*Predictions for the 2008 United States Presidential Election: A Bayesian Approach*

(Last Updated Using Final State Polling Data)

#### Background and Motivation

The results from the 2000 and 2004 United States Presidential Election suggested that it can be difficult to predict the winner of the presidential election based on popular vote. In fact, it is possible that the popular vote and the electoral college vote can lead to significantly different results.

This web site provides up-to-the-minute estimates for the probability that the two presidential candidates (Senator Barack Obama (D-IL) and Senator John McCain (R-AZ)) win the election, the expected number of Electoral College votes for each candidate, and the probability that each candidate will win 300 or more Electoral College votes.

#### Technical Analysis and Assumptions

The mathematical model employs Bayesian estimators that use available state poll results (at present, this is being taken from Rasmussen, Survey USA, and Quinipac, among others) to determine the probability that each candidate will win each of the states. These state-by-state probabilities are then used in a dynamic programming algorithm to determine a probability distribution for the number of Electoral College votes that each candidate will win in the 2008 presidential election.

#### Swing Scenarios:

1) Undecided voters can have a significant role on the outcome of the election. In fact, they are likely to be the ultimate deciders of who will win this election. To address this source of error, five different scenarios are considered:

Neutral Scenario : The prior distribution of the Bayesian estimators for undecided voters are split 48%-48%-4% between Senator Obama, Senator McCain, and the independent candidates, in all states.

Strong Democrat Swing Scenario : 10% of undecided voters are assumed to vote for Senator Obama, with the remaining 90% of the undecided voters split 48%-48%-4% between Senator Obama, Senator McCain, and the independent candidates, in all states.

Mild Democrat Swing Scenario : 5% of undecided voters are assumed to vote for Senator Obama, with the remaining 95% of the undecided voters split 48%-48%-4% between Senator Obama, Senator McCain, and the independent candidates, in all states.

Strong Republican Swing Scenario : 10% of undecided voters are assumed to vote for Senator McCain, with the remaining 90% of the undecided voters split 48%-48%-4% between Senator Obama, Senator McCain, and the independent candidates, in all states.

Mild Republican Swing Scenario : 5% of undecided voters are assumed to vote for Senator McCain, with the remaining 95% of the undecided voters split 48%-48%-4% between Senator Obama, Senator McCain, and the independent candidates, in all states.

Each of these scenarios is considered individually. The Neutral Scenario provides an unbiased handling of undecided voters. The Strong Democrat and Republican Swing Scenarios provide two extreme envelopes around which the results obtained can be judged and evaluated. The Mild Democrat and Republican Swing Scenarios provide realistic possibilities if late breaking information surfaces that shift voter preferences.

2) Polls show figures that are for likely voters, as opposed to registered voters. If a greater number of registered voters show up to vote on November 4, this means that the poll numbers may not be representative of the actual voters.

3) Maine and Nebraska split their electoral college votes (4 and 5, respectively) based on their congressional districts. At present, these two states are treated like every other state (all or nothing).

#### Limitations of Results

The results presented are a direct function of the quality of the state poll data being used. Any biases in this data can lead to misleading and false results, and hence, invalid conclusions. The results of this analysis have been obtained as part of an academic, educational exercise to demonstrate the power of statistics and operations research to analyze data of significant importance and practical interest.

#### Election Result Predictions (if the Election was held Today)

The following histograms represent the frequency distribution for the Electoral College vote totals resulting from the mathematical model using a weighting of several polling data, if the election was held today. The poll weights are based on the age of the poll, with more recent polls given greater weight and older polls given less weight. Note that since polls often focus on likely voters, then if a larger number of registered voters show up to vote, that are not considered likely voters, then the poll numbers may not be representative of the actual voters.

#### Neutral Scenario

If the election was held today, there is a probability that Senator Obama would win the election, he would be expected to win Electoral College votes, and there is a probability that he will win more than 300 Electoral College votes.

**Figure 1: **Distribution of Electoral College Votes for Senator Obama under Neutral Scenario

If the election was held today, there is a probability that Senator McCain would win the election, he would be expected to win Electoral College votes, and there is a probability that he will win more than 300 Electoral College votes.

**Figure 2: **Distribution of Electoral College Votes for Senator McCain under Neutral Scenario

#### Strong Democrat Swing Scenario

If the election was held today, there is a probability that Senator Obama would win the election, he would be expected to win Electoral College votes, and there is a probability that he will win more than 300 Electoral College votes.

**Figure 3: **Distribution of Electoral College Votes for Senator Obama under Strong Democrat Swing Scenario

If the election was held today, there is a probability that Senator McCain would win the election, he would be expected to win Electoral College votes, and there is a probability that he will win more than 300 Electoral College votes.

**Figure 4: **Distribution of Electoral College Votes for Senator McCain under Strong Democrat Swing Scenario

#### Mild Democrat Swing Scenario

If the election was held today, there is a probability that Senator Obama would win the election, he would be expected to win Electoral College votes, and there is a probability that he will win more than 300 Electoral College votes.

**Figure 5: **Distribution of Electoral College Votes for Senator Obama under Mild Democrat Swing Scenario

If the election was held today, there is a probability that Senator McCain would win the election, he would be expected to win Electoral College votes, and there is a probability that he will win more than 300 Electoral College votes.

**Figure 6: **Distribution of Electoral College Votes for Senator McCain under Mild Democrat Swing Scenario

#### Strong Republican Swing Scenario

**Figure 7: **Distribution of Electoral College Votes for Senator Obama under Strong Republican Swing Scenario

**Figure 8: **Distribution of Electoral College Votes for Senator McCain under Strong Republican Swing Scenario

#### Mild Republican Swing Scenario

**Figure 9: **Distribution of Electoral College Votes for Senator Obama under Mild Republican Swing Scenario

**Figure 10: **Distribution of Electoral College Votes for Senator McCain under Mild Republican Swing Scenario

#### Possibilities of a Tie

There are numerous combinations of states that can lead to a tie (269 Electoral College votes for both candidates). However, only a small fraction of such combinations are likely to occur.

These results will be regularly updated as new poll data becomes available.