I made some updates to my State Election Map! The most obvious one is including the 2020 data, just in time for the Electoral College vote today. But wait, there’s more!

Each year now includes:

**Tipping point state**– this is the “decisive” state that provides the Electoral College win. More specifically, I use FiveThirtyEight’s definition, which is to sort every state by the election winner’s margin, and add up electoral votes until they get to 270. (with one exception, see note below about Maine/Nebraska) If you subtract this state’s margin from the overall national popular vote you can calculate the electoral college split. This is one way to look at how close the election was.**Closest state (by percentage)**– Simply the state that was closest to a tie. (by percentage and not raw votes)**Minimum number of additional losing-party votes so the losing-party would have won**: If you had a magic wand and could conjure up votes for the losing party to make them win, in what states would you add those votes to have to conjure up the minimum number possible? This is another measure of how close the election was; for example, in 1976 Carter won 297-241, and the tipping point state was Wisconsin which was D+1.7%, but a mere 18,490 more Republican votes in Ohio and Hawaii(!) would have let Ford win, which is extremely close.**Graph of how each state changed since the last election**: This data was already available on a per-state basis (by clicking on the state), but seeing it on a per-year basis can show some interesting trends.

Note about Maine and Nebraska – these states are alone in allocating their electoral votes per congressional district, which is an irritant for visualizations like these 🙂 (and why I hadn’t wanted to add electoral vote data before) My solution was lazy, simple, and only a little wrong: I show the correct EV total for each election, but for the rest of the EV calculations ignore the split votes.

Some interesting observations of the data:

- I added the “minimum number of votes to change the result” metric because I remember hearing that about Trump’s win in 2016 – if Clinton had gotten just 77,000 or so more votes in Michigan, Pennsylvania, and Wisconsin, she would have won, which is much closer than the 306-232 electoral vote victory. Which is true! But it turns out that by this metric, Biden’s win in 2020 was even closer – he had the same 306-232 electoral vote victory, but only
**~76,000**more votes would have made Trump win. In this case it was across 4 states instead of 3, which I guess makes it a little more unlikely. - The split between the popular vote and tipping point state, which was just under 3% in 2016 and talked about a lot, increased to almost
**4%**in 2020, which is pretty scary! Part of the problem is that Pennsylvania and Wisconsin got a little more Republican-leaning relative to the popular vote. (although Michigan became a little more Democratic-leaning) - You can compare the 2020 election to 2016 and get an idea of which states disliked Clinton the most. Obviously this isn’t an exact science, but the clear winner to me, to my surprise, is
**Vermont**! It’s the state with the biggest D shift from 2016 to 2020 (+9.0%), and it doesn’t seem to be because the state is generally trending Democratic. (like Colorado, which had the second highest D shift) Conveniently, the third highest D shift was in Delaware, Biden’s home state. - The new graph makes it clear how much Utahns didn’t like Trump – the shift from 2012 (when, admittedly, Romney was running) to 2016 was
**D+30%**! That’s the biggest shift between elections since Hawaii moved D+36.5% between 2004 and 2008. I think there’s research showing that home state effects are larger if your state is smaller, which these seem to be consistent with.

The “minimum number of votes to change the result” calculation turned out to be more interesting than I thought. (I’m going to assume that an R won the election for the sake of concreteness) At first I thought it would be a simple matter of taking the closest state that the R won by percentage, add however many votes it takes to make the D win, and repeat with the next closest state until the overall result changes. But there are two reasons this won’t work:

- You might end up adding unnecessary votes. If the R won the electoral votes 280-258, and the closest state the R won had 3 EV, and the next closest state the R won had 12 EV, there’s no need to flip the votes in the 3 EV state – the 12 EV state is sufficient by itself!
- Since a state’s EVs aren’t exactly proportional to its population (much less the number of people who voted), just looking at the closest states by percentage may not be the right order to look at things.

After thinking about this a little, it sounded a lot like a 0-1 knapsack problem, but not quite. The knapsack problem means you’re picking some things to add to a knapsack that can only hold a certain number of pounds, and you want to maximize the value of the items. In this case, we’re trying to pick states so that their “weight” (EVs) is greater than a certain value instead of less than, and we’re trying to minimize the “value” (number of votes to flip) instead of maximize.

I thought about trying to use negative weights and values to turn this into the knapsack problem, but I couldn’t get it to work out. Eventually I realized that we could flip it around – look for the states to keep in the R’s column that have at most 268 EVs, and maximize the votes the R has, which is exactly the same as what we want.

The knapsack problem is NP-complete, and I was worried it would be slow to run, and also I love Rust now (see my Rust posts), so I decided to calculate it offline and just load the results in the UI. I found an example implementation of the knapsack problem in Rust and adapted it for my use (see my implementation here). It turns out with a maximum weight of 268 and only at most 50 states, the whole algorithm runs in less than a second, so this might have been overkill. But it was fun!

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