ELECTION 2008:

BOILING DOWN THE HUNDREDS OF POLLS INTO GRASPABLE

ESTIMATES OF WHO'S LIKELY TO WIN THE U.S. PRESIDENCY

Alan Reifman, Ph.D.,

Professor, Human Development & Family Studies

For this talk, I put on my methodologist-statistician and political-

observer hats. The Electoral College system of U.S. presidential

elections means that, in reality, we have to watch 50 separate state

elections (plus D.C.), rather than a single federal election. Further, there

are approximately 20 polling outfits (often working on behalf of a

newspaper or television station) that release pre-election surveys, with

great frequency. In a close election year (as this November's contest

appears to be), therefore, even highly motivated citizens may have a

difficult time aggregating the large volume of polls into a graspable

estimate of who is likely to win the election. Fortunately, a number of

polling-analysis websites have sprung up, each of which applies some

type of statistical analysis to distill the collection of polls into probability

estimates of each candidate winning. Other sites present graphical

representations of trends, which also serve to simplify the

information. Such approaches -- which I will discuss -- include

converting poll results into win probabilities for each candidate;

computer simulations; and local (loess or lowess) regression.

Department of Mathematics & Statistics, Texas Tech University, September 10, 2008

http://en.wikipedia.org/wiki/Image:US_Electoral_College_Map.PNG

• Each state’s EV’s = No. of U.S. House seats (based on pop’n) + 2 U.S. Senate Seats

• All states (except NE & ME) winner-take-all; even if candidate narrowly wins state’s

popular vote, he or she still gets 100% of state’s EV’s

• Need 270 Electoral Votes to win the presidency

Many states are overwhelmingly D

or R leaning and thus not contest-

ed (see dark blue and red below),

but the remaining states are

competitive to varying degrees

The Electoral College System

http://www.electoral-vote.com/

In Each of the “Swing” States, Many Polls Are Taken,

Requiring Some Type of Within-State Aggregation (“Meta-Analysis”)

• Simple Averaging (Arithmetic Mean): http://www.realclearpolitics.com/

• Weighted Average: http://www.fivethirtyeight.com/

Typical Poll

Report Format

Smith…….53%

Jones……47%

Margin of Error

+/- 3%(which includes

possibility the race

is really 50/50)

Based on Ayres, Super Crunchers, pp. 202-204

True value of parameter will be

within point estimate +/- MoE,

with 95% confidence

Normal curve from: http://www.gseis.ucla.edu/courses/ed230a2/notes/z1.html

5350 56

Extra 2.5% on this side

would also indicate winning;

hence Smith would have…

97.5% probability

of winning, hardly a

“statistical dead-heat”

http://www.washingtonmonthly.com/archives/individual/2004_08/004536.php

Which is consistent with…

http://politicalarithmetik.blogspot.com/2006/11/from-poll-margin-to-wins-polls-as.html

A More Empirical Approach

State-by-State Candidate Win Percentages Can Then Be Used

to Conduct Simulations of the Overall Election

As a simplified example, suppose our best estimate is that Obama has a

60% probability of winning a given state and McCain has a 40% probability…

1

60

61

100

OBAMA

“WINS”

McCAIN

“WINS”

HAVE COMPUTER

GENERATE A

RANDOM

NUMBER

BETWEEN

1-100

ONE “ELECTION”

CONSISTS OF A

SIMULATION FOR

EVERY STATE;

THOUSANDS OF

ELECTIONS CAN

BE SIMULATED

http://www.fivethirtyeight.com/ 10,000 simulations per day

http://hominidviews.com/ 100,000 simulations per day

Thanks to Peter Westfall for bringing this to my attention

LOcally Estimated Scatterplot Smoothing (LOESS) Regression

http://www.pollster.com/faq/map_faq.php

http://www.fivethirtyeight.com/2008/06/we-know-more-than-we-think-big-change-2.html

http://en.wikipedia.org/wiki/Local_regression

“

”

*

*Also LOWESS,

with W for Weighted

http://n-steps.tetratech-ffx.com/PDF&otherFiles/stat_anal_tools/LOESS_final.pdf

http://election.princeton.edu/

Other Useful Websites

http://stochasticdemocracy.blogspot.com/

http://election-projection.net/

(not to be confused with http://www.electionprojection.com)

Scroll down to “Probability of Win by State,” then click on color bars

Also see: http://election-projection.net/mathematics.html

Postscript