Can Donald Trump win the election? Here’s the mathematical reason why it’s impossible for him to become President

Not only must Trump win every state that Mitt Romney and John McCain won before him, but he must win states that they were not able to win

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If one is to believe the latest polls, then the race to decide the next president of the United States is incredibly tight. The ABC/Washington Post (29 October) has Hillary Clinton narrowly ahead of Donald Trump, 49 per cent – 47 per cent, the LA Times/University of Southern California (30 October) has Trump in the lead 47 per cent to 43 per cent, whilst NBC News (30 October) has Clinton with a lead of  51 per cent to 44 per cent.

National polling is meaningless when it comes to Election Day, because as Al Gore discovered in 2000, the winner of the presidential election is not the candidate who receives the most votes. In fact, on four different occasions (1824, 1876, 1888, and 2000), the person who won the election received fewer votes than their “losing” opponent.

The winner of the presidential election is the candidate who wins an absolute majority of votes in the US Electoral College.

US election night: everything you need to know

The Electoral College comprises one elector per delegate of each state to the US Congress, plus the District of Columbia (Washington DC). For example, the state of Wyoming sends three delegates to Congress – one member of the House of Representatives and two members of the Senate – thus Wyoming has three Electoral College votes. Meanwhile, California has 53 members of the House of Representatives plus two senators, so it has 55 Electoral College votes. There is a total of 538 votes at stake in the Electoral College. To win the presidency, a candidate needs to win an absolute majority, or half plus one. The magic number therefore is 270.

Public polling is outdated, and frequently wrong. In November 2012, the final Gallup and Rasmussen polls of that year’s election campaign had Mitt Romney ahead of Barack Obama. We can therefore ignore the polls and instead look at the results of the Electoral College from the last four elections for a good indication of what the result will be.

All fifty states plus the District of Columbia, can be assigned to one of five categories. If a state has voted for the same party in each of the past four elections, then it can be classified as “safe Democrat” or “safe Republican”. If a state has voted for one party in three of the past four elections, then it can be classified as “likely Democrat” or “likely Republican”.  This leaves the states that have voted for each party fifty percent of the time, known as “toss up” or “swing” states.

We already know what many of the results on Election Day will be. California will vote for Clinton, and Wyoming will vote for Trump. In fact, Clinton has 19 “safe” states for a total of 242 Electoral College votes, whilst Trump has 22 “safe” states, giving him 180 Electoral College votes.

If we look to the “likely” category, then Clinton has three states and Trump has two, for a revised Electoral College total of 257 to 206. This leaves just five states as “toss ups”, which is why the candidates’ campaigns are focused on Colorado, Florida, Ohio, Nevada, and Virginia.

Incidentally, the Democratic party has won each of these five states in both of the last two elections.

The Electoral College highlights the incredibly partisan nature of American politics, because months before Election Day, we already know how 80 per cent of the fifty states plus DC, will be voting. If we add the “likely” states, then that number increases to 90 per cent.

If Clinton wins all the states that the Democratic Party historically wins, then she only needs to win Florida, or Ohio, or Virginia. Any one of these states will give her enough Electoral College votes to put her above the required 270. Similarly, if Clinton wins both Colorado and Nevada, then she will win. In other words, Clinton does not need to win Florida or Ohio.

On the other hand, Trump needs to win every traditional Republican state, as well as Florida, Ohio, and Virginia, plus one other. If Trump does not at least all three of the big swing states, then he has no mathematical chance at winning a majority in the Electoral College. Not only must Trump win every state that Mitt Romney and John McCain won before him, but he must win states that they were not able to win.

Trump v Clinton: US Election forecast – 6 November

This is why Clinton has a significant advantage. As long as she wins the traditional Democratic states, she can concentrate her resources on winning one or two of the swing states. If she does this, she will be president.

An even bigger problem for Trump is that the divisive nature of his campaign is allowing his opponent to expand the electoral map. Clinton is actively campaigning, and is increasingly becoming competitive in the ‘likely’ Republican state of North Carolina, as well as the traditionally safe Republican states of Arizona, Georgia, and Missouri. The result is that Trump is limited in his ability to campaign and direct advertising dollars to the swing states, as he is being forced to focus his attention and energy on retaining traditional Republican states. Clinton’s campaign is forcing Trump to play defence in his own backyard.

As a result Trump has to divert his attention from the swing states, and shore up his vote in states that he should not have to worry about. This spreading of his already thin resources is seeing Clinton take the lead in each of the swing states. Of these states, Clinton appears to have a narrow lead in North Carolina, which if she does win on Election Day, then the swing states become irrelevant.

Despite what the public polls suggest, and even with her latest email scandal, the election is Clinton’s to lose, and it appears mathematically unlikely that she will.

Bryan Cranston is an online lecturer in politics, and PhD candidate at Swinburne University, Australia

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