Here we are, five days removed from an election that shocked many people. Whereas many cats expected a Hillary Clinton landslide (and indeed, she won the popular vote), instead they got a decisive Trump electoral victory; by the time the smoke settles, the final electoral score will be Trump 306 – Clinton 232.

Predictably, the Clinton Cable News Network published a piece a few days back suggesting that votes for the Gary Johnson and Jill Stein, the major 3rd party candidates, likely helped Trump win. On my social media feeds, there was some anger directed at both.

In this post, I will show why that supposition is false – ’cause honestly, I’ve had enough.

First, let’s look at CNN’s hypothesis. The article alleges that votes for Johnson and Stein potentially cost Clinton four states – Florida (29 EVs), Michigan (16 EVs), Pennsylvania (20 EVs), and Wisconsin (10 EVs); for each state, CNN contends that just half of Johnson’s votes plus all of Stein’s votes give Clinton the edge in all four states – and a decisive 307-231 electoral victory.

While it is true that Clinton would’ve won if she got a sizable chunk of the 3rd-party vote, this assumes (incorrectly – and quite frankly, disingenuously) that 3rd-party votes are votes taken from the Democratic candidate. First, a quick look at several alternative scenarios.

[1. What if all Jill Stein voters voted for Clinton?]

All else equal, if all Jill voters voted for Clinton instead, two states (Michigan and Wisconsin) flip; however, Trump still wins electorally, 280-258.

[2. What if all Gary Johnson voters voted for Clinton?]

All else equal, if all Gary voters voted for Clinton instead, you get CNN’s scenario (FL, MI, PA, and WI flip and Clinton wins 307-231). Combined with scenario 1 above, this means that votes for Jill Stein did not cost Clinton the race, nor could such votes help Clinton.

[3. What if all Jill Stein voters and all Gary Johnson voters voted for Clinton?]

All else equal, with both Gary and Jill’s votes, Clinton flips Arizona in addition to the four states in scenario 2 for a 318-220 electoral edge.

Aside from Gary Johnson and Jill Stein, some states had other 3rd-party candidates on the ballot. (Amusingly, Nevada even had “none of these candidates” as an option – and that option got 3% of the vote there!) In this scenario, Clinton flips Utah in addition to AZ, FL, MI, PA, and WI for a 324-214 electoral edge.

So 3rd-party votes cost Clinton, right? Wrong!

Why?

Because, again, not all 3rd-party votes were votes taken from Clinton! So how can we estimate how many 3rd-party votes would’ve gone to Clinton (or Trump)? Let’s discuss.

[Methodology]

I took the state-by-state election results (available by simply searching “election 2016 results” on Google; interactive data are available before the first result) and exit poll data (both as of November 11th), created an Excel file, and ran some numbers.

First, for the 28 states where exit polling data were available, I recorded registered Democrat, Republican, and Independent voter proportions; then, I recorded the percentages for Clinton, Trump, Johnson, Stein, or other 3rd parties. For the remaining states, I used national exit poll data (see table below).

[Fig. 1] Exit poll data for 28 states; for the remaining 23 (indicated by the ^^ mark under the “N” column), I used national exit poll data.

The columns highlighted in light blue are results for Democrats; I used light red and light purple for results among Republicans and Independents, respectively. The “Adjusted HRC %” and “Adjusted Trump %” columns represent the estimated proportion of Clinton and Trump voters, respectively, after applying 3rd-party votes proportionally based on the following formula:

padj = p + (p * ∑ p3rd) {1}

where p is the original proportion of voters for a candidate and ∑ p3rd is the sum of the 3rd-party share for a given state. For example, among Democrats in California, exit polls show 92% of respondents voting Clinton, 5% voting Trump, and 1% each voting for Johnson, Stein, and other candidates. The adjusted proportions for Clinton and Trump, respectively, using Equation {1} are:

padj, Clinton = 0.92 + (0.92 * 0.03) = 0.9476
padj, Trump = 0.05 + (0.05 * 0.03) = 0.0515

You will notice that the two numbers do not add to 1; this is due to rounding error. Next, I calculated the weighted average of Democrat, Republican, and Independent percentages for Clinton and Trump, respectively, with this formula:

where pDpR, and pI are the proportions of Democrat, Republican, and Independent exit poll respondents, respectively, in each state, and pD-adj, pR-adj, and pI-adj are the respective proportions of Democrats, Republicans, and Independents voting either Clinton or Trump in each state after applying the 3rd-party adjustment via Equation {1}. I listed these results in the “Weighted Average HRC %” and “Weighted Average Trump %” columns.

Finally, I used these weighted averages to estimate how many 3rd-party votes would go to Clinton or Trump; those results appear in the six columns to the right of the weighted averages. You will notice some zeroes in those columns; this is because Jill Stein was not on the ballot in six states and only some states had other 3rd-party candidates on the ballot.

[Results]

After adding the respective share of 3rd-party votes to Clinton and Trump’s total, we get this result:

[Fig. 2] Results after adding proportionate share of 3rd-party votes to Clinton and Trump’s state-by-state totals.

Notice that the result is exactly the same as those of the actual election! Clinton still wins the popular vote, but Trump’s 306-232 electoral advantage stands.

Let’s take this a step further; suppose that we allocate proportionate shares of Gary Johnson’s votes to each candidate, but give Clinton all of Jill Stein’s votes. (This is a modified version of the CNN hypothesis, using a proportionate share of Gary Johnson’s votes instead of half-and-half; incidentally, the proportionate share gives Clinton a slight edge.) Let’s see what happens:

[Fig. 3] Results after modifying the table in Fig. 2 to give Clinton all of Jill Stein’s votes.

Again, Trump still wins electorally, 290-248 (Michigan flipped for Clinton in this scenario, though Trump just barely hangs on to Wisconsin). This effectively disproves the CNN hypothesis. As it turns out, for Clinton to win in this scenario, she not only needs all of Jill Stein’s votes, but all other 3rd-party votes! (Even then, her electoral lead is just 284-254; PA, UT and WI flip.)

[Discussion]

There is a widespread belief on social media that Gary Johnson/Jill Stein voters cost Clinton the election; articles such as the CNN article linked above helped stoke those fires. However, the evidence does not support that contention. While there are scenarios where Clinton could’ve won, they all involve very large shares of the 3rd-party vote; what’s more, after applying the proportionate shares in my model, the net change in votes is just under 100,000 in Clinton’s favor!

So basically, you can stop blaming Gary Johnson and Jill Stein voters for Clinton’s loss.

That said, why is Trump’s electoral advantage relatively robust? Allow me to explore a few possibilities.

Defectors

The exit poll data show that some registered Democrats voted for Trump and some registered Republicans voted for Clinton; I call these “defectors.” The exit poll data suggest there are more of the former than the latter. To see if this was true of the population, I ran a difference-of-means hypothesis test on the data using α = 0.05. Here are the results:

[Fig. 4] Results of the difference-of-means hypothesis test for defectors.

The results suggest that there is a difference between the share of “defectors” among registered Democrats and Republicans (specifically, more of the former). However, since exit poll data are only available for 28 states, I re-ran the test for just those states to check for robustness:

[Fig. 5] Results of the difference-of-means hypothesis test for defectors in states where exit poll data were available.

Suddenly, our result is different. The one-tailed p-value (used to test the alternate hypothesis of different means) is no longer significant. However, the difference-of-means hypothesis test is less reliable for smaller samples, which means this doesn’t necessarily controvert the previous result.

Independents

As expected, larger proportions of Independents voted 3rd party than did Democrats and Republicans. Interestingly, exit poll data suggest registered Independents lean Republican, with larger shares voting Trump than Clinton. This would support the hypothesis that votes for 3rd-party candidates hurt Trump more than they did Clinton. To see if Independents generally lean Republican, I ran another difference-of-means hypothesis test using α = 0.05.

[Fig. 6] Results of the difference-of-means hypothesis test for Independents.

The results strongly suggest that Independents lean Republican, further suggesting Trump received a decisively higher share of the Independent vote than Clinton. As with defectors, I re-ran the test for just those states with exit poll data available:

[Fig. 7] Results of the difference-of-means hypothesis test for independents in states where exit poll data were available.

Even here, the one-tailed p-value is on the order of 10-5, suggesting very strong evidence that Independents lean Republican.

Another nail in the Gary Johnson/Jill Stein-cost-Clinton-the-election coffin. Rather than try to cast blame on others for her loss, cats should consider that Clinton just wasn’t a good candidate for the Democrats to run against Trump.

Y’all should’ve Felt The Bern.

N.B.: You will notice asterisks next to some states in the tables above:

• One asterisk: State with less than 100% of precincts reporting as of November 12th,
• Two asterisks: For Maine, which splits its electoral votes, and
• Three asterisks: State with less than 90% of precincts reporting as of November 12th.