ELECTION SIMULATION MODEL (Excel)
created by TruthIsAll
Interactive Election Simulation (zip)
This workbook contains a full analysis of the 2004 election, based on four sets of polls:
(1) Pre-election State polls
(2) Pre-election National Polls (18)
(3) Post-election State exit polls
(4) National Exit poll
The model can be used to run simulations, calculate probabilities and perform "sensitivity analysis" to see the effects of changes in assumptions on the electoral and popular vote. The model provides a strong circumstantial case for those who believe the election was stolen. Kerry won the pre-election state and national simulations, which are confirmed by the State and Preliminary National exit polls. Bush won only the Final Exit Poll, which was matched to the recorded vote.
There are only two possible explanations: either the pre-election AND exit polls were wrong - or massive fraud occurred.
The following worksheets are selected by clicking the tab at the bottom of the screen:
Model description; links to: polling data sources; EIRS database; related mathematics
Data input and summary analysis
Set calculation code = 1 to run the simulation/projection using final PRE-ELECTION polls.
Set calculation code = 2 to run the simulation based on EXIT polls.
Undecided voter allocation - set to Kerry percentage (default is 75%)
Exit Poll Cluster effect - percentage increase in calculated MoE (default is 30%)
Monte Carlo Simulation of 200 state pre-election and 200 state exit polls
Projections and analysis of 18 national pre-election polls
Analysis of National Exit Poll demographic timelines:
a) Preliminary (13047 respondents) updated Nov. 3 at 12:22 am.
b) Final Exit Poll (13660 respondents) updated Nov. 3 at 1:25 pm.
Ask "what-if": analyze the effects of changing demographic weights and percentages on the national totals.
Discussion and Sensitivity Analysis of the "Voted in 2000" demographic.
Vote margin sensitivity to Gore 2000 turnout and Kerry new
voter share using actual 2000 weights, assuming 100% Bush 2000 voter turnout.
Constrained optimization solution ("Solver" algorithm) for the true vote based on
a) the 2-party vote
b) exit poll precinct error (WPE)
c) response rate for 1250 precincts in 5 partisanship groups.
Uses Excel "Solver" to derive a feasible true vote based on
a) the final 2-party vote,
b) State exit poll deviations and
c) response rates for 5 states grouped from high Bush to high Kerry.
Comparative analysis for state and national exit polls
Demographic Voter statistics from the U.S. Census Bureau, Population Vote Survey, November 2004.
The Gender split matched the state exit
poll to within 0.25% and the National exit poll within 0.50%
Ohio Exit Poll Demographic Analysis vs. National Exit Poll
The model produces the following:
-Popular vote percentage/win probability bassed on pre-election state polls.
-Electoral win probability based on 200 Montte Carlo simulated election trials
-Exit Poll percentages and deviations from tthe final recorded vote.
Pre-election state polls are from Zogby, ARG, Gallup, etc.
Kerry's projected vote is the poll
percentage plus the undecided voter allocation.
Undecided voters traditionally break for the challenger by 60-80%.
Adjust this margin up or down to see the
effects on popular and electoral votes.
Review the expected electoral vote and win probabilities.
Play "what if" by changing just two inputs: undecided voter allocation and cluster effect.
Calculate the undecided voter allocation necessary for Kerry to win 50% of the popular vote and 270 electoral votes.
Enter the cluster effect as a percentage increase in the theoretical calculated Exit Poll MoE.
The number of states deviating beyond the exit poll MoE will decrease as the cluster effect increases.
Review the following simulation output:
Electoral and popular vote split and win probabilities.
Deviation probabilities for pre-election polls.
Deviation probabilities for exit polls.
Kerry had a slight lead in the 18 Pre-election poll weighted average: 47.55% - 47.30% and was poised to win.
Challengers win a majority (70%+) of the
late undecided vote.
The Preliminary National Exit Poll (12:22am, 13047 respondents) followed the 4pm (8349) and 7:33pm (1027) timelines.
Kerry was leading at each point in the
The Final National Exit poll (13660 respondents) was posted at 1:25pm.
Demographic weights and percentages were adjusted to match the recorded vote.
Ask "what if" by changing exit poll demographic weights and vote percentages.
You can also change the exit poll "cluster" effect. Note how the popular vote split and corresponding deviation probabilities change.
Exit poll vote percentages do not all sum to 100% horizontally, perhaps due to roundoff.
Effects on Kerry/Bush percentages and
probabilties are minimal.
Demographics are calculated independently.
Key demographics for what-if analysis:
Gender - Preliminary: Kerry share of female vote: 54%; in the Final: 51%.
How Voted in 2000 - Preliminary: 41% Bush / 39% Gore; in the Final: 43 / 37%.
Party ID - Preliminary: 38% Democrat / 35% Republican / 27% Independent; in the Final: 37 / 37 / 26%
POLL SAMPLE-SIZE AND MARGIN OF ERROR
The Law of Large Numbers is the basis for statistical sampling. All things being equal, polling accuracy is directly related to sample size - the larger the sample, the smaller the margin of error (MoE). In an unbiased random sample, there is a 95% probability that the vote will fall within the MoE of the sample mean.
In the state pre-election polls, about 600 were polled (4% MoE). But the 30,000 national total sample lowers the aggregate MoE.
In 18 pre-election national polls the sample-size ranged from 800 (3.5% MoE) to 3500 (1.7%).
The total 27,000 sample reduces the
combined MoE to 0.6%.
The post-election state exit polls sampled 114,000 nationwide, with respondents ranging from 600 (4% MoE) to 2800 (1.8%).
In the National Exit Poll of 13047 respondents, the MoE was 0.88% before the "cluster effect". Kerry won 51%-48%.
Assuming a 1,0% MoE, the probability was 97.5% that he would win at least 50% of the vote.
Monte Carlo Simulation- a randomization process of repeated experimental "trials" applied to a mathematical system model.
This simulation consists of 200 trial "elections" to determine the expected Electoral Vote and win probability.
The state win probability is based on the final exit poll split. A typical state poll consists of 600 sample-size with 4% MoE.
The Electoral Vote is calculated for Kerry and Bush for each of the 200 election trials. The average electoral vote is the arithmetic mean of the 200 trials. The median EV (the middle value) is usually within a few votes of the average.
Margin of error - is based on poll sample size and given by the formula:
MoE = 1.96* Sqrt (P*(1-P)/n) at the 95% confidence level, where P and 1-P is the vote split.
Returns the normal distribution for the specified mean and standard deviation.
This Excel function has a very wide range of applications in statistics, including hypothesis testing.
X is the value for which you want the distribution.
Mean is the arithmetic mean of the distribution.
Standard_dev is the standard deviation of the distribution.
Cumulative is a logical value that determines the form of the function.
If cumulative is TRUE, NORMDIST returns the cumulative distribution function; if FALSE, it returns the probability mass function.
Calculate the probability Kerry would win Ohio based on the exit poll.
Ohio Exit Poll - 12:22am update, 1963 sample-size
Mixt Vote Kerry Bush
Male 47% 2.64 51% 49%
Female 53% 2.98 53% 47%
Total 100% 52.06% 47.94%
Votes 5.63 2.93 2.70
Kerry winning margin: 232 thousand votes.
Note: change Sample size and / or Cluster effect to see the effect on the probability:
Sample Size 1963
Cluster effect 20%
Adj. MoE 2.65%
Std Dev = 1.35% (Adj. MoE / 1.96)
The input parameters to the Normal Distribution function:
Probability = NORMDIST (Kerry, Bush, StdDev, TRUE)
are given by:
Kerry = 52.06%
Bush = 47.94%
StdDev = 1.35%
Probability Kerry won Ohio for a given cluster effect:
Cluster 0% 10% 20% 30% 40% 50%
MoE 2.21% 2.43% 2.65% 2.87% 3.10% 3.32%
Prob 96.6% 95.2% 93.6% 92.0 90.4% 88.8%
Returns the individual term binomial distribution probability.
Use BINOMDIST in problems with a fixed number of tests or trials, when the outcomes of any trial are only success or failure,
when trials are independent, and when the probability of success is constant throughout the experiment.
For example, BINOMDIST can calculate the probability that two of the next three babies born are male.
BINOMDIST (number_s, trials, probability_s, cumulative)
Number_s is the number of successes in trials.
Trials is the number of independent trials.
Probability_s is the probability of success on each trial.
Cumulative is a logical value that determines the form of the function.
If Cumulative is TRUE, then BINOMDIST returns the cumulative distribution function,
the probability of at most number_s successes.
If Cumulative is FALSE, then BINOMDIST returns the probability mass function,
the probability of exactly number_s successes.
Determine the probability that the state exit poll MoE is exceeded in at least N states.
The probability that at least N states would exceed the MoE (non-success) is equal to
1 - the probability that at most N-1 states would fall within the MoE (a success).
P = .025 (1 in 40) is the probability of a given state vote exceeding the MoE.
Therefore the probability that at most N-1 states fall within the MoE is:
Prob = BINOMDIST (N-1, 50, P, TRUE)
N = 16 states exceeded the MoE in favor of Bush.
CALCULATE THE PROBABILITY:
Enter the number of states outside the MoE: 16
Prob (16) = 1- BINOMDIST (15, 50, 0.025, TRUE)
The probability is 5.24E-14 or 1 in 19,083,049,268,519
Final NEP, 1:25pm, 13660 respondents
(Matched to recorded vote count)
ELECTION INCIDENT REPORTING SYSTEM (EIRS)
LINKS TO STATISTICAL AND PROBABILITY TOPICS