In the 2000 US presidential election, changing just 269 votes in Florida from George W. Bush to Al Gore would have changed the outcome of the entire national election. Similar results in nearly a third of the country’s presidential elections, and five national popular vote winners did not become president, even in 2000 and 2016.
The Electoral College divides a large election into 51 smaller ones, one for each state, plus the District of Columbia. Mathematically speaking, this system is built to ensure virtually close victories, making it highly susceptible to efforts to change the minds of voters or the records of their elections. In fact, under certain circumstances, the Electoral College system is four times more vulnerable to manipulation than a national popular vote.
Few votes, great consequences.
In at least 18 of the 58 US presidential elections held between 1788 and 2016, the popular vote count may have seemed like a clear winner, but looking closer at the number of votes needed to change the outcome of the Electoral College , the choice was actually very close.
That shows how the Electoral College makes meddling much easier and more effective when an adversary, be it a voting machine hacker or a propaganda and disinformation campaign, changes only a small fraction of the votes in some states.
In 1844, for example, James Polk defeated Henry Clay by 39,490 votes in an election that saw 2.6 million people cast their votes. But if only 2,554 New Yorkers – 0.09% of the national total – had voted differently, Clay would have become the eleventh president of the United States.
The closest Electoral College victory, except in the 2000s, came in 1876, when Rutherford B. Hayes lost the popular vote to Samuel Tilden by some 250,000 votes, but won the Electoral College by a single vote.
The election was disputed, and the northern and southern states reached a political compromise that gave Hayes the White House in exchange for ending the occupation of federal troops from the former Confederate states. That dispute could have been avoided if only 445 South Carolinians – 0.01% of the national vote – had voted for Tilden instead of Hayes.
Even elections that look like relative fugitives are touchy. Barack Obama won in 2008 by almost 10 million votes, but the result would have been completely different if a total of 570,000 people in seven states had voted for John McCain, just 0.4% of the participating voters.
For outside influence to change the popular vote winner, propagandists and misinformation vendors would have had to change the votes of 5 million people, nearly 10 times as many.
Is the popular vote less vulnerable?
For mathematicians like me, it is instructive to try to calculate exactly how vulnerable an election result is to changes in one or more popular votes. We try to choose the “best” method, among all the hypothetical ways to get lots of votes and determine the winner of the election.
Suppose we organize an election between Candidate A and Candidate B, in which each has an equal chance of winning. Then imagine that once the popular votes are cast, an opponent observes the counts and changes a fixed number of popular votes, in a way that changes the outcome of the elections. A majority vote has the fewest options for an opponent to reverse the result. So, in this sense, the majority vote is the “best”.
Of course, it is not realistic to think that an opponent would know the detailed vote counts. But this scenario provides a useful analogy because it is extremely difficult to predict how people will vote, and equally difficult to calculate how an adversary could attack certain voters and not others.
Electoral corruption due to random vote changes
There is another way to simulate an adversary’s potential to somehow change votes. This time, instead of one opponent changing a fixed number of votes, suppose there is a 0.1% chance that the opponent will change any vote to the other candidate. This assumption could be reasonable if there are adversaries working for each candidate. By allowing the vote changes to be totally random, we simplify the calculations and still end up with a reasonable approximation of how all the various factors interact with each other.
Then, using probability tools such as the Central Limit Theorem, it is possible to calculate that in elections with a large number of voters there is, on average, about a 2% chance that 0.1% of corruption to the random vote changes the result of a majority vote. On the other hand, for the Electoral College, the chances of successful interference increase to more than 11%, if each state is assumed to be the same size. By adjusting the size of the states to reflect the actual number of voters in the US states, the chance of interference is still over 8%, four times the chance of a majority vote.
That four-to-one ratio doesn’t change, as long as an adversary’s chance of changing a vote is relatively small: the Electoral College system is four times more susceptible to vote changes than the popular vote.
Furthermore, among democratic voting methods, the majority voting method is more resistant to random vote changes. Therefore, according to these criteria, there is no other democratic voting method that is better than majority voting to protect against electoral interference.
The previous calculations only examined elections with two candidates. Determining the smallest possible probability of a change in the outcome of democratic elections with more than two candidates is much more difficult. Building on the work of many people, I have made some recent progress that demonstrates that plurality voting is more resistant to the corruption of random voting.
There is no better method of voting. Each approach has undesirable flaws, such as the possibility of a third-party candidate entering the race to change the winner of the election. Voting in order of preference also has its shortcomings. But it is clear that when trying to protect an election from outside influence, the Electoral College is much weaker than a popular vote.
Steven Heilman, PSTN Assistant Professor of Mathematics, University of Southern California – Dornsife College of Letters, Arts and Sciences
This article is republished from The Conversation under a Creative Commons license.
