To get a feeling for whether Obama or McCain will be elected, the Electoral College system makes it clear that state-wide polls are more informative than national polls. Nevertheless, it is hard to keep all of the state-wide numbers in mind and it is very convenient to see the current trend by paying attention to the national polls. But this dichotomy raises a critical question: How good or bad is the agreement between the two ways of assessing the election?
To answer this question, I have made the following assumptions:
- The relative weighting of the different states is determined by their populations. Specifically, I have used estimated population numbers from the Information Please Almanac for 2007; the link is: http://www.infoplease.com/...
- The use of populations for weighting is equivalent to assuming that the fraction of voters in each state is the same. Clearly, this is wrong in detail for a variety of reasons, but it is by far the simplest model.
- The current fraction of the populations in each state that will vote for McCain or Obama is given by the polling averages for that state in the Real Clear Politics tables. Some states (for instance, Hawaii) have not been polled often or recently because there is little doubt about how the state will decide. In such cases, I took the most recent poll as the best estimate of what is happening. For Washington, DC I did not find a good number so I assumed that 75% would vote for Obama and 25% for McCain. The rather small size of the population of DC means, however, that little error will be introduced.
- The formula for calculating the fractional vote for each candidate is:
sum(cand_pct_in_state*state_pop)/sum(state_pop).
In other words, you multiply the percentage from the RCP table in a state times the state population, sum these values over all states and then divide by the total population of the US.
- Bottom line. When you do all of this, you find that Obama is likely (right now) to get 49.7% of the vote and McCain is likely to get 43.5%. These numbers are reassuringly close to the current average of national polls from RCP of 50.0 and 44.0. In other words, the overall state-wide and national estimates are in excellent agreement and the distribution by state for the electoral college greatly favors Obama.