Tipping point and resource allocation

This post is about understanding the concept of the "tipping point" state in presidential elections and why presidential campaigns should allocate their resources based on tipping point. By the end of this post, you'll understand not only how to calculate the tipping point, but also why campaigns should allocate proportional to the tipping point.

What is the tipping point state?

The tipping point state is the state whose electoral votes push the winner over 270 electoral votes. To figure out which state does this, you sort the states by vote margin and add them up until you get to 270. The table below shows this simple running sum that gets us to the tipping point in the 2016 election:

Here we see that Wisconsin gets Clinton from 268 to to 278, which clinches the win. 

Why do we care about the tipping point state?

The reason we care about the tipping point state is that campaigns only matter in really close elections, so we want to make sure that if the election is close the campaign resources were allocated wisely. If the election is a landslide in either direction then all of the campaign resources wouldn't make a difference. 

A helpful way to think about it is to think about the election as coming down to one state like Florida in 2000 or Ohio in 2004. If Gore had won Florida (margin of ~500 votes) the outcome of the whole election would have changed. If Al Gore could have magically seen into the future, he would have moved resources from Pennsylvania (margin ~200k) into Florida in a heartbeat. This is because a few hundred votes lost in PA don't materially change the outcome of the election, but a few hundred votes gained in FL do.

How to forecast the tipping point state

To do this forecasting we're going to use really dumb math because dumb math is easy to understand and hard to break. Fancy math is hard to understand (so it can be wrong without you knowing) and easy to break (too many moving parts.) 

We'll start with the 2016 election results and add in some error. I'm going to specify two types of variation for this analysis: uniform swing and state variation. 

Uniform swing is the correlated movement across all states between the two political parties. This is to say that when things get better in Ohio they also get better in Florida and Colorado. Wave elections, which are becoming more common every cycle, are largely dominated by uniform swing. 

State variation is just random variation at the state level. This allows some freedom of movement at the state level that can either go against national trends or move with national trends.

So our 2020 forecasts look like this:

2020 forecast ~ 2016 results + uniform swing + state variation

We can do this many times to look at how frequently each state shows up as the tipping point. Here's a simple STATA script to do the trick:

gen trump_share = trump / (trump + clinton)

gen uniform_swing = runiform(-0.05, 0.05)

replace uniform_swing = uniform_swing[1]

gen state_variation = runiform(-.02, 0.02)

gen trump_adj = trump_share - uniform_swing/2 - state_variation/2

Results

I ran the script above 10k times and counted how often each state was the tipping point state. Here are the results:

State	Tipping Point
Florida	44%
Pennsylvania	18%
Wisconsin	17%
Michigan	15%
Minnesota	2%
New Hampshire	1%
North Carolina	1%
Arizona	1%
Nebraska, 2nd	< 1%
Nevada	< 1%

We see Florida is the overwhelming favorite to be the tipping point state. In fact FL is about as likely to be the tipping point state as PA, WI, and MI combined. Additionally, once we get past MI, the likelihood of being tipping point falls off a cliff with MN coming in at 2% likelihood. 

One important thing to note is that uniform swing does not affect tipping point likelihood. In a wave year for Democrats the tipping point states are exactly the same as a wave year for Republicans. To demonstrate this, here's the tipping point likelihood broken down by good years and bad years for Democrats:

State	Bad year	Good year
Florida	44%	44%
Pennsylvania	18%	19%
Wisconsin	16%	17%
Michigan	16%	14%
Minnesota	2%	2%
North Carolina	1%	1%
New Hampshire	1%	1%
Arizona	1%	1%
Nebraska, 2nd	< 1%	< 1%
Nevada	< 1%	< 1%

This is a huge deal. This means that a campaign shouldn't change its allocation strategy if national mood begins to shift-- a campaign should only change its allocation strategy if uncorrelated state-specific movement is observed.

Allocation on tipping point likelihood

So now lets get back to the idea of why a campaign should allocate proportional to tipping point likelihood. When a campaign spends resources to win votes, it is specifically trying to win the tipping point vote. Every vote after that is nice to have, but doesn't affect the outcome of the race. Since electoral votes are awarded at the state level, that means that the likelihood of winning the tipping point vote for each voter is exactly proportional to the likelihood of being in the tipping point state.

So we definitely want to win the tipping point vote in the tipping point state, but don't campaigns need to play on a broad map to make sure that they win not only the tipping point state but also all the states that contribute to 270? Allocation based solely on tipping point would tell us that CO is "safe" and that we don't need to spend any resources there. This gets back to the two types of variation that we inserted into our estimates-- uniform swing and state variation. 

We know from historical elections that movements based on national partisan preference are substantially larger than state level variations (I'll save the details for another post)-- usually by a factor of 4 or 5. This means that when a state like Colorado is close then states like FL, PA, and WI are safely being won by Republicans. And when a state like Ohio is close, Democrats are already winning in MI, NH, and AZ. Since state level variation is such a small share of the total movement, we don't have to worry as much about protecting safe states or going after states to put up a big electoral landslide.

This is all to say that if we could divine the future and perfectly forecast which state would be the tipping point, campaigns best bet would be to place all the resources in the tipping point state. Since there's uncertainty around which state is likely to be the tipping point, campaigns should allocate their resources proportional to the likelihood that the state is the tipping point-- so if Wisconsin is the tipping point state 17% of the time, a campaign should spend $17 for every $100 it raises to fund efforts to win votes in WI. This allocation strategy leads to a much more focused and narrow map than presidential campaigns usually execute. 

Other considerations for allocation

Two additional factors need to be considered when determining a holistic allocation strategy: national partisan sentiment and dynamic campaigning.

National partisan sentiment is probably the single biggest factor in determining who will win the White House. That +/-5pp swing that we baked into our sims is enormous and will explain the outcome of most elections. This means that the majority of campaign resources and brain-space should be focused on building a favorable national partisan sentiment rather than trying to win marginal votes in the tipping point state. This type of work is qualitatively different than the allocation that we're talking about and focuses more on national narrative and media strategy broadly. I'll avoid talking about what this looks like (this is the public internet, after all) but it's worth calling this out as an essential component of the campaign mix.

Dynamic campaigning refers to the idea that presidential races don't exist in a vacuum. If Republicans are campaigning in a place like MN which only has a 2% likelihood of being the tipping point state, it is absolutely worth it to compete there. This is because opposing campaigns want to keep the state variation in check-- when only one side campaigns, campaign effects can get big fast. I'll also avoid talking about this at length as well. 

Caveats on tipping point calculations

Finally, I'd like to caveat the tipping point calculations. 

The baseline estimates of support only use 2016 presidential election results. A more robust calculation would include 2018 election results and 2020 polling. 

The national and state variation estimates are illustrative and should be calculated at the state level. Some states are more likely to move with national partisan trends than others, and to appropriately estimate how much uncorrelated movement each state has should be calculated both over time and up and down the ballot.