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Commentary
The electoral college is bad for democracy. Math can fix that
Come the general election on November 5, one-third of Massachusetts voters might as well stay home. That’s the fraction of the state’s voters who will likely vote for Donald Trump and whose ballots will be rendered worthless through a combination of the Electoral College and a winner-take-all system. All 11 of the state’s electoral votes are preordained to go to Joe Biden, depriving over 1 million Massachusetts voters of a voice.
This leads naturally to the question: What are some mathematical ways in which our presidential electoral systems skew the will of the people, introduce a power imbalance between states and disenfranchise voters?
But first, let’s add some context.
When deciding how to elect a president, delegates to the Constitutional Convention of 1787 could not agree. By the time it was settled, the matter had been voted on 30 times, more than any other. The myriad proposals included election of the president by state governors or by (some subset of) the Congress. Election by popular vote was also considered, meaning that every citizen votes and everybody’s vote carries the same weight. The issue was finally passed to the Committee on Unfinished Parts (obviously named by a time-traveling Monty Python) consisting of a representative from each of the 11 states.
That committee put forward a solution: Each state will choose electors, and there will be as many of them as is the size of the state’s delegation in Congress — the number of state’s representatives to the House of Representatives, plus two senators. It was meant to appease the southern states, who had already scored a major win with the three-fifths compromise (three of every five slaves were counted when determining a state’s total population). The electors cast votes for president. Whoever they pick — not you and me — will go to the White House. Our role is merely advisory.
Mathematics can suggest better democratic processes while being unencumbered by partisanship and politics.
Which brings us back to math. Because sometimes we vote differently than the Electoral College. For example, Hillary Clinton in 2016 received 3 million more votes than Donald Trump, but lost the Electoral College, 304 to 227 (a candidate needs 270 to win). This has happened four other times in U.S. history. The discrepancy is a consequence of the winner-take-all system used in every state except Maine and Nebraska. A candidate can eke out a win in enough states to lock down the Electoral College while another candidate can win by a landslide in the other states, resulting in a dramatic difference between the electoral and popular vote counts.
Here’s a thought experiment: Imagine that shortly before the 2020 elections, about 5,000 Democrats living in Arizona decided to move to California, and 5,000 Republicans from California moved to Arizona. A similar swap happens with 6,000 Democrats from Georgia and as many Republicans from Alabama. Finally, 10,000 Wisconsin Democrats switch places with 10,000 Minnesota Republicans.
What’s happened is that 41,000 people have moved. Meanwhile, no state’s population count has changed, and neither has anyone’s political opinion. But now Trump would have carried Arizona, Georgia and Wisconsin by the tightest of margins, earning him enough electoral votes to become president instead of Joe Biden. (The winner in California, Alabama and Minnesota is unchanged.) The same analysis unfolds in 2000, 2004, and 2016; the winner would have changed had there been a few thousand voters in a handful of states voting differently.
The Democratic voters who brought Biden the victory in those three swing states were more “valuable” to him there. If they had lived somewhere else, their vote would not have mattered as much. This is one way the Electoral College amplifies voices in some states and diminishes them in others.
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Here is another. California is our most populous state, with about 39,700,000 people and 54 electoral votes. Dividing these numbers gives about 735,000, the number of Californians per electoral vote. In Wyoming, with population of 585,000 and 3 electoral votes, this number is 195,000. This means that a voter in Wyoming has almost four times the power of a California voter. There’s nothing special about California and Wyoming — the disparity in the ratio of people per representative runs the gamut across states.
One might argue that the imbalance of power is simply an unfortunate byproduct of the Federalist ways, and that this is a small price to pay for maintaining the autonomy of the states. But how many of us feel an allegiance to our state when we vote for president? Or are we thinking of ourselves as individuals, expressing our opinion alongside every other American across the U.S. as we choose a person whose mandate will be to represent all our interests equally? I know I am.
No other democracy uses anything like the Electoral College. It is a relic of a particular time, tainted with the legacy of slavery and the Framers’ mistrust in the capacity of the people to make the best choices for themselves. About 65% of Americans agree that it must go. Replacing the Electoral College by the popular vote (in combination with ranked choice voting) would be ideal. But since that would require a Constitutional amendment, it is unlikely to happen.
An elegant workaround would be the National Popular Vote Interstate Compact, an agreement of states to allocate their electoral votes to the popular vote winner regardless of the results in those states. So far, the legislatures of 17 states plus Washington, D.C. have committed to the compact, totaling 209 electoral votes. Unfortunately, getting to 270 (which is when the compact becomes binding) might be difficult. The Electoral College works to the benefit of most of the remaining states because they are smaller and enjoy the attention the system affords them, or because their preferred presidential candidate has in recent past benefitted from it.
If we cannot eliminate or circumvent the Electoral College, a partial solution would be to allocate electoral votes proportionally in each state so that, for example, a third of Massachusetts’ electoral votes would go to Trump this November.
Either way, the Electoral College no longer makes sense. But it is only a symptom of a larger problem. Much of the mechanics of our democracy — our civic infrastructure — is algorithmic and mathematical, and this math is outdated, inappropriate for our time and often simply discriminatory. Plurality voting causes vote-splitting and spoilers that elect candidates who are not the true will of the people; single-winner districts are susceptible to gerrymandering that leaves millions of voters without a voice; party primary systems elect extremists and fringe candidates with a small base; and the House of Representatives is so insufficient in size that meaningful representation is impossible. The Electoral College is merely a convergence of all the bad math fueling our political engine.
Mathematics can suggest better democratic processes while being unencumbered by partisanship and politics. Its power lies in its formalism, universal objectivity and emotional detachment. I have seen this power through my interactions with students who enroll in my Math and Politics class at Wellesley College and the network of people that have gathered around the Institute for Mathematics and Politics that I run. Once they see our democracy through a mathematical lens, they are without fail outraged at how discriminatory and disenfranchising its mechanisms are. They see no alternative but to relegate them to history books and institute better ones.
My new book gives concrete suggestions for repairing our democracy with mathematically sound practices. They include ranked choice voting, an increase in the size of the House of Representatives, independent districting commissions, multi-member districts and the elimination of the Electoral College. Implementing such reforms would bring us closer to a democracy that represents us better and speaks for more of us. That’s just simple math.
