Transcript A More Empirical Approach State-by

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 politicalobserver 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
The Electoral College System
• 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 contested (see dark blue and red below),
but the remaining states are
competitive to varying degrees
http://en.wikipedia.org/wiki/Image:US_Electoral_College_Map.PNG
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/
True value of parameter will be
within point estimate +/- MoE,
with 95% confidence
Typical Poll
Report Format
Smith…….53%
Jones……47%
53
50
56
Margin of Error
+/- 3%
Extra 2.5% on this side
would also indicate winning;
hence Smith would have…
97.5% probability
of winning, hardly a
“statistical dead-heat”
(which includes
possibility the race
is really 50/50)
Based on Ayres, Super Crunchers, pp. 202-204
Normal curve from: http://www.gseis.ucla.edu/courses/ed230a2/notes/z1.html
Which is consistent with…
http://www.washingtonmonthly.com/archives/individual/2004_08/004536.php
A More Empirical Approach
http://politicalarithmetik.blogspot.com/2006/11/from-poll-margin-to-wins-polls-as.html
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…
HAVE COMPUTER
GENERATE A
RANDOM
NUMBER
BETWEEN
1-100
ONE “ELECTION”
CONSISTS OF A
SIMULATION FOR
EVERY STATE;
THOUSANDS OF
ELECTIONS CAN
BE SIMULATED
1
OBAMA
“WINS”
60
61
McCAIN
“WINS”
100
http://www.fivethirtyeight.com/
http://hominidviews.com/
10,000 simulations per day
100,000 simulations per day
Thanks to Peter Westfall for bringing this to my attention
LOcally Estimated Scatterplot Smoothing (LOESS) Regression*
*Also LOWESS,
with W for Weighted
“
”
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
http://n-steps.tetratech-ffx.com/PDF&otherFiles/stat_anal_tools/LOESS_final.pdf
Other Useful Websites
http://election.princeton.edu/
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
http://stochasticdemocracy.blogspot.com/