.77080800




Alabama




9




4,627,851




6,831,295.33




0.068313




0.0000000147613




0.80972600




South
Carolina




8




4,407,709




6,069,888.50




0.060699




0.0000000137711




0.75540900




Louisiana




9




4,293,204




6,831,295.33




0.068313




0.0000000159119




0.87284300




Kentucky




8




4,241,474




6,069,888.50




0.060699




0.0000000143108




0.78501600




Oregon




7




3,747,455




5,309,288.50




0.053093




0.0000000141677




0.77716700




Oklahoma




7




3,617,316




5,309,288.50




0.053093




0.0000000146774




0.80512700




Connecticut




7




3,502,309




5,309,288.50




0.053093




0.0000000151594




0.83156600




Iowa




7




2,988,046




5,309,288.50




0.053093




0.0000000177684




0.97468400




Mississippi




6




2,918,785




4,548,395.00




0.045484




0.0000000155832




0.85481200




Arkansas




6




2,834,797




4,548,395.00




0.045484




0.0000000160449




0.88013800




Kansas




6




2,775,997




4,548,395.00




0.045484




0.0000000163847




0.89878100




Utah




5




2,645,330




3,789,159.00




0.037892




0.0000000143240




0.78573800




Nevada




5




2,565,382




3,789,159.00




0.037892




0.0000000147703




0.81022500




New
Mexico




5




1,969,915




3,789,159.00




0.037892




0.0000000192351




1.05514000




West
Virginia




5




1,812,035




3,789,159.00




0.037892




0.0000000209111




1.14707300




Nebraska




5




1,774,571




3,789,159.00




0.037892




0.0000000213525




1.17128900




Idaho




4




1,499,402




3,029,352.20




0.030294




0.0000000202037




1.10827200




Maine




4




1,317,207




3,029,352.20




0.030294




0.0000000229983




1.26156700




New
Hampshire




4




1,315,828




3,029,352.20




0.030294




0.0000000230224




1.26288900




Hawaii




4




1,283,388




3,029,352.20




0.030294




0.0000000236043




1.29481100




Rhode
Island




4




1,057,832




3,029,352.20




0.030294




0.0000000286374




1.57089700




Montana




3




957,861




2,272,199.25




0.022722




0.0000000237216




1.30124300




Delaware




3




864,764




2,272,199.25




0.022722




0.0000000262754




1.44133000




South
Dakota




3




796,214




2,272,199.25




0.022722




0.0000000285375




1.56542100




Alaska




3




683,478




2,272,199.25




0.022722




0.0000000332447




1.82362900




North
Dakota




3




639,715




2,272,199.25




0.022722




0.0000000355189




1.94838400




Vermont




3




621,254




2,272,199.25




0.022722




0.0000000365744




2.00628100




DC




3




588,292




2,272,199.25




0.022722




0.0000000386237




2.11869300




Wyoming




3




522,830




2,272,199.25




0.022722




0.0000000434596




2.38396900


2 comments:

todd said...

1. That's the most incredible thing I've ever read.

2. I have no idea what it means.

3. I think you just endorsed Oprah. Does that make me ignorant?

Don Dodson said...

It means that one person voting Obama in Vermont cancels out your vote, my vote, and my wife's vote for McCain. How does that make you feel?

If you vote based on Oprah's endorsement, that makes you ignorant.