Election Model Methodology: A Primer
For all those non-mathematicians and non-statisticians who may be interested, this is a simple guide to the methodology used in my election simulation model:
You can find the latest poll analysis here:
http://www.geocities.com/electionmodel/There are generally three methods used to track elections and predict a winner. Each makes certain assumptions.
The first method analyzes economic factors: growth, jobs, inflation, etc. Forecasters claim to have had success using this approach (after all, this is what they do for a living). They create an econometric-like model which employs multiple regression/factor analysis to derive a formula based on these variables in order to predict the popular vote.
For the life of me, I can’t figure out how some of these forecasters can predict a 58% popular vote for Bush considering the economic pain inflicted since Jan. 2001. But that’s not an issue I wish to discuss here.
A second method tracks national polling trends and projects the potential movement of undecided or third party voters. There are about 15 major national pollsters. This method also seeks to predict the popular vote. Predicting a majority vote does not mean the winner will gain 270 electoral votes – but this extremely rare event can only in extremely tight elections where the popular vote spread is less than 0.5%. In fact, in a 51-49 popular vote split, there is virtually ZERO probability that the popular vote winner would lose in the Electoral College. It didn’t happen in 2000, because Gore won Florida while he also received 543,000 more votes than Bush (a 0.5% spread).
The third method tracks individual state polls in order to predict electoral votes. The focus is on the hard-fought twenty or so battleground states.
In my election model, I employ methods two and three. I believe that polls are pretty good indicators, provided that they are fresh and non-biased. And they have been pretty accurate as a whole. Why not just use the information that the real voters are telling us?
Like many others, I use the polling results as a starting point, and then make assumptions for the allocation of undecided/other voters to Kerry and Bush. The undecided voters usually split 2-1 for the challenger (Kerry).
To illustrate this important point: If a poll is tied 45-45, then Kerry is really “winning” by 52-48%, since he can expect to receive 7% or more of the undecided 10% (based on historical polling results).
An advantage of national polling is its simplicity. To determine who is “ahead” in the horse race, we only need a single number: the poll point “spread”: between the candidates. If the spread exceeds the polling margin of error (the MoE is typically +/-3% for nationwide polls of 1000 sample size) it is a statistical fact that the current leader has at least a 95% chance of winning the election. But that is just the probability for ONE poll only.
If, however, THREE polls (3000 sample size) are considered, the MoE tightens to +/-1.80%. Let’s assume a 52-48% average spread. The probability that the leader will receive somewhere between 50.2-53.8% (a 3.60% range) of the vote is also 95%. If we add 2.5% for the possibility that he will exceed 53.8%, he now has a 97.5% + cumulative probability of exceeding 50.2% of the vote.
For fifteen polls, the MoE is a very-tight 0.80%. This means that for the same 52-48 % spread, the probability is 95% that the leader will receive between 51.2% and 52.8% of the vote. In this case, the probability of EXCEEDING 50% is 99.99+%.
The bottom line: Assuming Kerry has an average 52%-48% lead in 15 polls the day before the election, then if he loses, it will be due to something OTHER than mere CHANCE.
The 95% confidence interval around the mean comes right out of Statistics 101. The MoE is 1.96 times the standard deviation, which is a statistical measure of the spread of polling results around the mean. The standard deviation is used in the normal distribution (the bell-shaped curve) to determine a confidence interval around the sample MEAN poll result.
But ultimately, the winner must get at least 270 electoral votes. How do we calculate the probability of an election win using the latest state polling results? We extend the method used for the national polls: we now calculate the probabilities of winning each state. To get at the probability of an electoral vote win, we combine these individual probabilities by running a computer election simulation. State polls typically sample 500-600, so the MoE is wider (+/-4%) for each state.
Each candidate has a state win probability based on the latest state poll. In a 50-50 poll split, both have 50% probability of winning the state. If the split is 60-40, the probability of the leader winning the state is 99.999%. It gets interesting when the polls are close, say 51-49%. In this case, the leader has a 69% chance of winning the election. For a 52-48 split, it’s about 83%. For a 53-47 split, it’s 97%.
Now, let’s get back to the probability of Kerry winning at least 270 votes. Its called Monte Carlo simulation: we let the computer “run” 1000 election trials to determine Kerry’s probability of winning 270 Electoral Votes.
In each election trial, we generate a RANDOM (RND)) number between 0 and 1 for EACH state and COMPARE it to the probability of Kerry winning the state.
For example, if the RND generated for FL is .55 and Kerry has a .60% probability of winning FL, he wins the state. If, on the other hand, the RND is .75, then FL goes to Bush. In the same fashion, the computer generates random numbers for all the states and assigns electoral votes to the winner. It does this 1000 times, so we are in effect running 1000 simulated election trials. Say Kerry wins 980 trials. Then he has a 98% chance of winning. In my election model, we calculate Kerry’s average and maximum electoral votes for the these trials.
In today’s run, Kerry won 948 trials, so he has a 94.8% probability of winning the election. He received an average of 323 electoral votes in the 1000 trials.
One advantage of this method is the limited poll “whiplash” in EV's as the "close" states change hands daily in the polls. The changes in EV in the simulation model are minimized. The simulation does not produce the wild ups and downs in EV as do most other models, which just assign the state's EV to the latest poll leader (even if he leads by just 1%).
Hopefully, this clarifies the methodology. Using national and state models has the advantage of providing a mathematical confirmation between the two approaches .
The main point is this: we need to analyze as many polls as possible and recognize the fact that this REDUCES the overall margin of error and we can have more confidence in the results.
A final word, perhaps one that cannot be over-emphasized: The analysis produces a PROBABILITY of a Kerry win, assuming the election were held TOMMORROW. It does not PREDICT a Kerry win. There IS a difference. The model cannot determine the probability that the ELECTION WILL BE STOLEN CYBERSPACE.
I assume a fair election – but I don’t expect one. Not with the BFEE involved.
TIA.
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