By J. F. Kolacinski,
and B. Payne
Elmira College
We start with a couple of comments, addressing some questions or comments posted last week.
We continue to use the RCP Average where it’s available or the most recent state poll where it isn’t, but we’re still using historical data for a lot of states (specifically the average of the results of the last four presidential elections in that state). Specifically we are still using historical data in Alaska, Arkansas, Delaware, DC, Hawaii, Idaho, Kansas, Kentucky, Mississippi, Montana, Nebraska, Nevada, New Mexico, North Dakota, Oklahoma, Oregon, Rhode Island, South Carolina, South Dakota, Tennessee, Texas, Vermont, Washington and Wyoming. Most of these states are either reliably red or reliably blue so they probably aren’t skewing our estimates very much, but it will be interesting to see what we get as we start to see data from these states. And of course, our estimates should improve.
Flerzo is correct that there are known relationships between how the polls change in different states although the simulator assumes the states are operating independently. That will introduce some inaccuracy into the results but, I suspect (hope) it is small. Those interdependencies should be accounted for at least partially in the poll numbers themselves. However, if I were to undertake a significant rewrite of the Maple program we’re using, I’d prioritize work on separating out the individual congressional districts in Nebraska and Maine and to add in the ability to consider more candidates.
The colors on the map are determined (essentially) by poll numbers rather than by the probability that a candidate will win a state. If a candidate is polling at 55%, the probability that he or she will win the state is quite a bit better than that. I’ll take that up, time permitting, in a later entry.
Polling Updates:
The national polling data again looks to be moving in Sec. Clinton’s direction. The Real Clear Politics Average, currently has Clinton 46.4% and Trump at 39.6%, a margin of 6.8%. That’s an entire percentage point wider than it was last week.
We have updated information in 9 states.
The first polls from Colorado and Maine are have been added. In Colorado, the polling looks very similar to the historical average so there’s very little change there. The polling looks slightly better for the Republicans than the historical data in Maine. The state shifts from solidly democratic to weakly democratic but that’s in actuality a shift from just above the cut-off to just below it.
Polls look better for Mr. Trump in North Carolina and Pennsylvania. The shift is tiny in North Carolina. Pennsylvania shifts from weakly democratic to toss-up based on two recent polls showing Trump leading there.
The RCP Average has shifted toward Sec. Clinton in five states: Wisconsin, Arizona, Florida, Virginia and Ohio. The shift in Wisconsin is tiny. The changes in the other states are somewhat larger. Florida and Virginia shift from toss-ups to weakly democratic while Ohio and Arizona remain toss-ups.
If we add up the electoral votes in the “solidly democratic” and “weakly democratic” categories we get 279 EV, nine more than are needed for victory.
Probability Estimate:
As usual, we estimate our probabilities by simulating a number of state-by-state national elections using the “U.S. Presidential Election Calculator” which can be found here:
< www.maplesoft.com/...>. This application runs on Maple, a professional-grade mathematics program.
Data was taken from www.realclearpolitics.com (retrieved 27 June 2016). The RCP Average was used when one was available. Otherwise the most recent poll was used. Where no polling data was available, we took the average of the last 4 presidential elections.
Poll data was adjusted to eliminate the possibility that a third-party candidate could win the race using the following formula:
% for Candidate A/(% for Candidate A + % for Candidate B).
One thousand simulated elections were run.
Clinton won 99.6% of the time, while Trump won 0.4% of the time. None of the simulations were ties. This is not a significant change from last week.
The mean electoral result was:
Clinton: 325.4 EV
Trump 212.6 EV.
That’s roughly half an electoral-vote better for Mr. Trump on average.
Some Notes on the Map
This week’s map is generated by the same process as last week’s. In a state, based on the RCP Average, the conditional probability that a voter chooses Clinton assuming he or she chooses either Clinton or Trump is given by:
P(Clinton|Clinton or Trump) = % for Clinton/(% for Clinton + % for Trump)
The key for the map is as follows:
Solidly Democratic (Dark Blue) 100% > P(Clinton|Clinton or Trump) > 55%
Weakly Democratic (Light Blue) 55% > P(Clinton|Clinton or Trump) > 52%
Toss-Up (Gray) 52% > P(Clinton|Clinton or Trump) > 48%
Weakly Republican (Light Red) 52% < P(Trump|Clinton or Trump) < 55%
Solidly Republican (Dark Red) 55% < P(Trump |Clinton or Trump) < 100%