The Political Geography of Chance

What are Joe Biden's and Donald Trump's chances to win the 2024 election?  The answers depend on their ability to win in seven "swing states" that collectively account for 93 electoral votes:  Pennsylvania (19 votes), North Carolina (16 votes), Georgia (16 votes), Michigan (15 votes), Arizona (11 votes), Wisconsin (10 votes), and Nevada (6 votes).  Setting these states aside, Biden can expect 226 votes and Trump can expect 219 votes from the “safe states.”  

The results in each of the swing states in 2020 were extremely close.  Each was decided by less than 3% of the vote, giving both candidates a realistic chance of winning any of them this year.  What follows is an a priori assessment of the candidates' chances based on two assumptions:  (1) outcomes are in doubt in only the seven swing states listed above and (2) Biden and Trump have an equal chance of winning any of them. 

With seven swing states, there are 128 possible scenarios that could produce the final Electoral College totals. These range from Biden winning all seven to Trump winning all seven and any win-loss combination between.  Among these scenarios, Biden wins in 71 and Trump wins in 57.  This gives Biden a 55% (71/128) chance of winning and Trump a 44.5% (57/128) chance.

The "coin flip" assumption I am making, giving each candidate an equal chance of winning in any particular swing state, is important.  Most prognosticators look beyond the mere logical possibilities and speculate as to why one candidate or another has a greater or lesser chance of winning in a swing state.  They look at polling results, economic conditions, concurrent ballot initiatives, campaign spending, and other factors to handicap the race.  That is, they look for reasons to reject the coin flip assumption.

This is a perfectly good enterprise, but with more than seven months until Election Day, it's hard to know how political conditions will unfold in any particular swing state.  Furthermore, any argument I have seen for or against Biden or Trump comes with noteworthy caveats.  Right now, a coin flip doesn't seem to be a bad estimate of the chances in any particular swing state.  

In any case, the coin flip assumption provides a baseline upon which we can do additional analyses.  For example, we can see how a candidate's chance of winning it all changes when we assume a victory in any one of the seven swing states.  Recall, considering only safe states, Biden's chance of winning is 55.5% and Trump's is 44.5%.  If we assume a candidate wins one swing state, the possible scenarios are reduced to 64, and his chance of winning it all increases as follows.

If Biden wins PA, his chance increases to 79.5% (51/64).
If Biden wins NC, GA, or MI, his chance increases to 72% (46/64).
If Biden wins AZ or WI, his chance increases to 65.5% (42/64).
If Biden wins NV, his chance increases to 61% (39/64).

If Trump wins PA, his chance increases to 69% (44/64).
If Trump wins NC, GA, or MI, his chance increases to 61% (39/64).
If Trump wins AZ or WI, his chance increases to 54.5% (35/64).
If Trump wins NV, his chance increases to 50% (32/64).

We can do a similar calculation assuming a candidate wins not just one swing state, but two.  Assuming a candidate wins two states, the possible scenarios are reduced to 32.  Since PA is the biggest prize, we’ll assume it is one of those two states.

If Biden wins PA and NC, GA, or MI, his chance increases to 94% (30/32).
If Biden wins PA and AZ or WI, his chance increases to 90.5% (29/32).
If Biden wins PA and NV, his chance increases to 81% (26/32).

If Trump wins PA and NC, GA, or MI, his chance increases to 87.5% (28/32).
If Trump wins PA and AZ, WI, or NV, his chance increases to 78% (25/32).

Some of the 128 possible scenarios result in very close electoral outcomes.  There are four in which a change in just one electoral vote alters the outcome.  This would bring the results in Maine and Nebraska into the calculation, because Maine and Nebraska allot some of their electors by congressional district.  

Maine Congressional District 1 and Nebraska Congressional District 2 could possibly become meaningful.  Neither district is within the 3% threshold I am using to identify swing states, but I suspect congressional districts are more volatile than whole states; so these two districts might well vote differently in 2024 than they did in 2020.  Biden lost ME-1 in 2020.  If he wins it this time, he'll win in three more scenarios among the 128.  Trump lost NE-2 in 2020.  If he wins it this time, he'll win in one more scenario.  If both districts flip this year, then they will have no combined effect on the outcome.  This suggests that the Maine and Nebraska districts have only a very small chance of coming into play, but never say never.

One final comment:  Biden and Trump normally need to win at least four swing states to win it all, but there are some scenarios  in which they will prevail by winning just three swing states:  Biden wins it all by winning PA and any one of NC, GA, MI, plus one of the remaining five big electoral vote states ( (NC, GA, MI, AZ, or WI).  He also prevails if he wins NC, GA, and MI (without PA).  This gives him 11 3-state paths to victory.  In contrast, Trump has only three 3-state paths to victory which are by winning PA and two of NC, GA, or MI.  

So the math is pretty clear:  PA is uniquely critical to the outcome of the race.  

The results in PA have been razor thin whenever Trump has been on the ballot.  In 2016, Trump won PA by 0.724% (44,292 votes).  In 2020, Biden won PA by 1.165% (80,555 votes).  Of course, much has happened since the Election Day 2020, but as we have a rematch of the same, very well-known and polarizing candidates, PA is likely to be both close and decisive.  If we want to look beyond the a priori coin flip possibilities and examine substantive reasons why one of the candidates might win it all, looking at Pennsylvania is the best place to start.