Coming up Trumps

Okay, time to quickly run out the major international race: the US presidential election. This year due to time constraints we will not be analyzing the House or Senate races except to note that 24 of the 34 Senate seats for election are currently held by Democrats or Democrat-caucusing Independents, which means they have more to lose and less room to expand; this is a tough senate year for Democrats.

First Pass

Fortunately, we have polling for most electoral college (EC) races, as shown below. The exceptions are Alabama (9 EC votes), DC (3), Hawaii (4), Idaho (4), Illinois (19), Kentucky (8), Louisiana (8) and Mississippi (6); in all of these races the lack of polling seems to stem from these being such strong foregone conclusions, that in the table below they are treated as having polled 100% for their likely candidate (entries in italics).

Race	EC Seats	Harris Lead
Alabama	9	-100.0
Alaska	3	-8.0
Arizona	11	-1.6
Arkansas	6	-15.0
California	54	23.0
Colorado	10	12.0
Connecticut	7	16.0
Delaware	3	18.5
DC	3	100.0
Florida	30	-6.5
Georgia	16	-1.2
Hawaii	4	100.0
Idaho	4	-100.0
Illinois	19	100.0
Indiana	11	-16.5
Iowa	6	-4.3
Kansas	6	-5.0
Kentucky	8	-100.0
Louisiana	8	-100.0
Maine	2	8.6
M1	1	22.7
M2	1	-6.0
Maryland	10	28.3
Massachusetts	11	27.7
Michigan	15	1.5
Minnesota	10	6.3
Mississippi	6	-100.0
Missouri	10	-11.5
Montana	4	-18.0
Nebraska	2	-15.0
N1	1	-6.0
N2	1	10.0
N3	1	-48.0
Nevada	6	-0.6
New Hampshire	4	5.0
New Jersey	14	16.0
New Mexico	5	6.4
New York	28	18.5
North Carolina	16	-1.2
North Dakota	3	-27.0
Ohio	17	-6.8
Oklahoma	7	-16.0
Oregon	8	12.0
Pennsylvania	19	-0.1
Rhode Island	4	14.0
South Carolina	9	-11.7
South Dakota	3	-26.5
Tennessee	11	-21.0
Texas	40	-7.4
Utah	6	-25.5
Vermont	3	32.0
Virginia	13	8.8
Washington	12	20.6
West Virginia	4	-27.0
Wisconsin	10	0.8
Wyoming	3	-38.5

On these counts Trump wins with 287 electoral college votes to Harris’ 251.

Second Pass

However, seven of these races (Arizona – 11 EC votes, Georgia - 16, Michigan -15, Nevada – 6, North Carolina – 16, Pennsylvania – 19 and Wisconsin – 10) have a candidate leading by less than 2 percentage points (the next closest race is Iowa where Trump leads by 4.3 pp). These seven races are considered the battle ground seats that will win the election. Without these Trump has 219 EC votes and Harris leads with 226.

Obviously, with 7 races in play there are 2^7 = 128 possible combinations of outcomes in these seats. However, the number of paths to victory can be cut down from this (e.g. both candidates can win by winning every state, but both candidates can also win by winning every state but Nevada. Treating both of these as separate scenarios is redundant, when we can just ignore Nevada completely).

There are 20 distinct paths to victory for Harris, who needs 44 further EC votes. Some of these far more probable than others:

1. Pennsylvania, Georgia and North Carolina (51 EC votes);
2. Pennsylvania, Georgia and Michigan (50);
3. Pennsylvania, Georgia and Arizona (46);
4. Pennsylvania, Georgia and Wisconsin (45);
5. Pennsylvania, North Carolina and Michigan (50);
6. Pennsylvania, North Carolina and Arizona (46);
7. Pennsylvania, North Carolina and Wisconsin (45);
8. Pennsylvania, Michigan and Arizona (45);
9. Pennsylvania, Michigan and Wisconsin (44);
10. Pennsylvania, Arizona, Wisconsin and Nevada (46);
11. Georgia, North Carolina and Michigan (47);
12. Georgia, North Carolina, Arizona and Wisconsin (53);
13. Georgia, North Carolina, Arizona and Nevada (49);
14. Georgia, North Carolina, Wisconsin and Nevada (48);
15. Georgia, Michigan, Arizona and Wisconsin (53);
16. Georgia, Michigan, Arizona and Nevada (48);
17. Georgia, Michigan, Wisconsin and Nevada (47);
18. North Carolina, Michigan, Arizona and Wisconsin (53);
19. North Carolina, Michigan, Arizona and Nevada (48); and
20. North Carolina, Michigan, Wisconsin and Nevada (47).

Notably, half of these only require 3 of the 7 battle grounds. There are 21 paths to victory for Trump, but all-bar-one require a constellation of 4 states, and Pennsylvania is essential for all but 6 of these:

1. Pennsylvania, Georgia and North Carolina (51);
2. Pennsylvania, Georgia, Michigan and Arizona (61);
3. Pennsylvania, Georgia, Michigan and Wisconsin (60);
4. Pennsylvania, Georgia, Michigan and Nevada (56);
5. Pennsylvania, Georgia, Arizona and Wisconsin (56);
6. Pennsylvania, Georgia, Arizona and Nevada (52);
7. Pennsylvania, Georgia, Wisconsin and Nevada (51);
8. Pennsylvania, North Carolina, Michigan and Arizona (61);
9. Pennsylvania, North Carolina, Michigan and Wisconsin (60);
10. Pennsylvania, North Carolina, Michigan and Nevada (56);
11. Pennsylvania, North Carolina, Arizona and Wisconsin (56);
12. Pennsylvania, North Carolina, Arizona and Nevada (52);
13. Pennsylvania, North Carolina, Wisconsin and Nevada (51);
14. Pennsylvania, Michigan, Arizona and Wisconsin (55);
15. Pennsylvania, Michigan, Arizona and Nevada (52);
16. Georgia, North Carolina, Michigan and Arizona (58);
17. Georgia, North Carolina, Michigan and Wisconsin (57);
18. Georgia, North Carolina, Michigan and Nevada (53);
19. Georgia, North Carolina, Arizona and Wisconsin (53);
20. Georgia, Michigan, Arizona and Wisconsin (52); and
21. North Carolina, Michigan, Arizona and Wisconsin (52)

Harris only needs Pennsylvania for about half of her paths, but because it so severely cuts down Trumps options, and enables most of her 3-state routes, it will be an important state for both candidates.

So the question is, how easily can Harris flip the states nominally counted for Trump? That’s always hard to estimate, but we can look back on 2020 for some estimation. (We will be ignoring 2016 because of how wildly wrong the polling turned out, and all previous presidential elections because theirs was the methodology that failed in 2016).

If we compare the comparable 2020 polling with the actual 2020 results, we see bad news for Harris; only 8 of the 54 races had any movement towards the democrats relative to the polling; most polling once again underestimated Trump’s support. If that plays out again this year, it will lock in a win for Trump.

Race	Biden Lead (Polls)	Biden Lead (Results)	Difference
Alabama	-19.0	-25.5	-6.5
Alaska	-5.6	-0.1	5.5
Arizona	2.2	0.3	-1.9
Arkansas	-25.3	-27.6	-2.3
California	29.4	29.2	-0.2
Colorado	11.4	13.5	2.1
Connecticut	22.0	20.1	-1.9
Delaware	22.0	19.0	-3.0
DC	89.0	86.8	-2.3
Florida	2.7	-3.4	-6.1
Georgia	0.2	0.2	0.0
Hawaii	34.0	29.5	-4.5
Idaho	-18.0	-30.8	-12.8
Illinois	18.6	17.0	-1.6
Indiana	-9.0	-16.1	-7.1
Iowa	-1.6	-8.2	-6.6
Kansas	-8.7	-14.6	-5.9
Kentucky	-17.0	-25.9	-8.9
Louisiana	-20.5	-18.6	1.9
Maine	11.6	9.1	-2.5
M1	22.8	23.1	0.3
M2	1.2	-7.4	-8.6
Maryland	28.3	33.2	4.9
Massachusetts	36.3	33.5	-2.8
Michigan	5.5	2.8	-2.7
Minnesota	9.8	7.1	-2.7
Mississippi	-17.0	-16.6	0.4
Missouri	-7.6	-15.4	-7.8
Montana	-5.4	-16.4	-11.0
Nebraska	-12.0	-19.1	-7.1
N2	3.0	6.5	3.5
Nevada	5.0	2.4	-2.6
New Hampshire	11.0	7.4	-3.7
New Jersey	19.2	15.9	-3.3
New Mexico	13.0	10.8	-2.2
New York	28.0	23.1	-4.9
North Carolina	0.3	-1.4	-1.7
North Dakota	-20.0	-33.3	-13.3
Ohio	-0.9	-8.0	-7.1
Oklahoma	-20.0	-33.1	-13.1
Oregon	20.0	16.1	-3.9
Pennsylvania	3.7	1.2	-2.5
Rhode Island	26.0	20.8	-5.2
South Carolina	-7.0	-11.7	-4.7
South Dakota	-10.5	-26.2	-15.7
Tennessee	-9.0	-23.2	-14.2
Texas	-1.3	-5.6	-4.3
Utah	-9.5	-20.5	-11.0
Vermont	45.0	35.4	-9.6
Virginia	11.8	10.1	-1.7
Washington	22.0	19.2	-2.8
West Virginia	-17.0	-38.9	-21.9
Wisconsin	9.2	0.6	-8.6
Wyoming	-29.0	-43.4	-14.4

Can we use this to calculate the likelihood of seats flipping for Harris?

Well, the best result for Republicans in 2020 compared to the polling was West Virginia where the Democrats result fell 21.9 pp below polling. So we can imagine any seat where Harris leads with 22 or more points is effectively assured to remain in her camp. Conversely, the Democrats best result (vs polling) was in Alaska where the result was 5.5 pp better. So any seat where Harris trails by 5.5 points or more can be considered unreachable for the sake of our calculations (though in reality, anything could happen). Only 8 races (12.96% of all races with data) saw any movement to the Democrats.

At first this looked like a 3^rd order polynomial trend line would be a good fit for predictions, but when this applied to the data it’s actually not great, particularly in the range of data we are most interested in (red box).

Instead, I’ll just box the data up. As noted above, only 8 races (12.96%) saw any movement to the Democrats at all. 7.41% saw a gain over 1 pp. 5.56% saw a gain over 2 pp. So let’s round this to:

• 0 pp gain on polls = 13% probability
• 1 pp = 7.5%
• 2 pp = 5.5%

with intervening values evenly dispersed. For example, Arizona is polling with Trump at a 1.6 pp lead, so for this to go to Harris that’s given a 6.3% probability.

~15% of races in 2020 would have held leads like those in Wisconsin (0.8 pp) and Michigan’s (1.5 pp); 9 races had swings below 0.24 pp to Trump and the remaining 45 had larger than 1.61 pp. (This is actually around 16.7% of races shifting enough to erase the Democrat margins, but given the large window between 0.24 and 1.61 some sever rounding has been applied).

Now the individual probabilities of each of Harris’s paths to victory end up very small when multiplying several numbers this low. Strictly speaking, as they are not mutually exclusive, the total probability of any of these occurring is less than the sum, but even taking the sum as an upper estimate, that’s still only a 1.2% chance of Harris winning.

 

Race	Probability	Paths to Victory (Harris)
Pennsylvania	12.3%
Georgia	7.1%
North Carolina	7.1%
Michigan	15.0%
Arizona	6.3%
Wisconsin	15.0%
Nevada	8.5%
CUMULATIVE PROBABILITY:		0.1%	0.1%	0.1%	0.1%	0.1%	0.1%	0.1%	0.1%	0.3%	0.0%	0.1%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%

Now that’s what the numbers say. We’re using 2020 polling errors (which on average give Republicans a 5pp boost in any given race) to a neck-and-neck polling, so that was always going to point to a strong Trump result. I would NOT put much faith in the precise numbers here as there are so many caveats and variables to consider. But I WOULD propose that Harris has an uphill battle ahead of her today, much tougher than perhaps the reporting has indicated.

My prediction, then, is a narrow Trump victory. But it will be close.

Harris’s most likely path to victory is to win Michigan, Pennsylvania and Wisconsin, so if she does win that’s where I’d expect to see it emerge.