It’s testament to the intricacies of the Electoral College that there’s even any debate about who will win the United States Presidential election. Since Joe Biden announced his candidacy, the number of times that incumbent President Donald Trump has led him in the polling average is… well, precisely zero. Were this election decided on a simple plurality of the vote, then the commentariat would have confidently called this election a long time ago.

To state the obvious: this isn’t the case. The election is instead decided indirectly; voters technically back a slate of delegates pledged to vote for a candidate for the presidency. There are many inherent flaws to this system – it makes smaller states disproportionately important, it allows a very small group of voters in a few crucial states to essentially decide the election, and it can technically result in a President nobody wanted, if the delegates break ranks – but the one flaw in particular I want to focus on here is the possibility that the final tally of the delegates is 269-269 – in other words, a tie.

As it turns out, this is a reasonably difficult scenario to calculate. Making a few assumptions – namely, that there are only two candidates who win delegates, each state assigns all its delegates by the manner intended by state law, and that delegates do not go rogue and vote for a candidate they weren’t pledged to – we discover that there are an extraordinary number of possible outcomes. Accounting for the 51 delegates assigned at-large for states and territory, and the five congressional districts that independently assign their delegates (but also realising that – in the two states that split their delegation – at least one of the districts must go to one of the two candidates), we realise that there are a total of 2^54 (18,014,398,509,481,984, or around 18 quadrillion) distinct electoral college maps.

Courtesy of 270 to Win: three possible, if unlikely, ways the Electoral College could tie.

This is, to say the least, a very large number of combinations, and it would be virtually impossible to check each of these to see if they resulted in a tie. Eliminating a significant chunk of these would result in very little; even if my computer could check a billion combinations a second (which, for the record, it cannot), then it would still take half a year to complete. Instead, I resorted to using statistical methods; I ran a simulation of a billion presidential elections to see how many of them would tie.

To conduct this experiment, I assumed a very basic model: we have two candidates, Candidate A and Candidate B, and every delegate that Candidate A doesn’t win, Candidate B does. Hence I only really need to pay attention to one of their delegate counts, and if it’s 269, then I know that the other candidate must have exactly the same number. I first assumed that each candidate would win a random number of states (insofar as we can rely on computer randomness), and then picked a random selection of possible delegate numbers, totalled them, and checked if it was 269 exactly. Around sixteen hours later, the calculations finally completed: out of a 1,000,000,000 randomly-generated Electoral College combinations, 1,791,121 of them resulted in a tie (with a 99% confidence interval of between 1,787,676 and 1,794,565 ties) – hence, the probability of the Electoral College tying is only around 0.0018%.

Thank God, you may think, confident that the Electoral College will never tie. But that’s not the end of the story. Firstly, that probability is still there, no matter how small it is. Secondly, it is still a gargantuan number. 0.0018% of 254 works out to be approximately 32 trillion ways the Electoral College could tie. Thirdly, and perhaps most importantly – any given election will probably be much closer, and hence – by eliminating the possibilities that candidates will have smaller numbers of delegates – the chance of both candidates receiving the same number of delegates vastly increases. If we assume that both candidates will receive at least 200 delegates, then the probability of a tie goes up to 0.007%  (using the same methodology as above, but ignoring all combinations in which one candidate receives fewer than 200 delegates) - still a small overall chance, but four times as likely as the base case.

Courtesy of 270 to Win: one worryingly plausible way that the Electoral College could tie.

Of course, this is essentially a hypothetical question; although one can envisage some scenarios for the 2020 election in which there is a tie, none of them seem that plausible or likely to happen. But we’re here now, so let’s continue to investigate it further. What happens if there is a tie? This is where we must split up the elections of the President and the Vice President, which are (on a purely legal note) strangely independent of each other, per the 12th Amendment.

The Vice President, in this case, would be elected by the Senate, who would choose between the top two Vice Presidential candidates in the Electoral College. Per the Constitution, they would have to receive the votes of a majority of all Senators to be elected – 51 votes. Were this to happen in 2020, there’d be a huge potential for disaster – a 50-50 Democrat-Republican Senate is a relatively plausible outcome, so if every Senator voted down party lines, there would be a stalemate. Moreover, although this has never been judicially tested, the incumbent Vice President would be unlikely to be able to cast the tiebreaking vote as they would normally do in this situation, as the Constitution specifies that the candidate must receive a “majority of the whole number [of Senators]” (from the 12th Amendment); the Vice President, legally, does not count as a Senator. Regardless, this could result in a legal grey area, as Article 1, Section 3, Clause 4 states:

‘The Vice President of the United States shall be President of the Senate, but shall have no Vote, unless they be equally divided.’

Whether or not the incumbent Vice President could allow themselves to be reelected by casting the deciding vote is therefore somewhat in doubt. To confuse matters further, at the time of writing, the Supreme Court consists of an even number of Justices,* and although this situation is unlikely to persist, a tie on any decision as to whether or not the Vice President could cast the deciding vote on this matter would make the situation even more chaotic.

As for the President, the situation becomes even more maddening. The House of Representatives would choose the President from among the top three vote-getters in the Electoral College, but in an even more contrived way. Rather than each member casting a single vote (which would all but guarantee a Democrat victory), the delegation of each state would vote as a single bloc, with a majority of delegations – 26 – required to elect the President. A tie in the delegation would result in no vote being cast. If one were banking on this outcome, then it would make competitive at-large districts, such as Alaska and Montana, increasingly important for deciding the outcome. To emphasise how utterly deranged this method is, one need only look at how little support a candidate needs to become President in this situation.

Considering that any such candidate only needs to win the support of over half of the delegation of each state, then adding up the states with the fewest delegates and then assuming that they win just over half, the total number of votes needed is… 58. In fact, this is so utterly lopsided that the largest number of votes any candidate would be required to win from a state is 4. On a completely separate note, this would also deprive Washington D.C. of any impact on the Presidential Election, given its non-voting congressional delegation, but were it counted as a state, then the total number of votes required would be as low as 55. If this doesn’t emphasise how much power is given to smaller states, I don’t know what does.

If, somehow, the House of Representatives and the Senate both tied in their decisions for the Presidency and Vice Presidency, then two options remain. The first is that the Speaker of the House of Representatives would assume the Presidency - but in the case that the House tied on even that, then the next in line to the Presidency would be the President Pro Tempore of the Senate - who, while technically elected, is by convention the longest-serving member of the Senate. Assuming that tradition was retained, then this series of ties could end up with the election of 87-year-old Chuck Grassley as the 46th President of the United States, who, earlier this month, posted a bizarre series of tweets about a lost ‘pidgin’ on Twitter. 

So, there you have it, folks. If you didn’t think the Electoral College was bizarre enough as it is, just know that there are several trillion ways that 58 people could decide the next President of the United States. And failing that, convention would dictate that a slightly detached octogenarian would assume the office. Democracy truly is a precious thing.

* At the time of publishing, Amy Coney Barrett has been confirmed to the Supreme Court, breaking any potential tie.