On Tuesday, November 3rd, 2020, citizens of the United States will be heading to the polls to elect their President, and the Republican incumbent Donald Trump is facing a monumental challenge from the Democratic nominee, Joe Biden. With just a little over a month to the elections, pollsters and pundits are on overdrive, analysing the data that is coming in daily. So too are the analysts engaged by each campaigner to evaluate the chances of success and provide strategic guidance to their team.
Electoral systems vary significantly across countries. And the one followed in the US, when compared with other major democracies around the world, is among the easiest to understand. This year, there are only two candidates on the ballot, representing the two major parties. So, we can think of the Presidential electoral process as a two-person game, played out over the vast map of the US. The President is elected not based on the nationwide popular vote, but on who wins the ‘electoral college’. This, in turn, consists of a total of 538 electors apportioned to 50 states and the District of Columbia (D.C.). California, the largest state in the US, has the maximum number of electors (55), while 6 states and D.C. have the least number of electors (3). The game is similar to a winner-take-all, meaning that the candidate who wins the popular vote in any state wins all the electoral votes of that state. The candidate who wins 270 electoral votes becomes the President.
It is as simple as this, but for one complication, which typically doesn’t affect the overall outcome. Indeed 48 out of the 50 states and the District of Columbia allocate all its electoral college votes to the candidate who wins the popular vote. However, the two states of Maine and Nebraska split their electoral college votes according to the popular vote and the plurality of votes in each of the state’s congressional district. Going by current projections, Biden is expected to win all the electoral votes in Maine, while Trump is almost certain to win in the Republican stronghold of Nebraska.
When statisticians calculate a candidate’s chances of winning the Presidency, they rely upon polling data from individual states to quantify the candidate’s chances of winning each state and, subsequently, use these state-wide numbers to calculate the candidate’s overall probability of winning the electoral college. Thus, national polls reflecting each candidate’s share of the popular vote, while more reliable in terms of statistical errors than state polls, do not necessarily reflect the probability of winning the presidency. It’s precisely this volatility in the state polls that played a part in the predictions going awry in 2016. The national polls were quite accurate in predicting the share of the popular vote in 2016, which Hilary Clinton won by about 2 percentage points, but the state-wide polls, especially in some key Democratic-leaning states like Pennsylvania and Michigan, failed to capture the movement towards Trump. Statistical estimates currently place Biden’s odds of winning at 3:1 over Trump, but a Trump win is not unlikely — his chances are roughly the same as getting two heads in two tosses of a coin.
What makes the US elections even simpler to follow is that one does not need to keep track of polls and the numbers in all 50 states. This is because several states are already etched deeply in favour of one of the two parties. By all present indications, there are 19 states and the District of Columbia, with a combined worth of 229 electoral college votes, which firmly support Biden, while 22 states amounting to 170 electoral college votes heavily favour Trump.
Let’s assume that these trends hold. This means, effectively, the election this year will be determined by 9 states, carrying a total of 139 electoral college votes that could swing in favour of either party. These toss-ups, often referred to as “swing” or battleground states, are Florida, Pennsylvania, Ohio, Michigan, Georgia, North Carolina, Arizona, Wisconsin and New Hampshire. While Michigan, Pennsylvania and Arizona have been polling very favourably for Biden throughout the summer, these states were carried by Trump four years ago, and there may still be enough volatility among voters to justify their remaining as toss-ups. Likewise, states like Georgia and North Carolina may be leaning slightly towards Trump, but there is enough uncertainty surrounding their poll numbers to place them as toss-ups. With these 9 states at play, there are a total of 512 distinct paths to the White House. Of these, 446 paths lead to a victory for Biden, 62 result in a win for Trump and 4 yield a tied outcome where both candidates split the electoral college equally (269 electoral votes each).
Mathematically, then, Biden has about 7 times as many paths to the White House as does Trump. That might seem like the game’s up already, but that’s not quite how it works. What matters is the electoral college votes. In the current scenario, Biden needs 41 points and Trump needs 64 points to win. Biden is ahead, but not by that much and a few crucial states can still make all the difference.
Take Michigan and Pennsylvania that carry 36 electoral votes between them and have agreed on their candidate in every Presidential election since 1980. The importance of these two states to a Biden victory cannot be undermined. At least one of these two states feature in 358 of the 446 paths to Biden’s victory. If Biden wins these two states, he will be just 6 electoral votes short of the Presidency, and Trump can beat him only if he wins all the remaining 7 states. Interestingly, Michigan and Pennsylvania have not just been polling consistently in favour of Biden throughout the summer, but have consistently voted Democratic since 1992, until Trump upended this trend in 2016. If Biden wins these two states, then he needs to win only one of the 7 states to win the Presidency. On the other hand, Trump cannot afford to lose any of the 7 states, which seems a tall order right now, but it is worth remembering that he won all of those 7 states in 2016. If he retains these 7 states, while losing Michigan and Pennsylvania, he will still be the next President.
Among the various other possible scenarios, here’s a fascinating prospect. Let’s suppose that Biden wins Michigan, Pennsylvania and New Hampshire and Trump wins the remaining 6 states. We then have an electoral college tie. And in the event of a tie, the election goes to the House of Representatives, where each state delegation has one vote. Here, the Republicans hold a slight edge in the current numbers, although this can also change with the upcoming elections, where, along with the President, citizens will be voting to elect a number of their state representatives.
Going by the polls, or the number of paths leading to the Presidency, this election appears to currently heavily favour Biden. However, with three upcoming Presidential debates and the nomination of a new supreme court justice, there is still ample time for movement in the polls and the race could shift in either direction. The early evening of November 3rd in the US will provide enough hints at how the night will play out. Victories for Biden in Michigan and Pennsylvania will point towards a big night for the Democrats on November 3rd, while close races in those states with Trump retaining most of the states he won in 2016 could spell a repeat of 2016 for the President.
The author is Professor and Chair of the UCLA Department of Biostatistics.