Guest Pollster | March 14, 2008
Topics: Barack Obama , Hillary Clinton , John McCain , Karl Sigman , Robert Erikson , SurveyUSA
(Today's Guest Pollster's contribution comes from Professors Robert S. Erikson and Karl Sigman of Columbia University.)
In late February, SurveyUSA interviewed 600 registered voters in every state for a total of 30,000 interviews, ascertaining preferences in a McCain-Obama and a McCain-Clinton race. The focus was a new set of electoral maps of red and blue states based on who led each state in the survey. Based on who won each state in the SurveyUSA survey, Obama defeats McCain 280 to 258 while Clinton defeats McCain 276 to 262 in the Electoral College.
Of course SurveyUSA's mammoth undertaking at best presents a snapshot of the states at one point in time. And even if all the niceties of polling were perfectly met, the allocation of states as "red" or "blue" is problematic due to sampling error. Here, we take the analysis of the SurveyUSA 50 state polls one step further. Rather than assign states based on who leads in the state surveys, we assign states probabilistically to the Democratic or Republican candidate based on the SurveyUSA state polls. Then, based on these probabilistic estimates, we ask the question, given the SurveyUSA results, what are odds of an Obama or Clinton victory in the Electoral College?
To do this, we conducted one million simulations (in MATLAB) of the Obama-McCain contest and then one million more simulations of the Clinton-McCain matchup. In each case we assume that the state estimates were correct except for sampling error. Using sampling theory and the assumption of simple random sampling, we draw one million estimates of the vote for each state. In each case we draw from a normal distribution with the observed mean (percent Democratic vs. percent Republican) and the standard deviation determined by the number of respondents in the state reporting a preference (always slightly under 600).
What do our results show? First, we pooled the state polls to ascertain the national vote, weighing each state's percent in proportion to the size of its House delegation. We also assign the District of Columbia as a 436th district and assign each Democratic candidate 85 percent of the vote to McCain's 15 percent. With these assumptions, the national popular "vote" is tight as of late February. Obama wins 51.5 percent versus McCain's 48.5 percent. Clinton also wins by an even razor thin margin, 50.7 to 49.3. With 30,000 cases, both estimates are statistically significant. McCain would be in the actual popular vote lead less than one time in 20.
That being said, our simulations yield a 88% chance of Obama beating McCain (with 306 Electoral College votes on average versus 233 for McCain), and a 74% chance of Hillary beating McCain (with 285 Electoral College votes on average versus 253 for McCain). About one percent of our simulated outcomes were Electoral College ties. (We ignored within-state variation in Maine and Nebraska, which divide their electoral votes by district.)
On the one hand, we find the expected numbers of electoral votes (the average from the simulations) for Obama or Clinton to be slightly higher than SurveyUSA reports. On the other hand, there is sufficient variance in the outcomes, so that McCain wins a nontrivial portion of the simulations, even with Obama as the opponent. Our two million simulations remind us that the popular vote winner is not always the Electoral College winner, although probably due mainly to chance -- the lottery aspect of the Electoral College -- and not any identifiable partisan bias in the 2008 Electoral College.
We thank Linda Liu for her technical assistance.