Thursday, July 3, 2008

Return on Investment

Our continuously-updated list of Tipping Point States -- recently represented with a snazzy new map -- tells you which states are most likely to determine the outcome of this year's election. As described in the FAQ:

'Tipping Point States' are those states that tip the outcome of the election from one candidate to the other. In each simulation run, the states are lined up from best to worst for each candidate. The states are marked off sequentially until the candidate reaches 270 electroal votes. The state responsible for putting the candidate over the top to 270 electoral votes is the tipping point state for that simulation run.
Naturally, Tipping Point States are usually going to be those associated with large electoral vote counts. It's much more likely that a state like Pennsylvania, which has 21 electoral votes, will make the difference between winning and losing the election than something like Montana, which has 3. The goal of the Tipping Point States metric is to balance which states are closest to the median of the electorate with the value of each state in the Electoral College -- and it generally comes up with pretty intuitive results.

However, it is not necessarily the case that the states with the highest Tipping Point number will represent the best return on investment for the candidate. While Pennsylvania is more likely to swing the election than Montana, it is also many times more expensive. Of course, a campaign will still want to invest more in Pennsylvania than it does in Montana in the aggregate. But which state is better on a dollar-per-dollar basis?

To get at this, what we can do is divide a state's Tipping Point percentage by its population (more specifically, it's eligible voter population). What this implicitly assumes is that the expense of competing in a state is proportional to its eligible voter population. Strictly speaking, this is not true, especially when it comes to television buys, where there are a lot of idiosyncrasies related to the geography of different TV markets (something I'll be writing more about in the near future). But it's a reasonably safe and neutral assumption for our purposes here.

This calculation produces a ratio, whose value is meaningless in the abstract, but which can be compared to the ratio in the country as a whole (in other words, we're taking the ratio of the ratios). The ratio figures, for instance, that a dollar spent in Pennsylvania is about 3.5 times more likely to influence the outcome of the election than one spent in the nation as a whole. This is what we call the "Return on Investment Index". Which states have the highest ROIs?



The top state is New Mexico, which produces an ROI almost 6 times higher than the nation at large. Why New Mexico? We project it to be very close to the median of the electorate. Right now, we are predicting a 2.7-point victory for Barack Obama in New Mexico, versus a 3.7-point victory in the national popular vote. Strictly speaking, the states that deserve the most attention are not those that are closest at any given moment, but rather those that are closest to the national average. If, say, Barack Obama has built a 12-point lead in August, you will probably start to see some weird things like Mississippi being a toss-up. But that doesn't mean the Obama campaign should at that point begin to invest heavily in Mississippi, because the only time the decision to invest in an individual state matters is when the election is close. If that hypothetical 12-point lead in August reverted back to a 1-point lead in October -- the only contingency that matters, it is very likely that Mississippi would no longer be one of the closer states. Likewise, even though Obama has a "safe" lead in Pennsylvania now, he cannot stop campaigning there (nor can McCain), because if the election tightens, Pennsylvania is liable to be within a couple of points.

The other small advantage in an investment in New Mexico is that small states have more electoral votes per eligible voter: New Mexico offers one electoral vote for every 274,000 eligible voters, whereas Pennsylvania offers one per 449,000.

Overall, the map suggests a slightly more defensive-minded resource allocation strategy than the one that the Obama campaign is employing currently. It doesn't look like states like Oregon and Iowa are going to be all that close now, for instance, but it also doesn't look like the election is going to be all that close; if the polls tighten, they may be vulnerable. At the same time, the calculation validates the Obama campaign's decision to put resources into states like North Dakota (which ranks 10th by this metric), Montana (14th) and Alaska (17th). By contrast, Florida ranks just 25th. It's running about 6 points behind Obama's national averages, and it's extremely expensive to compete in.

79 comments

Anonymous said...

TYPO:Tipping Point States' are those states that tip the election of the outcome. . .

Did you intend to write "flip the election outcome . . . " (not "election of the outcome")

Anonymous said...

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Sugerfunk said...

I just wanted to make a point about demographic/regional reactions. If Obama loses some of his lead -- say 3 points -- it seems unlikely to me that he loses 3 points equally everywhere. Maybe a position on offshore drilling (just an example) could irritate people in the South (say even up to 8% of them) but lose no support on the Northeast and West coasts. Couldn't this create a 3-point drop that is not felt equally everywhere? In fact, couldn't his national poll numbers be weakened but his support could actually strengthen in a place like Oregon? I guess I have my doubts over the equal distribution of the support that puts him over the top in national votes. Maybe some of his support in certain regions is "softer" than other regions.

P.S I don't see any porn ads on this site -- I don't know what that previous commenter was talking about.

obsessed said...

Great post! All the details on Tipping Point states will be greatly appreciated by many, especially myself.

QUESTION: Why is it that smaller states get more EVs per capita? Will the census correct that or is it inherently build into the system?

obsessed said...

I don't see any porn ads on this site

Maybe the guy meant "candidate X".

This whole site is top quality porn for us political junkies!

Nate said...

Sugar,

Actually, another new change that's coming online is that we are going to have a specific estimate of the variance/volatility of the polling in each state. So something like New Hampshire, where the polls have moved a lot, will have a larger range of possible outcomes associated with it than somewhere like Oregon, where they haven't.

Sugerfunk said...

QUESTION: Why is it that smaller states get more EVs per capita? Will the census correct that or is it inherently build into the system?

I can answer this one. It is built into the system. It was originally designed to protect agricultural and rural interests from the "tyranny" of the majority -- city slickers :-). It is the same reason every state gets 2 Senators regardless of population.

The number of electoral votes for each state is actually determined by the number of Representatives in the House + the number of Senators. That's why every state has a minimum of 3. The only other place that gets electoral votes is D.C. which also gets 3 via the 23rd Amendment to the Constitution.

JeffC said...

This is awesome. It totally quantifies a concept I had thought about several times without being able to quantify.

A couple comments to previous posters:

1. If he drops, does he drop equally across the board. Theoretically, no but I believe practically yes. I don't think that there will be that much more regional variation for changes, some states have Rep. tilt others have Dem. If he drops nationally by 3, I think he might drop by 1.5 in some states and 4.5 in others, but I don't see many issues that could cause serious collapse.

2. EV is based on total congresspeople. Senators + Reps. Reps are based on population. Sens aren't. CA might have 53 times VT's population. That means it gets 53 reps to VT's 1. Since they both have 2 sens, VT gets a much higher EV proportion.

judas_priest said...

Obsessed:

It's inherent in the system. Each state's EVs are the sum of its number of representatives + the number of senators (2). If state A has 1 representative and State B, with 20 times, the population, gets 20, they get 3 and 22 EV's respectively.

Modeler said...

Very cool. This is basically a measure of how much impact voters in a given state will have on the election. It's the degree to which the electoral college makes voters in some states more important than others.

The reason the ranking looks more defensive is because Obama is currently favored; as you mention, this ranking favors states that are near the middle of the electorate, which are always more "safe" for the leading candidate. I'm a little surprised Missouri doesn't rank higher.

Nate, it's great to see you're adding the per-state variance. You could use this to develop another ROI metric in terms of EV / resource. A simple approach would be to assume that X resources spent in a state of population P shifts the mean expected outcome proportional to X/P. You could then figure out the optimal allocation of resources to maximize the number of expected electoral votes. This analysis would focus more on "Toss-up" states, and provide an indication of how to get the most EVs out of these states. My guess is that this metric is similar to the one used by the Obama campaign, which is why their resource allocation appears to be a little more agressive.

PS -- I see no porn ads on this site. If you are, you should probably check your computer for adware/virus infections.

JeffC said...

I know you said you'd get to this later, but I would be curious to see something that included this + cost of media/voter in a state.

For example, reaching NH voters often means buying Boston TV time. Its extremely expensive and 90% of the people you are talking to don't live in a swing state. ND TV is absurdly cheap. If you can calculate it like that, it might be better to spend a $1 in ND than NH even if ND has a lower ROI

Mike J. said...

It might be very interesting for these purposes to see the states that set off your 'recount' scenarios (in which a state is decisive and closer that .5%). For purposes of figuring out the most cost-effective way to campaign, you might also consider substituting some absolute number of votes (say 30,000) for the percentage. Though Pennsylvania media is more expensive that Montana media, it's not obviously more expensive on a per-viewer basis.

If you could figure out the states that are most likely to be decisive and within 30,000 votes, you could answer the question of what state you would campaign in, if you could change 15,000 votes by campaigning in that state. That seems like a useful question to me.

Randall said...

Another way of phrasing the relative value metric, which may produce different answers from your 'tipping point' approach, is 'what is the relative probability that a single vote (or a hundred votes) flipped in this state would flip the election's outcome?' That seems like the most unambiguous definition of the value of a vote in a state.

I've done some calculations from this premise, trying to quantify how much the electoral college slants things toward swing states, and the results were surprising. You're in a good position to take a crack at the same calculations; you might try that.

Anonymous said...

I hope you include that graphic as a standard graphic in your right-side frame???

Sugerfunk said...

Nate,

That's really cool that you are planning the variance/volatility statistics. One thing perhaps to keep in mind -- it might make sense to use the weight of the different pollsters (without the date) as a factor because some polls may show a "wild" swing due to poor methodology and/or small sample size.

But you were probably planning to do that already. :-)