### Presidential Election

Pollsters and pundits from both sides of the political spectrum agree that the presidential race is too close to call. Voter preference in many toss-up states keeps fluctuating daily between President Bush and Senator Kerry within the polling margin of error. Given this uncertainty, how useful are predictions that rely only on the raw percentages in favor of each candidate and ignore the statistical margin of error? How does one make a prediction about the overall outcome that takes into consideration (a) the limited sample size used in most polls, and (b) the sampling error of the poll itself?

Using data from 2.004k.com as reported by Andrea Moro (who also has links to other probabilistic prediction websites), I have developed a simulation-based prediction of the outcome of the presidential election. Here is how my model works:

- I first allocate undecided voters to either the incumbent or the challenger on a state-by-state basis.

- Then, for each state, I simulate the likely percentage of Kerry votes assuming it follows a normal distribution with (a) mean based on the poll results plus undecided allocation and (b) standard deviation based on the polling error.

- The winner for each state is allocated all of the state's electoral votes.

- The results are tallied for 5000 simulations to provide the average electoral votes for Kerry and also the probability of Kerry winning more than 270 electoral votes.

SCENARIO | Kerry electoral votes | Kerry win probability |

Undecided voters split between
Kerry and Bush | 260 | 25.72 |

Undecided voters favor Kerry 2:1 | 295 | 87.84 |

Scroll down for a graph showing the projected distribution of Kerry's electoral votes for these two scenarios. The blue bars denote the outcomes corresponding to a Kerry victory. It's fascinating to note how sensitive the predictions are to assumptions regarding the behavior of undecided voters. I will keep updating the table and the figures on a daily basis, time permitting.

Until then, 10-4.

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