How to (Theoretically) Win a 2-Party Presidential Election with Just 21.8% of the Popular Vote

In an extreme case, consider the following electoral map:

Of course, this is nonsensical as DC is red and Texas is blue, but let’s assume this happened for the sake of argument. Despite the map being overwhelmingly red, the red states win the electoral vote by only the slightest margin of 270 to 268.

Let us assume that every single state was nearly evenly split, something like 50.01% to 49.99%. Then even though the red states won the electoral vote, the blue states contain 56.4% of the population, thus the blue candidate actually wins the popular vote 56.4% to 43.6%, a huge lead.

Now, suppose the vote was nearly even in the red states, but let the blue candidate win 100% of the vote in all the blue states. Then the red candidate wins only 21.8% of the popular vote, yet still wins the election, despite 78.2% of the electorate voting against him.

List of states in our hypothetical model: Red – Wyoming, District of Columbia, Vermont, North Dakota, Alaska, Rhode Island, South Dakota, Delaware, New Hampshire, Montana, Maine, Hawaii, Nebraska, West Virginia, Idaho, New Mexico, Nevada, Utah, Kansas, Arkansas, Mississippi, Iowa, Connecticut, South Carolina, Minnesota, Alabama, Oklahoma, Kentucky, Oregon, Colorado, Washington, Louisiana, Wisconsin  Maryland, Tennessee, Arizona, Indiana, Massachusetts, Missouri, and North CarolinaBlue – Virginia, Michigan, New Jersey, Pennsylvania, Georgia, Ohio, Illinois, Florida, Texas, New York, and California.

Note: After I wrote this post, I googled the 21.8% and found a few cases where people used intense computer computation with exponential-time algorithms to figure this out.

I was shocked when I discovered these methods, as my own method was extraordinarily simple, taking all of two minutes in Excel, with otherwise no number-crunching: just list out the states in ascending order of population per electoral vote, and then go down the list until you get to 270 or more. The list I got started with Wyoming, and went all the way down to Georgia. However, this added up to 271, so I searched for any way to shave off 1 electoral vote. As it turns out, there was a way: I replaced Georgia (16 electoral votes) by North Carolina (15 electoral votes), which has a smaller population.

Bonus Round #1:

Now pretend there are more than 2 parties. Then it is possible to win 270 with an even smaller percentage of the popular vote. Let n be the number of parties. Then you can win with 43.6/n % of the popular vote. The 2-party example of 21.8% is just a special case of this. For example, with 3 parties the red candidate just needs to win a 33.34% vs 33.33% vs 33.33% plurality in each of the required states, so to win the presidency, he only needs to win 43.6/3 %, or 14.5%, of the popular vote.

Bonus Round #2:

Let’s go back to 2 parties. Someone on Facebook asked:

What if the electoral college reps were voted in based on district? The representatives are based on members of congress, right? So what if every state did what Maine and Nebraska does and allow their representatives to split? Two elected based on statewide votes, the rest by congressional district. Keeps the small states relevant to the campaign while making the electoral process more representative.

As it turns out, the answer doesn’t change if we let electors vote by district. Just let the red candidate win every single district in every single red state listed above by one vote. Then it’s still an electoral win with 21.8% of the popular vote.

The number does change, however, if we remove the two state votes from each state and have the vote counted purely by district. Then a candidate must win 23.2% of the popular vote (win the 219 smallest districts by a marginal amount, outright lose the other 217 districts).


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