TruthIsAll
06-24-2008, 07:47 AM
The Election Model: Monte Carlo Electoral Vote Simulation
TruthIsAll
The Election Model tracks state and national polls to project the popular vote as well as the expected electoral vote and win probability. It consists of two independent models:
a) Monte Carlo Electoral Vote Simulation - calculates the expected EV and win probability using projections based on the latest state polls.
b) National Model – projects national vote shares from a moving average projection based on the latest national polls.
Based on the latest June 25 state polls, the simulation determined that if the election was held that day, Obama would win by 358-180 electoral votes with 52.8% of the 2-party vote. Since he won 4999 of 5000 simulated elections, his win probability was virtually 100%.
A caveat: the Election Model assumes that the True Vote will be the same as the official Recorded Vote. It never is. Every election is marred by a combination of uncounted and miscounted votes. That is a historical fact. Nevertheless, we continue to run our models hoping that this time the True Vote will be equal to the Recorded Vote and the election will be fraud-free.
Projecting state and national vote shares
A major advantage of national polls in projecting vote share is their relative simplicity. The poll split represents a snapshot of the total electorate. If the polling spread exceeds the margin of error (3% for a 1000 sample) then the leader has a minimum 97.5% probability of winning - assuming the poll is an unbiased sample. If three independent national polls are done on the same day, that is essentially equivalent to a single 3000 sample with a 1.8% MoE. Assuming a 52-48% split, the probability is 95% that the leader will receive 50.2-53.8%. The probability is 97.5% that his vote share will exceed 50.2%.
In the Monte Carlo model, two-party vote shares are projected for each state. The latest polls are adjusted for an assumed allocation of undecided voters. In the simulation, 5000 election trials are executed to determine the expected (average) electoral vote and win probability.
A major advantage of Monte Carlo is that the results are hardly affected by minor daily deviations in the state polls. On the other hand, electoral vote projections from media pundits and Internet bloggers use a single snapshot of the latest polls to determine a projected electoral vote split. This approach has the advantage of simplicity, but can be very misleading since it often results in wild electoral vote swings. Snapshot projections cannot provide a robust expected electoral vote split and win probability. That’s because unlike the Monte Carlo method, they fail to consider the two bedrocks of statistical analysis: The Law of Large Numbers and the Central Limit Theorem.
For example, assume that Florida's polls shift from 46-45 Obama to 46-45 McCain. This would have a major impact in the electoral vote split. On the other hand, in a Monte Carlo simulation of 5000 election trials, the change would have just a minimal effect on the expected (average) electoral vote and win probability. The 46-45 poll split means that the race is much too close to clearly project a winner; both Obama and McCain have a nearly equal chance.
Typical state polls sample 600 voters with a 4% margin of error (MoE). National polls of 1000-2000 sample size have a 2.5-3% MoE. The probability of winning a state is based on the 2-party poll split and the MoE, after adjusting for undecided voters.
Monte Carlo simulation methodology
1. The 2-party vote share is projected for each state is after allocating undecided voters. The win probability is then calculated based on the projected vote shares. For example, assuming a 50-50 projection and a 4% MoE, each candidate has a 50% probability of winning the state. For a 51-49 split, there is a 69% probability; 83% for 52-48%; 93% for 53-47; 97% for 54-46.
The MoE is 1.96 times the standard deviation, a statistical measure of volatility. The standard deviation and projected vote share are input to the normal distribution function in order to determine the probability of winning at least 50% of the two-party vote.
2. In a simulated election trial, a random number (RND) between 0 and 1 is generated for each state. The RND is compared to the probability of winning the state. The winner is determined by whichever value is higher.
For example, if the latest Oregon poll indicates that Obama has a 90% probability of winning, then if the RND is less than 0.90, Obama wins Oregon’s 7 electoral votes; if the RND is greater than .90, McCain wins. The same test is applied in each state (comparing the RND to the state win probability) determine who wins the state. The winner of this election trial is the candidate who has won least 270 EV.
3. The process is repeated 5000 times (election trials). The probability of winning the electoral vote is just simple division; it’s equal to the number of trial wins divided by 5000. The expected electoral vote for each candidate is the average of the 5000 trials.
To repeat, there are two major advantages of the simulation method:
1) minor shifts in state polls have minimal impact on the expected EV.
2) The probability of winning the electoral vote is a simple calculation: the number of election trial wins/total number of election trials.
Undecided Voter Allocation
The only assumption used in the model is the allocation of undecided/other voters. Historically, 70-80% of undecided voters break for the challenger. For example, if the race is tied at 45-45, a 60-40 split of undecided voters results in a 51-49% projected vote share. The win probability is calculated using the projected vote shares as input to the normal distribution function.
Some may disagree with the base case undecided voter allocation assumption. That's why a sensitivity analysis of five (5) scenarios of undecided voter allocation is executed to project the individual state (and aggregate) vote shares to determine the corresponding electoral vote, aggregate national vote shares and the win probability.
In summary, the Election Model projects the latest national and state polls after adjusting for the allocation of undecided voters. The probability of winning each state is calculated. A Monte Carlo simulation of 5000 election trials is executed using the individual state win probabilities to determine the expected final electoral vote and win probability. If the independent national and state projections are in close agreement, that is a strong confirmation that the models are consistent and are probably representative of the True Vote.
TruthIsAll
The Election Model tracks state and national polls to project the popular vote as well as the expected electoral vote and win probability. It consists of two independent models:
a) Monte Carlo Electoral Vote Simulation - calculates the expected EV and win probability using projections based on the latest state polls.
b) National Model – projects national vote shares from a moving average projection based on the latest national polls.
Based on the latest June 25 state polls, the simulation determined that if the election was held that day, Obama would win by 358-180 electoral votes with 52.8% of the 2-party vote. Since he won 4999 of 5000 simulated elections, his win probability was virtually 100%.
A caveat: the Election Model assumes that the True Vote will be the same as the official Recorded Vote. It never is. Every election is marred by a combination of uncounted and miscounted votes. That is a historical fact. Nevertheless, we continue to run our models hoping that this time the True Vote will be equal to the Recorded Vote and the election will be fraud-free.
Projecting state and national vote shares
A major advantage of national polls in projecting vote share is their relative simplicity. The poll split represents a snapshot of the total electorate. If the polling spread exceeds the margin of error (3% for a 1000 sample) then the leader has a minimum 97.5% probability of winning - assuming the poll is an unbiased sample. If three independent national polls are done on the same day, that is essentially equivalent to a single 3000 sample with a 1.8% MoE. Assuming a 52-48% split, the probability is 95% that the leader will receive 50.2-53.8%. The probability is 97.5% that his vote share will exceed 50.2%.
In the Monte Carlo model, two-party vote shares are projected for each state. The latest polls are adjusted for an assumed allocation of undecided voters. In the simulation, 5000 election trials are executed to determine the expected (average) electoral vote and win probability.
A major advantage of Monte Carlo is that the results are hardly affected by minor daily deviations in the state polls. On the other hand, electoral vote projections from media pundits and Internet bloggers use a single snapshot of the latest polls to determine a projected electoral vote split. This approach has the advantage of simplicity, but can be very misleading since it often results in wild electoral vote swings. Snapshot projections cannot provide a robust expected electoral vote split and win probability. That’s because unlike the Monte Carlo method, they fail to consider the two bedrocks of statistical analysis: The Law of Large Numbers and the Central Limit Theorem.
For example, assume that Florida's polls shift from 46-45 Obama to 46-45 McCain. This would have a major impact in the electoral vote split. On the other hand, in a Monte Carlo simulation of 5000 election trials, the change would have just a minimal effect on the expected (average) electoral vote and win probability. The 46-45 poll split means that the race is much too close to clearly project a winner; both Obama and McCain have a nearly equal chance.
Typical state polls sample 600 voters with a 4% margin of error (MoE). National polls of 1000-2000 sample size have a 2.5-3% MoE. The probability of winning a state is based on the 2-party poll split and the MoE, after adjusting for undecided voters.
Monte Carlo simulation methodology
1. The 2-party vote share is projected for each state is after allocating undecided voters. The win probability is then calculated based on the projected vote shares. For example, assuming a 50-50 projection and a 4% MoE, each candidate has a 50% probability of winning the state. For a 51-49 split, there is a 69% probability; 83% for 52-48%; 93% for 53-47; 97% for 54-46.
The MoE is 1.96 times the standard deviation, a statistical measure of volatility. The standard deviation and projected vote share are input to the normal distribution function in order to determine the probability of winning at least 50% of the two-party vote.
2. In a simulated election trial, a random number (RND) between 0 and 1 is generated for each state. The RND is compared to the probability of winning the state. The winner is determined by whichever value is higher.
For example, if the latest Oregon poll indicates that Obama has a 90% probability of winning, then if the RND is less than 0.90, Obama wins Oregon’s 7 electoral votes; if the RND is greater than .90, McCain wins. The same test is applied in each state (comparing the RND to the state win probability) determine who wins the state. The winner of this election trial is the candidate who has won least 270 EV.
3. The process is repeated 5000 times (election trials). The probability of winning the electoral vote is just simple division; it’s equal to the number of trial wins divided by 5000. The expected electoral vote for each candidate is the average of the 5000 trials.
To repeat, there are two major advantages of the simulation method:
1) minor shifts in state polls have minimal impact on the expected EV.
2) The probability of winning the electoral vote is a simple calculation: the number of election trial wins/total number of election trials.
Undecided Voter Allocation
The only assumption used in the model is the allocation of undecided/other voters. Historically, 70-80% of undecided voters break for the challenger. For example, if the race is tied at 45-45, a 60-40 split of undecided voters results in a 51-49% projected vote share. The win probability is calculated using the projected vote shares as input to the normal distribution function.
Some may disagree with the base case undecided voter allocation assumption. That's why a sensitivity analysis of five (5) scenarios of undecided voter allocation is executed to project the individual state (and aggregate) vote shares to determine the corresponding electoral vote, aggregate national vote shares and the win probability.
In summary, the Election Model projects the latest national and state polls after adjusting for the allocation of undecided voters. The probability of winning each state is calculated. A Monte Carlo simulation of 5000 election trials is executed using the individual state win probabilities to determine the expected final electoral vote and win probability. If the independent national and state projections are in close agreement, that is a strong confirmation that the models are consistent and are probably representative of the True Vote.