Why Electoral College bands are not created equal

 

State	2008 lead      Â	Poll average      Â	Elec College Votes  Â	Cumulative ECV
Nevada	12.5	5	6	243
Wisconsin	13.9	3.5	10	253
New Hampshire	9.6	3.5	4	257
Ohio	4.6	1.8	18	275
Iowa	9.5	1	6	281
Colorado	9	1	9	290
Virginia	6.3	1	13	303
Florida	2.8	1	29	332
North Carolina	0.3	-1	15	347
Missouri	-0.1	-6.3	10	357
Montana	-2.4	-9	3	360
Indiana	1	-16	11	371

 

We can think about the US presidential election by considering three factors: the national swing away from or towards Obama since 2008, the predictable state-specific shifts (either to be added to or subtracted from the national swing in individual states since 2008), and a random jiggle to be applied to the vote shares in individual states, to take account of unknown state-specific factors and pure chance.

We can estimate the state-specific shifts, i.e. the extent to which a given state will buck the national swing because of known demographic and economic factors, by looking at state polls.

The table shows some key parameters for the battleground states. The second column shows the lead Obama achieved over McCain in 2008; if there were no state-specific shifts and no jiggle, we could predict whether Obama would win a given state in November simply by applying the expected national swing to the 2008 figures.

But we can do better than that: the third column shows the latest average poll figures from Real Clear Politics, which gives us an estimate of the effect of state-specific shift. (You could equally use Nate Silver’s predicted leads for each state to do this analysis).

The table is ranked in order of decreasing Obama poll lead in each state. Let’s start by making two simplifying assumptions: first that the individual state polls correctly capture state-specific shift since 2008, and secondly that there’s no random jiggle. With those assumptions, the result in a given state would depend only on whether the national swing at the election differs from the national swing that polls are showing.

Using RCP’s averages, the central forecast is that Obama will win all the states in the table down to and including Florida (this is the RCP ‘No Toss-Ups’ map). That would give him 332 Electoral College votes; see the last column, which shows the cumulative total EC votes down to and including a specific state in the table, assuming Obama wins all the easier states such as Pennsylvania as well.

Now consider what happens if Obama does a bit better that the polls currently show. To win the next state on the list, North Carolina, he would need to do at least 1% better, taking him to 347 EC votes. This is still within the 330-349 band in Ladbrokes’ Electoral College Votes market. Then things remain stable as we increase the national lead further; Obama remains stuck at 347 EC votes until we assume he is doing 6.3% better, when Missouri falls to him, taking us into the next band with 357 EC votes.

Now look at what happens if Obama does a bit worse nationally than the polls currently suggest. If his lead is just 1% worse, he might fail to win Florida, taking him down to 303 EC votes. However, at that 1% drop in support he’s also at risk of losing Colorado, Virginia and Iowa as well, potentially taking him down to 281 EC votes.

Thus, whilst the 330-349 band covers a chunky -0.9% to +6.2% change in Obama’s assumed national lead, the 310-329 band is unlikely to be a winner because it only happens if he wins Florida but loses Colorado, Iowa, and/or Virginia (but not all three of those)

The 330-349 band is therefore substantially more likely than the 310-329 band, and, in general, the probability distribution of EC votes is non-symmetrical.

Of course to do a full analysis we need to add in a bit of ‘jiggle’, to take account of the fact that the states might not fall neatly in the order we are expecting, and consider the correlation between shifts in different states. Luckily, Nate Silver at fivethirtyeight.com does all this work for you.

Every time he updates his model, he publishes an Electoral Vote Distribution bar chart, showing his estimated probabilities for given numbers of EC votes. It is a very uneven distribution indeed, with big peaks at exactly 332 (currently 8% probability) 347 (6%), and 303 (5%).

No doubt forecasts will shift around right up to Nov 6th, but, if you’re betting on the EC bands, this is an invaluable resource for figuring out which bands are created more equal than others.

Richard Nabavi is a long standing contributor to PB.