Thursday, October 25, 2012

Election Model: Independence

Someone asked a great question on this post today: why does my "most likely winning electoral vote total" for Barack Obama include him winning Florida, where he's currently an underdog? Shouldn't any map where Obama wins Florida be a little less likely than the same map just with Florida flipped?"

As I was writing up the answer I thought "actually this could be it's own short post." And I wanted to use a picture, so here we are.

The short answer is state outcomes cannot be considered independent from each other, they are interrelated and the model treats them that way. If Obama wins VA and CO, that tells us something about his chances of winning FL or NH or NC.

There be math yonder.

The question:

I believe I am not understanding the statistics behind the "most likely winning EV total". I assume this means E [ EV | Obama wins ]. 

To get to the answer in your model (332), Obama has to win VA, CO and FL. For this to be the most likely winning EV total, it would have to be the case that among the following events:
1. Obama wins VA, CO, FL
2. Obama wins 1 or 2 of these states
3. Obama wins none of these states (i.e., OH decides it)
Event #1 is the most likely.

But using the probabilities in your model,
P(VA, CO, FL) = 0.172592
P(VA, CO, not FL) = 0.202608

Doesn't that make 303 more likely than 332 (i.e., FL in the Romney column)?

State outcomes aren't independent. The model simulates a national outcome then simulates state outcomes relative to it. This allows for state to state variation and recognizes national trends (like we saw following Romney's debate one victory). If the president is winning VA and CO that means he's also more likely to be winning FL.

This example makes for a great illustration of why models which do assume state independence are making mistakes. I ran your two scenarios through the model and came up with the following:

Notice how Obama is much more likely to win FL if he wins CO and VA. I don't mean to imply a causal relationship (winning VA will help him win FL) just a correlation (if he's wins VA and CO then he must have done well and probably won FL too).

The reason 'Obama wins everything blue + the tossups' is his most likely winning total is in simulations where he does well on election night, and wins all the states he's favored in, the President will also be a favorite to win the toss-up states too

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