Log in

View Full Version : 7/15 Election Model PROBABILITY MATH: MONTE CARLO, NORMDIST AND THREE-CARD MONTE



TruthIsAll
07-16-2008, 05:27 AM
2008 Election Model
A Monte Carlo Electoral Vote Simulation

TruthIsAll

Updated: July 15

http://www.geocities.com/electionmodel/2008ElectionModel.htm

Assuming that Obama will win 60% of the undecided vote, then based on the latest state polls, the Election Model projects that he will win 54.8% of the two-party vote with 420 electoral votes - if the election is fraud-free and held today. With 55% of the undecided voters, he will have 54.0% with 393 electoral votes. Since Obama won all 5000 Monte Carlo simulation election trials, his electoral vote win probability is 100%.

Based on the latest 5 national polls average projection (including just-released NYT/CBS and ABC polls), he would win 53.92% of the popular vote.

One might ask “What are you smoking? Nothing is 100%”. Well, based on the results of 5000 Monte Carlo simulation trials, the win probability is 100%. Current poll-based forecast models which give McCain more than a 3% win probability are mathematically incorrect. By inflating McCain’s win probability, they unintentionally provide potential cover for another stolen election.

Of course, the probabilities will change daily as the state polls change.This is the relationship between the aggregate state 2-party vote share and the Monte Carlo EV win probability:
Aggregate share 50.2 50.9 51.7 52.5 53.2
Win Probability 69.2 93.1 99.1 99.9 100.0

The bottom line is this: Fifty state polls and 5 national polls confirm that Obama is leading by 54-46% with an increasing trend over the past six weeks. The Law of Large Numbers (LLN) is in effect. The more polls, the more samples, the greater the confidence that the sample mean is close to the True Mean. So if we accept what the LLN is telling us: with 54% of the two-party vote, Obama is an absolute 100% lock to win the Electoral Vote.

How is the “win probability” calculated? Is it based on the electoral vote or the popular vote? The Election Model calculates it both ways. And the probabilities match – an outcome which not only confirms both methods but is also intuitively satisfying. The calculations are based on a Monte Carlo simulation (for the electoral vote) and normal distribution (for the popular vote).

State Model Win Probabilities
Why is the Monte Carlo (MC) simulation method used to calculate the expected (mean) EV and the electoral vote win probability? For several reasons:
1) Unlike academic election models which attempt to forecast the popular vote based on a regression analysis using economic and political time-series months in advance of the election, MC determines the probability of winning the electoral vote based on the latest polls right up to the election, 2) MC uses individual state win probabilities, as opposed to the simple win-no win scenarios in media-created election models, 3) MC is a powerful tool for analyzing complicated systems when analytical solutions are impractical or impossible.

Obama and McCain can both either win OR lose a competitive state. In each MC election trial, the winner is determined by a random process based on state win probabilities which are in turn determined by the latest poll. For example, assume that Obama is projected to win Florida’s 27 EV with 51% of the popular vote (based on the latest polls). Many electoral vote calculators would simply add the 27 EV to the Obama column to determine his projected electoral vote total. But this is an over-simplification; McCain has a 31% probability of winning Florida based on his 49% vote share; Obama has 69%.

In each of 5000 election trials, Obama’s 69% probability is compared to a random number (RND) between zero and one. If the RND is less or equal to 0.69, Obama wins Florida’s 27 EV; otherwise McCain wins. The comparison test is applied in all the states. The winner of the election trial is the candidate who has at least 270 EV. The electoral vote win probability is simply the number of winning election trials divided by 5000. Since Obama won all 5000 election trials, his win probability is 100%.

The Popular Vote win probability (for any given state as well as the national aggregate) is calculated by the Excel normal distribution function. We will show that Obama’s popular vote win probability closely matches his Monte Carlo EV win probability. Obama’s projected two-party vote share and the polls standard deviation (Stdev) are the only required inputs. The MoE (margin of error) =1.96* Stdev and therefore MoE/1.96 is the calculated Stdev in the Excel function.

Obama’s projected base case (60% UVA) vote share is V=54.79%. Assuming a 2.0% polling MoE, his popular vote win probability is 100%.
The Excel function is: = NORMDIST (54.79%, 50%, 2.0%/1.96, true)
Assuming a 3.0% MoE, the probability is 99.9%

For the 50% UVA projection scenario, V=53.25%; the win probability is 99.9% (2.0% MoE).Assuming a 3.0% MoE, the probability is 98.3%

National Model Win Probabilities
The National Model calculates the moving average projection based on 5 national polls. The base case 60% UVA scenario is assumed. The model provides a further confirmation of the State Model probabilities. The normal distribution function calculates win probabilities for all the moving averages using the MoE of the latest poll.

For example, the latest Gallup poll (2637 sample) has a 1.91% MoE. Based on the 53.92% moving average projection, there is a 99.997% probability that Obama will win the popular vote: 99.997% = NORMDIST (53.92%, 50%, 1.91%/1.96, true)

Election Fraud
In a true democracy, this would be a slam dunk for Obama.
McCain supports the most unpopular president in history with 25% approval.

But there’s a catch: It’s called Election Fraud.
The Democratic True Vote is always greater than the Recorded Vote.
A massive voter registration and GOTV effort is required to overcome the fraud.
Approximately 3-4 million of Obama’s votes will be uncounted.

Repeat a lie often enough and it becomes conventional wisdom. But that’s to be expected. Although the media commissioned the exit polls which indicated that Kerry won by 5%, they don’t question the mathematically impossible Final Exit Poll which was forced to match a corrupt vote count. Bush won the corrupt Recorded vote but lost the True vote. Past is Prologue. It would be foolish to assume a fraud-free election.

That’s why the Election Model now includes a fraud scenario analysis. Even assuming that 4% of total votes cast will be uncounted, McCain would need at least 10% of Obama’s votes switched to his column to win. In 2004 approximately 3% of all votes cast were uncounted. Bush stole 8.0% of Kerry’s votes (analysis below) to obtain his 3.0 million vote “mandate”.

Zogby was correct in 2004 when he projected that Kerry would win. Unfortunately, Bush won a rigged recorded vote. Kerry won the True Vote, but like Three-Card Monte, what you see is not what you get. Election forecasters and complicit media pundits who projected a Bush win avoid discussing the overwhelming evidence that the election was stolen. On the contrary, a complicit media relentlessly promotes the fictional propaganda that Bush won TWO elections.

This is a summary of where things stand today (view the polling detail at the bottom screen):


2008 Election Model
TruthIsAll
Updated: 7/15/08


Last State National State National Monte Carlo Simulation
Update Poll 5-poll 2-party 2-party Expected
7/15/08 Wtd Avg Average Projection Projection Electoral Vote

Obama 45.53 47.20 54.79 53.92 420
McCain 39.03 42.00 45.21 46.08 118

Sensitivity Analysis
Undecided voter allocation scenario
Obama 50% 55% 60% 65% 70%

State model: Projected aggregate vote share
Obama 53.25 54.02 54.79 55.56 56.34
McCain 46.75 45.98 45.21 44.44 43.66

MoE Probability Obama wins popular vote (NORMDIST)
2.0% 99.9 100.0 100.00 100.0 100.0
3.0% 98.3 99.6 99.91 100.0 100.0

Monte Carlo Probability Obama wins electoral vote
Trial Wins 5000 5000 5000 5000 5000
Probability 100.0 100.0 100.00 100.00 100.0

Obama Electoral Vote
Average 366 393 419 444 464
Median 364 392 420 446 468

Maximum 451 473 486 503 506
Minimum 284 319 345 360 373

95% Confidence Limits
Upper 411 442 469 491 503
Lower 321 344 369 398 426

States Won 31 34 35 40 41




2008 Election Fraud Scenario Analysis

The Election Model has been updated to include two key fraud variable factors: uncounted votes (net of votes padded) and switched votes. Historical evidence shows that over 75% of uncounted ballots are found in heavily Democratic minority precincts. These critical factors are never included in election forecasting models which permeate the media and the internet. In fact, there is no mention of fraud from professional pollsters, political forecasters in academia, media pundits or liberal bloggers on their web sites. But it’s understandable. No one wants to bite the hand that feeds them. Why should any of these interested parties discuss fraud when Democratic politicians won’t? Unlike impeachment, the dirty little secret of election fraud has always been off the table in Congress.

The base case projection assumes zero fraud. But if 4% of total votes cast are uncounted, McCain would need at least 10% of Obama’s votes switched to his column in order to win. This could be done by rigging strategically selected touch screens, optical scanners, punched cards, levers and central tabulators. Is it just a coincidence that Karl Rove is advising McCain?

The Election Model calculates projected vote shares and the electoral vote over a range of 36 uncounted and switched vote scenarios. The scenarios range from the True Vote (zero votes uncounted, zero switched) to Massive Fraud (5%, 10%). For simplicity, the model assumes that the scenarios apply equally in each state - admittedly an unrealistic assumption. But it provides a good approximation of the impact on the projected electoral vote and popular vote share.

In 2004, Bush won by an official 3.0m vote margin (62-59m). The official recorded vote was 122.3m. According to the 2004 Census, 125.7m votes were cast. Therefore, approximately 3.4m votes (2.74%) were uncounted. Historical evidence shows that the vast majority (75%) of uncounted ballots are found in heavily Democratic minority precincts. After the uncounted ballots are added to the official vote, the margin is reduced to 1.4m (62.9-61.5m). The 2004 Election Calculator Model (see below) determined that Kerry won by 66.9-57.1 million. Therefore, simple arithmetic shows that approximately 5.4m votes (8.0%) must have been switched from Kerry to Bush. Note that in Florida, Ohio and several other states, total votes recorded exceeded votes cast (vote padding exceeded vote suppression). Most states had more vote suppression than vote padding; the net difference was the number of uncounted votes.


2008 Election Calculator

This model projects Obama will win the True Vote by 71-59m (54 - 45%).
It is based on 2004 recorded and uncounted votes, mortality and 2004 voter turnout in 2008.
The True Vote is calculated using slightly modified 2004 NEP vote shares.




Voted Est. 2008 Calculated True Vote
in 2004 Turnout Votes Mix Obama McCain Other
DNV - 17.2 13.1% 59% 40% 1%
Kerry 95% 60.5 46.2% 89% 10% 1%
Bush 95% 51.6 39.4% 11% 88% 1%
Other 95% 1.6 1.2% 70% 11% 19%

Total 113.7 130.9 100% 54.1% 44.7% 1.2%
130.9 70.8 58.5 1.6



Calculation of Win Probabilities

Electoral Vote - based on a 5000 election trial Monte Carlo simulation:
The EV win probability is the number of winning election trials/5000.
The expected electoral vote is the average of the 5000 election trials.

Popular Vote I - based on the State aggregate vote share projection:
The win probability is calculated using the Excel normal distribution function.
It is calculated for both a 2% and 3% margin of error (MoE).
If Obama’s projected vote share =V, his popular vote win probability is calculated by
the Excel formula: = NORMDIST (V, .50, .02/1.96, true) assuming a 2% MoE.

Popular Vote II - based on the average vote share projection using the latest 5 National polls:
The win probability is calculated using the Excel normal distribution function.
The Excel formula: = NORMDIST (V, .50, .02/1.96, true).

Obama’s win probability in each state is also calculated by the normal distribution.
The probabilities are based on 4% margin of error and the projected state vote share.
For example, assume that Obama is tied with McCain in the latest polls at 45%.
With 60% of the undecided vote, he is projected to win the 2-party vote by 51-49%.
His probability of winning is 69%: =NORMDIST (.51, .50, .04/1.96, TRUE)


2004 Election Model Review

On Election Day 2004, Bush had a 48% approval rating.
The Final 2004 Election Model projected that Kerry would win 337-201 EV with 51.8%.
Preliminary State and National exit polls also indicated that Kerry won.
Bush was the official winner by 50.7- 48.3% with 286 EV.
And the Final National Exit poll was forced to match the fraudulent recorded vote.
Final state and national polls/projections are shown below.

The model produced a startling confirmation of the state and national models.
In the base case scenario, Kerry was assumed to win 75% of the undecided vote.
The Monte Carlo simulation determined that he would win 337 electoral votes.
Both models projected Kerry the winner with 51.8% of the two-party vote.
The final 5 national poll average projection was 51.8%.
The final 18 national poll average projection was 51.6%.

The Election Model projections were based on state and national Pre-election polls.
Kerry’s projected vote share was within 2.0% of his exit poll share in 23 states.
The 12:22am Preliminary National Exit Poll indicated that Kerry won by 51 – 48%.

Exit Pollsters Edison-Mitofsky released their 2004 Evaluation report in Jan. 2005.
E-M discussed polling methodology and provided summary statistics by state, region and voting method.Within Precinct Error (WPE) is the average deviation between unadjusted exit poll and recorded vote. It is more appropriate to call the difference a Within Precinct Discrepancy (WPD).

Kerry won the unadjusted (WPD) aggregate state exit poll by 52.0-47.0% (average of three measures).

The WPD exceeded 6% in 25 states for Bush and none for Kerry (equivalent to exceeding a 3% MoE);
exceeded 4% in 34 states for Bush and just 2 for Kerry (equivalent to exceeding a 2% MoE);
was less than 2% in 8 heavily Republican states (AR, ID, IN, KS, KY, MT, OK and TN);
was less than 2% in just one Democratic state (OR) the only state which votes 100% by paper ballot.

The 1:25pm FINAL National Exit Poll indicated that Kerry lost by 48 - 51%.
All FINAL National Exit Polls are 'forced' to match the Recorded Vote.
The 'forcing' of the 2004 Exit Poll numbers resulted in IMPOSSIBLE demographics.

Either the state and national Pre-election and Exit Polls were wrong or the Recorded Vote was fraudulent.

2004 Registered Voter (RV) vs. Likely Voter (LV) Polls
The national pre-election RV polls were closer to the True Vote than likely voter LV polls.
The LV polls, after adjustments, matched the RVs – and the unadjusted exit polls.

The 2004 Election Calculator Model applied 12:22am NEP vote shares to returning and new voters.
Kerry won a 67-57 million landslide, 53.2 - 45.4%.




Voted Est. 2004 Calculated True Vote
2000 Turnout Votes Mix Kerry Bush Other
DNV - 25.6 20.4% 57% 41% 2%
Gore 95% 49.7 39.5% 91% 8% 1%
Bush 95% 46.6 37.1% 10% 90% 0%
Other 95% 3.8 3.0% 64% 17% 19%

Total 100.1 125.7 100.0% 53.2% 45.4% 1.4%
Votes Cast 125.7 66.9 57.1 1.7

Recorded Vote share 48.3% 50.7% 1.0%
Recorded Vote 122.3 59.0 62.0 1.2

Unadjusted Exit Poll 52.0% 47.0% 1.0%
Deviation from True Vote -1.2% +1.6% -0.4%




Election Forecasting Methodology

Two basic methods are used to forecast presidential elections:
1) Vote share projections based on the latest state and national polls

In the Election Model, state and national projections are based on the latest polls.
Both state and national models allocate undecided voters to project the two-party vote.
The state model uses Monte Carlo simulation to determine the expected electoral vote.
The Election Model assumes the election is held on the latest poll date.

2) Projections based on historical time-series data (regression models).
These models forecast vote-share only and are usually executed months in advance of the election.

Monte Carlo Electoral Vote Simulation Overview
The objective is to calculate the expected electoral vote and win probability.
The win probability for each state is calculated based on the current projection.

For each of 5000 election trials, the winner of a state is determined as follows:
Obama’s state win probability (from 0 to 1) is compared to a random number (RND) from 0 to 1.
If his win probability exceeds the RND, Obama wins the state EV, otherwise McCain wins.

The winner of the election trial is the candidate who has at least 270 electoral votes.
The EV win probability is simply the number of winning election trials divided by 5000.