Wednesday, November 7, 2012

A better way of updating election outcomes

Written 12:30 Tuesday evening.

I don’t understand why pollsters never do this calculation.  At this moment Nevada is officially undecided.  However 80% of votes are cast with Obama leading 52 to Romney 46.  From these numbers we can easily calculate what percentage of voters Romney needs to take Nevada.  Let’s first calculate the number he needs to match Obama.

We can thing of this as the weighted average between the votes already counted and those yet to be counted.  This can be written out as the cast votes .8 and the uncast votes .2.  a is the proportion who vote Romney, (1-a) is the proportion that vote Obama.  Everybody votes in this approximation.
.8 * .46 + .2 * a = .8 *.52 + .2*(1-a)
Now we need only solve for a.  
P*R + (1-P)*a = P*O + (1-P)*(1-a)
P*R - P*O = (1-P)*(1-a) - (1-P)*a = (1-P)*(1-2a)
(P*R - P*O)/(1-P) = 1-2a
a = ½  -  (R - O)/2   * P/(1-P)
R is Romney voters, O Obama and P is the proportional that has already voted.
Using the previous example:
a = .5 - (.46-.52) * .8/.2                                                  
The above formula can be adjusted by making the totals into proportions.  I get Romney would need to win 74 percent of the remaining Nevada votes to win.  Probably unlikely.

A general formula can be defined as:
P*R + (1-P)*a = P*O + (1-P)*(1-a)

Now let’s look at Florida.

Wednesday morning. This state is very close, just using a "1 percent" margin is not sufficiently accurate for me.

PTotal = 4129360+4083321
R = 4083321 / PTotal
O = 4129360/ PTotal
Now we can easily calculate the P value from this.  .  Also, we have 94% of districts reporting. Thus :
So Romney only has a P value of .496175.  Finally let’s plug in the values above. 
a = .5  -  (R - O)/2   * P/(1-P)
a = 1/2  - (R-O)/2 * P/(1-P)

Thus we get that Romney would need win 59% of the remaining votes to take Florida.  This as opposed to Nevada is possible though at this point unlikely.

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